Proposed Chapters for Incorporating Travel Time Reliability into the Highway Capacity Manual (2013)

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Chapter 36/Travel Time Reliability Page 36-i Contents CHAPTER 36 TRAVEL TIME RELIABILITY CONTENTS 1. INTRODUCTION ................................................................................................... 36-1 Definitions ............................................................................................................. 36-2 Overview of the Methodology ............................................................................... 36-3 Required Input Data .............................................................................................. 36-5 Scope of the Methodology ....................................................................................36-14 Limitations of the Methodology ...........................................................................36-15 2. CONCEPTS ............................................................................................................ 36-17 Objectives for Reliability Analysis .......................................................................36-17 Performance Measures .........................................................................................36-17 Typical Travel Time Variability Values ...............................................................36-20 Data Acquisition ...................................................................................................36-23 Interpreting Results ..............................................................................................36-25 3. FREEWAY FACILITY METHODOLOGY ....................................................... 36-32 Overview ..............................................................................................................36-32 Framework............................................................................................................36-32 Scenario Generation .............................................................................................36-34 Facility Evaluation................................................................................................36-38 Performance Summary .........................................................................................36-41 4. URBAN STREET METHODOLOGY ................................................................. 36-42 Overview ..............................................................................................................36-42 Framework............................................................................................................36-42 Analysis Techniques .............................................................................................36-45 5. APPLICATIONS ................................................................................................... 36-48 Default Values ......................................................................................................36-48 Use Cases .............................................................................................................36-54 Use of Alternative Tools ......................................................................................36-57 6. EXAMPLE PROBLEMS ...................................................................................... 36-59 Example Problem 1: Reliability Evaluation of an Existing Freeway Facility ......36-59 Example Problem 2: Geometric Treatment ..........................................................36-68

Contents Page 36-ii Chapter 36/Travel Time Reliability Example Problem 3: Incident Management Treatment ....................................... 36-69 Example Problem 4: Safety Treatment ................................................................ 36-70 Example Problem 5: Demand Management Strategy .......................................... 36-72 Example Problem 6: Existing Urban Street Reliability ....................................... 36-75 Example Problem 7: Urban Street Strategy Evaluation ....................................... 36-92 7. REFERENCES ....................................................................................................... 36-98

Chapter 36/Travel Time Reliability Page 36-iii Contents LIST OF EXHIBITS Exhibit 36-1 High-level Representation of the Method for Estimating the Travel Time Distribution .................................................................................................. 36-5 Exhibit 36-2 General Data Categories Required for a Reliability Evaluation .............. 36-6 Exhibit 36-3 Temporal and Spatial Dimensions of Reliability ..................................... 36-8 Exhibit 36-4 Definitions of Freeway Facility Weather Events ..................................... 36-9 Exhibit 36-5 Derivation of Reliability Performance Measures from the Travel Time Distribution .................................................................................................36-18 Exhibit 36-6 Rankings of Selected U.S. Facilities by TTI, Mean TTI and PTI ...........36-21 Exhibit 36-7 TTI and PTI Distribution on U.S. Freeways and Urban Streets (AM Peak Period) .................................................................................................36-22 Exhibit 36-8 TTI and PTI Distribution on U.S. Freeways and Urban Streets (Midday Period) ...................................................................................................36-22 Exhibit 36-9 TTI and PTI Distribution on U.S. Freeways and Urban Streets (PM Peak Period) .................................................................................................36-23 Exhibit 36-10 Interrelationship Between Causes of Congestion and the Facility ........36-29 Exhibit 36-11 Example Matrix Allocating Annual Vehicle-Hours of Delay by Cause ...............................................................................................................36-30 Exhibit 36-12 Example Pie Chart of Congestion Causes ............................................36-31 Exhibit 36-13 Freeway Reliability Methodology Framework .....................................36-32 Exhibit 36-14 Demand Ratios for Urban Freeways (ADT/Mondays in January) ........36-35 Exhibit 36-15 Weather Effects on Capacity and Speed (70 mi/h Free-flow Speed) ....36-36 Exhibit 36-16 Incident Effects on Capacity .................................................................36-37 Exhibit 36-17 Example Work Zone Effects on Capacity for Lane Closure Scenarios ..............................................................................................................36-37 Exhibit 36-18 Example Scenario Attributes Generated by the Scenario Generator ....36-38 Exhibit 36-19 Example Speed–Flow Curves for Basic Freeway Segments After CAF and SAF Adjustments ..................................................................................36-40 Exhibit 36-20 Urban Street Reliability Methodology Framework ..............................36-42 Exhibit 36-21 Student’s t-Statistic ...............................................................................36-47 Exhibit 36-22 Default Urban Freeway Demand Ratios (ADT/Mondays in January) ............................................................................................................36-48 Exhibit 36-23 Default Rural Freeway Demand Ratios (ADT/Mondays in January) ............................................................................................................36-48 Exhibit 36-24 Default Freeway Incident Severity Distributions ..................................36-49 Exhibit 36-25 Default Freeway Incident Durations (min) ...........................................36-49 Exhibit 36-26 Default CAFs and SAFs by Weather Condition ...................................36-49 Exhibit 36-27 Default Urban Street Hour-of-Day Demand Ratios (ADT/AADT) ......36-50 Exhibit 36-28 Default Urban Street Day-of-Week Demand Ratios (ADT/AADT) .....36-50 Exhibit 36-29 Default Urban Street Month-of-Year Demand Ratios (ADT/AADT) ..36-51

Contents Page 36-iv Chapter 36/Travel Time Reliability Exhibit 36-30 Urban Street Weather-Related Default Values .................................... 36-51 Exhibit 36-31 Urban Street Incident Default Values .................................................. 36-52 Exhibit 36-32 Default Urban Street Incident Clearance Times .................................. 36-53 Exhibit 36-33 Default Urban Street Incident Distribution with Shoulder Presence ... 36-53 Exhibit 36-34 Default Urban Street Incident Distribution Without Shoulder Presence ............................................................................................................... 36-54 Exhibit 36-35 Use Cases of Travel Time Reliability .................................................. 36-54 Exhibit 36-36 List of Example Problems .................................................................... 36-59 Exhibit 36-37 Example Problem 1: Freeway Facility Schematic ............................... 36-59 Exhibit 36-38 Example Problem 1: Freeway Facility Segment Properties ................. 36-59 Exhibit 36-39 Example Problem 1: Demand Flow Rates (veh/h) by Analysis Period in the Base Dataset ................................................................................... 36-60 Exhibit 36-40 Example Problem 1: Demand Ratios Relative to AADT ..................... 36-61 Exhibit 36-41 Example Problem 1: Weather Event Probabilities by Season .............. 36-62 Exhibit 36-42 Example Problem 1: CAF, SAF, and Event Duration Values Associated with Weather Events ......................................................................... 36-62 Exhibit 36-43 Example Problem 1: Incident Time-based Probabilities by Demand Pattern ................................................................................................... 36-64 Exhibit 36-44 Example Problem 1: Probabilities of Combinations of Demand, Weather, and Incidents ........................................................................................ 36-65 Exhibit 36-45 Example Problem 1: Number and Types of Generated Scenarios ....... 36-65 Exhibit 36-46 Example Problem 1: Summary Reliability Performance Measure Results ................................................................................................................. 36-67 Exhibit 36-47 Example Problem 1: VMT-weighted TTI Probability and Cumulative Distribution Functions ...................................................................... 36-67 Exhibit 36-48 Example Problem 2: Freeway Facility Schematic ............................... 36-68 Exhibit 36-49 Example Problem 2: Summary Reliability Performance Measure Results ................................................................................................................. 36-69 Exhibit 36-50 Example Problem 3: Assumed Freeway Incident Durations (min) ...... 36-70 Exhibit 36-51 Example Problem 3: Summary Reliability Performance Measure Results ................................................................................................................. 36-70 Exhibit 36-52 Example Problem 4: Incident Probabilities by Demand Pattern .......... 36-71 Exhibit 36-53 Example Problem 4: Summary Reliability Performance Measure Results ................................................................................................................. 36-71 Exhibit 36-54 Example Problem 5: Demand Flow Rates (veh/h) by Analysis Period in the Base Dataset ................................................................................... 36-72 Exhibit 36-55 Example Problem 5: Comparison of VMT Demand by 15-min Analysis Periods .................................................................................................. 36-73 Exhibit 36-56 Example Problem 5: Summary Reliability Performance Measure Results ................................................................................................................. 36-73 Exhibit 36-57 Example Problem 5: Treatment Summary Comparison ...................... 36-74

Chapter 36/Travel Time Reliability Page 36-v Contents Exhibit 36-58 Example Problem 6: Urban Street Facility ...........................................36-75 Exhibit 36-59 Example Problem 6: Input Data Needs and Sources ............................36-76 Exhibit 36-60 Example Problem 6: Intersection #1 Signal Timing Data ....................36-77 Exhibit 36-61 Example Problem 6: Sample Weather Data for Lincoln, Nebraska ......36-80 Exhibit 36-62 Example Problem 6: Sample Generated Weather Events .....................36-81 Exhibit 36-63 Example Problem 6: Sample Demand Profile Calculations .................36-83 Exhibit 36-64 Example Problem 6: Locally Available Crash Frequency Data ...........36-84 Exhibit 36-65 Example Problem 6: Computation of Crash Frequency by Weather Type ......................................................................................................................36-85 Exhibit 36-66 Example Problem 6: Incident Determination for April 6, 9:00 a.m., for Segment 1-2 ....................................................................................................36-87 Exhibit 36-67 Example Problem 6: Incident Determination for January 10, 7:00 a.m., for Segment 1-2 ...................................................................................36-87 Exhibit 36-68 Example Problem 6: Sample Calculation of Incident Duration ............36-88 Exhibit 36-69 Example Problem 6: Reliability Performance Measure Results ...........36-90 Exhibit 36-70 Example Problem 6: Eastbound Travel Time Distribution ...................36-91 Exhibit 36-71 Example Problem 6: Confidence Interval Calculation for Eastbound Direction .............................................................................................36-92 Exhibit 36-72 Example Problem 6: Annual VHD by Cause .......................................36-92 Exhibit 36-73 Example Problem 6: Percentage of Annual VHD by Cause .................36-92 Exhibit 36-74 Example Problem 7: Results for Strategy 1 ..........................................36-95 Exhibit 36-75 Example Problem 7: Results for Strategy 2 ..........................................36-96 Exhibit 36-76 Example Problem 7: Results for Strategy 3 ..........................................36-96

Contents Page 36-vi Chapter 36/Travel Time Reliability

Chapter 36/Travel Time Reliability Page 36-1 Introduction 1. INTRODUCTION Travel time reliability reflects the distribution of travel time of trips using a facility over an extended period of time. This distribution arises from the interaction of a number of factors that influence travel times: • Recurring variations in demand, by hour of day, day of week, and month of year; • Severe weather (e.g., heavy rain, snow, poor visibility) that reduces capacity; • Incidents (e.g., crashes, stalls, debris) that reduce capacity; • Work zones that reduce capacity and (for longer-duration work) may also influence demand; and • Special events (e.g., major sporting events, large festivals or concerts) that produce temporary, intense traffic demands which may be managed in part by changes to the facility’s geometry or traffic control. There are two widely held ways that the same underlying distribution of travel times can be characterized. Each is valid and leads to a set of performance measures that capture the nature of travel time variability. They are: 1. Measures of the variability in travel times that occur on a facility or a trip over the course of time, as expressed through metrics such as a 50th, 80th, or 95th percentile travel time. 2. Measures of the reliability of facility travel times, such as the number of trips that fail or succeed in accordance with a pre-determined performance standard, as expressed through metrics such as on-time performance or percent failure based on a target minimum speed or travel time. For convenience, the remainder of this chapter uses the single term reliability to characterize both the variability-based and reliability-based approaches to characterizing the same facility travel time distribution. A sufficiently long history of travel times is required to establish a facility’s travel time distribution—a year is generally long enough to capture most of the variability caused by the factors listed above. The Highway Capacity Manual’s (HCM’s) freeway and urban street facility procedures (Chapters 10 and 16, respectively) describe average conditions along the facility during a user-defined analysis period, typically the peak 15 min of a peak hour, under typical conditions (e.g., good weather, no incidents). Because this value is an average, there will be times of the day or days during the year when conditions are better than the average, due to lower-than-average traffic demands. There will also be days when conditions are much worse, due to incidents, severe weather, unusually high demand levels, or a combination of these. Chapter 36, Travel Time Reliability, presents methods that can be used to describe how often particular operational conditions occur and how bad conditions Travel time reliability is influenced by demand variations, weather, incidents, work zones, and special events. The travel time distribution can be characterized in terms of travel time variability or in terms of the success or failure of a given trip meeting a target travel time. Reliability is quantified from the distribution of travel times on a facility. HCM freeway and urban street facility methods describe average conditions in the absence of severe weather and incidents during a defined analysis period; Chapter 36 describes how much conditions can be expected to vary from the average.

Introduction Page 36-2 Chapter 36/Travel Time Reliability can get. This chapter’s variability and reliability performance measures can be used as the basis for quantifying the degree of severity of level of service (LOS) F (oversaturated) conditions, for developing agency performance standards for oversaturated facilities, and for quantifying the impacts of physical and operational measures designed to improve travel time reliability. Because travel time reliability is a new concept for the HCM, this chapter devotes a number of pages to describing the reliability concept, how reliability can be measured, and how reliability can be applied to analyses to better inform their results: • The remainder of Section 1 presents definitions of reliability terms along with a high-level overview of the reliability methodology. • Section 2 presents travel time variability and reliability concepts, including performance measures, illustrative reliability results from U.S. freeway and urban street facilities, potential data sources, and guidance on interpreting reliability results. • Sections 3 and 4 describe at a high level the travel time distribution estimation methods for freeway and urban street facilities, respectively. These descriptions omit many of the computational details. Readers wishing a greater level of detail about the methods are referred to Chapter 37, Travel Time Reliability: Supplemental for the computational details. The cell formulas and Visual Basic macros in the FREEVAL-RL and STREETVAL computational engines, available in the Technical Reference Library in the online HCM Volume 4, provide the greatest level of detail. • Section 5 presents default values for the methods, describes potential applications (use cases) for reliability analyses, and addresses the role of alternative tools (such as simulation) in evaluating travel time reliability. • Section 6 provides seven example problems illustrating the application of the reliability methods to a freeway facility and an urban street facility. • Section 7 lists this chapter’s references. Chapter 37, Travel Time Reliability: Supplemental, provides the computational details of the reliability methodologies, presents variability statistics for a number of U.S. freeway and urban street facilities, and provides a method for measuring variability and reliability in the field. DEFINITIONS The following terms are used in this chapter: • Free-Flow Speed (freeways). The average speed of through traffic on the facility under low-flow conditions (see Chapter 9, Glossary). It may be measured from field data as the 85th percentile highest 5-min average speed of vehicles observed traveling the full length of the facility during uncongested periods (e.g., 7 a.m. to 9 a.m. on non-holiday weekends). • Free-Flow Speed (urban streets). The average running speed of through automobiles when traveling along a street under low-volume conditions and when not delayed by traffic control devices or other vehicles. This chapter describes the reliability methods at a high level. Specific details are provided in Chapter 37.

Chapter 36/Travel Time Reliability Page 36-3 Introduction • Travel Time. The time required for a motorized vehicle to travel the full length of the facility from mainline entry to mainline exit points without leaving the facility or stopping for reasons not related to traffic conditions or traffic control. • Travel Time Index (TTI). The ratio of the actual travel time on a facility to the theoretical travel time if traveling at free-flow speed. • Planning Time Index (PTI). The ratio of the 95th percentile highest travel time to the theoretical free-flow travel time. • Free-Flow Travel Time. The length of the facility divided by the estimated free-flow speed for the facility. • Scenario. A scenario is a unique combination of traffic demand, capacity, geometry, and traffic control conditions. It can represent one or more analysis periods, provided that all periods have the same unique combination of demand, capacity, geometry, and control. • Study Period. The time interval (within a day) that is represented by the performance evaluation. It consists of one or more consecutive analysis periods. • Analysis Period. The time interval evaluated by a single application of an HCM methodology. • Study Section. The length of facility over which reliability is to be computed. Since reliability is computed for through traffic only, the length of the facility should not be so long that through traffic is a low percentage of total traffic on the facility. The length of facility to be evaluated should be less than the distance a vehicle traveling at the average speed can achieve in 15 min. • Reliability Reporting Period. The specific days over which reliability is to be computed. For example, this might be all non-holiday weekdays in a year. • Holidays. Federal holidays as listed by the General Service Administration for federal workers plus any state and local holidays that may reduce facility demands by 10% or more from average levels. • Special event. Short-term events, such as major sporting events, concerts, and festivals that produce intense traffic demands on a facility for limited periods of time, which may be addressed by temporary changes in the facility’s geometry, traffic control characteristics, or both. Other terms not listed above use the definition given in Chapter 9, Glossary. OVERVIEW OF THE METHODOLOGY At its core, this chapter’s methodology for estimating the travel time distribution consists of hundreds of repetitions of the freeway and urban street facility methods presented in Chapters 10 and 16, respectively. In contrast to the base HCM facility methods, where the inputs to the model represent average values for a defined analysis period, this chapter’s method varies the demand,

Introduction Page 36-4 Chapter 36/Travel Time Reliability capacity, geometry, and traffic control inputs to the facility model with each repetition (scenario). The full range of HCM performance measures output by the facility model are assembled for each scenario and can be used to describe a facility’s performance over the course of a year or other user-defined reliability reporting period. Performance can be described on the basis of a percentile result (e.g., the 80th or 95th percentile travel time) or the probability of achieving a particular level of service (e.g., the facility operates at LOS D during X% of non-holiday weekday hours during the year). In addition, many other variability and reliability performance measures can be developed from the facility’s travel time distribution. This chapter’s method is sensitive to the main sources of variability that lead to travel time unreliability: • Temporal variability in traffic demand—both regular variations by hour of the day, day of the week, and month or season of the year; and random variations between hours and days; • Incidents that block travel lanes or otherwise affect traffic operations, thus affecting capacity; • Weather events that affect capacity and possibly also demand; • Work zones that close or restrict travel lanes, thus affecting capacity; and • Special events that produce atypical traffic demands that may require managing by special traffic control measures. Work zones and special events are location-specific parameters that must be provided by the analyst. Location-specific data related to traffic demand variability, incidents, and weather patterns are desirably provided by the analyst when available; however, this method also provides default values for use when local data are unavailable or the analysis does not require that level of precision. Scenarios are built from combinations of conditions associated with each source of travel time variability. For example, one scenario could represent demand volumes representative of Fridays in May, fair weather, and one lane closed for 30 min due to an incident that occurs during the p.m. peak hour. A probability of occurrence is associated with each scenario, based either on local data provided by the analyst or the method’s default data, and is used to develop a travel time distribution for the reliability reporting period. Exhibit 36-1 provides a high-level representation of the methodology for estimating the travel time distribution. The base dataset consists of all the data needed to evaluate the base HCM facility method for a single study period, plus data that describe the variations in demand, weather, etc. that occur over the course of the reliability reporting period, along with the frequency of a particular event’s occurrence. The scenario generator identifies all possible combinations of demand, weather, incidents, etc. and creates a set of scenarios in which the base facility demand and capacity is adjusted to reflect the changes in demand and capacity that occur under each combination of conditions. Each scenario is then given to the core HCM facility method, which calculates the facility travel time associated with each scenario. The individual facility travel times are then Input data beyond that needed for an HCM facility analysis consist of demand variation data, incident data, weather data, work zones, and special events. The first three types of data can be defaulted when not available locally. The method for estimating the travel time distribution calculates the performance of a series of scenarios representing different combinations of conditions that affect a facility’s demand, capacity, or both.

Chapter 36/Travel Time Reliability Page 36-5 Introduction compiled into the facility’s travel time distribution. This distribution can then be used to develop a variety of reliability and variability performance measures for the facility. Because of the hundreds (or even thousands) of scenarios that are generated, this method is only practical to implement though the application of software. Software automates the scenario generation process, performs the computations associated with the HCM facility method for each scenario, and stores and processes the output performance measures generated for each scenario. Source code listings for research-grade computational engines, FREEVAL-RL and STREETVAL, are provided in the Technical Reference Library in HCM Volume 4 for freeways and urban streets, respectively. The freeway and urban street methodologies for predicting travel time distributions described in this chapter are based largely on the products of a SHRP 2 project (1). Contributions to these methodologies from other research are referenced at the relevant points in the chapter. REQUIRED INPUT DATA HCM Facility Analysis Input Data As a starting point, all of the input data normally needed to apply the freeway or urban street facility method is required. These requirements are given in Chapter 10, Freeway Facilities and Chapter 17, Urban Street Segments. These data are referred to as an HCM dataset in this chapter. For some reliability evaluations, more than one HCM dataset will be required. One HCM dataset, the base dataset, is always required and is used to Exhibit 36-1 High-level Representation of the Method for Estimating the Travel Time Distribution Because hundreds or thousands of scenarios are generated, the method is only practical to implement through software.

Introduction Page 36-6 Chapter 36/Travel Time Reliability describe base conditions (particularly demand and factors influencing capacity and free-flow speed) when work zones and special events are not present. The base dataset can represent average demand conditions (annual average daily traffic; AADTs) or the demand measured on a specific day. This chapter’s methods factor these demands based on user-supplied or defaulted demand patterns to generate demands representative of all other time periods during the reliability reporting period. Additional HCM datasets are used, as needed, to describe conditions when a specific work zone is present or when a special event occurs. These datasets are called alternative datasets. The user must specify any changes to base conditions (e.g., demand, traffic control, available lanes) associated with the work zone or special event, along with the times when the alternative dataset is in effect. For example, if a work zone exists during a given month, then an alternative dataset is used to describe average conditions for the analysis period during that month. Summary of Additional Data Required for a Reliability Evaluation Beyond the data normally needed for an HCM facility operations evaluation, additional data are required to perform a reliability evaluation on a facility. Exhibit 36-2 lists the general categories of data that are required by facility type. Specific details are provided in the following subsections. Data Category Freeways Urban Streets Time periods Analysis period, study period, reliability reporting period. Analysis period, study period, reliability reporting period. Demand patterns Day-of-week by month-of-year demand factors. Can be defaulted. Hour-of-day (K) factors, day-of-week and month-of-year demand factors relative to AADT. Demand change due to rain and snow. Can be defaulted. Weather Probabilities of various intensities of rain, snow, cold, and low visibility by month. Can be defaulted. Rain, snow, and temperature data by month. Pavement runoff duration for a snow event. Can be defaulted. Incidents Probabilities of occurrence of shoulder and lane closures, and average incident durations. Alternatively, crash rate and incident-to-crash ratio for the facility, in combination with defaulted incident type probability and duration data. Probabilities of specific crash and incident types by location. Alternatively, segment and intersection crash frequencies. Crash frequency adjustment factors. Factors influencing incident duration. The latter two factors can be defaulted. Work zones and special events Changes to base conditions (alternative dataset) and schedule. Changes to base conditions (alternative dataset) and schedule. Nearest city Required when defaulted weather data used. Required when defaulted weather data used. Geometrics N/A Presence of shoulder. Traffic counts Demand multiplier for demand represented in base dataset. Day and time of traffic counts used in base and alternative datasets. Functional class N/A Urban street functional class required when defaulted demand patterns used. Note: N/A = not applicable. As shown in Exhibit 36-2, most reliability-specific inputs can be defaulted. Section 5, Applications, provides default values that allow analysts in “data poor” regions lacking detailed demand, weather, or incident data to apply this Exhibit 36-2 General Data Categories Required for a Reliability Evaluation

Chapter 36/Travel Time Reliability Page 36-7 Introduction chapter’s methods and obtain reasonable results. At the same time, the method allows analysts in “data rich” regions to provide local data for these inputs when the most accurate results are desired. Time Periods Analysis Period The analysis period is the time interval used for the performance evaluation. For freeway facilities, this value is always 15 min (see page 11-8). For urban street facilities, it can range from 15 min to 1 h, with longer durations in this range sometimes used for planning analyses. A shorter duration in this range is typically used for operational analyses. Additional guidance for determining the analysis period duration is provided in Chapter 16, Urban Street Facilities (see page 16-1). A shorter analysis period duration is desirable for urban street reliability evaluations because it reduces the minimum event duration threshold and thereby increases the number of incidents and weather events that are included in scenarios. In this regard, the structure of the urban street reliability methodology is such that events that are shorter than one-half of the analysis period duration are ignored (i.e., they will not be recognized in the scenario generation process). Study Period The study period is the time interval (within a day) that is represented by the performance evaluation. It consists of one or more consecutive analysis periods. A typical study period is 1.0 to 6.0 h in duration and is stated to represent specific times of the day and days of the week (e.g., weekdays from 4:00 p.m. to 6:00 p.m.). If oversaturated conditions occur during the study period, then at least the first analysis period should be undersaturated. The maximum study period duration is 24 h. The geometric design elements and traffic control features of the facility must be unchanged during this period. Thus, for urban streets, the intersection lane assignments and signal timing plan should be the same throughout the study period. Additionally for urban streets, if the directional distribution of traffic volume changes significantly during the day, then separate study periods should be established for each time period where the directional distribution is relatively constant. Reliability Reporting Period The reliability reporting period represents the specific days over which the travel time distribution is to be computed. A typical reporting period for a reliability evaluation is 6 to 12 months. It is specified by start and end dates as well as by the days of week being considered. The reliability reporting period is used with the study period to fully describe the temporal representation of the performance measure (e.g., average travel time on non-holiday weekdays from 4:00 p.m. to 6:00 p.m. for the current year). Exhibit 36-3 presents the relationships between the analysis, study, and reliability reporting periods. Shorter analysis periods allow more incidents and weather events to be considered in urban street reliability evaluations. If an urban street facility has two or more time-of-day signal timing plans, then a separate study period should be established for each plan period.

Introduction Page 36-8 Chapter 36/Travel Time Reliability Demand Pattern Data Demand pattern data are used by the reliability method to adjust base demands to reflect demands during all the other portions of the reliability reporting period. Both freeway and urban street facilities require day-of-week and month-of-year variability data. These data can be expressed as ratios of day- of-week and month-of-year demand relative to AADT, or as ratios relative to a specified day and month (e.g., Mondays in January). In addition, urban street facilities require hour-of-day factors (K-factors), expressed as a percentage of AADT. Freeway demand patterns are provided as a 7-day by 12-month matrix, with 84 total values. Urban street demand patterns are expressed as: • Hour-of-day factors for each hour of the study period (up to 24, but typically 6 or fewer in practice). • Day-of-week factors for each day included as part of the reliability reporting period (up to 7). • Month-of-year factors for each month included as part of the reliability reporting period (up to 12). The urban street method also allows the user to specify demand adjustment factors for rain and snow conditions, respectively. Default values for freeway and urban street demand are provided in Section 5, Applications. When local data are available (e.g., from a permanent traffic recorder station on a freeway), analysts are encouraged to use those data instead, to obtain the most accurate results. Exhibit 36-3 Temporal and Spatial Dimensions of Reliability The urban street method requires hour-of-day factors because it is designed to start with peak hour demands and expand them to peak period demands. The freeway method starts with peak period demands.

Chapter 36/Travel Time Reliability Page 36-9 Introduction Weather Data The reliability method uses weather data to adjust the facility’s capacity to reflect the effects of weather events on operations. The urban streets method also optionally allows adjustments to demand based on the presence of weather conditions. The specific types of weather data used in the freeway and urban street methods are sufficiently different that they are described separately below. Freeway Facilities The freeway facility method requires the probabilities of occurrence of eleven specific weather events, with a probability expressed as the fraction of time during the study period for the month that the weather event is present. These weather events correspond to ten of the weather conditions listed in Chapter 10 (Exhibit 10-15) for which capacity reduction effects of 4% or more have been documented (2), plus a “non-severe weather” category that encompasses all other types of weather that have no or minimal impacts on freeway capacities and speeds. Exhibit 36-4 defines the weather events used for a freeway facility reliability analysis. In addition to the probabilities of occurrence, an average duration is required for each of the ten severe weather events. Weather Event Definition Medium rain >0.10 ≤ 0.25 in./h Heavy rain >0.25 in./h Light snow >0 ≤ 0.05 in./h Light-medium snow >0.05 ≤ 0.10 in./h Medium-heavy snow >0.10 ≤ 0.50 in./h Heavy snow >0.50 in./h Severe cold <–4˚F Low visibility <1 ≥ 0.50 mi Very low visibility <0.50 ≤ 0.25 mi Minimal visibility <0.25 mi Non-severe weather All other conditions not listed above Default values have been developed for the probability of occurrence, in each hour of each month, of the eleven types of weather events for 101 metropolitan areas in the U.S. based on data from 2001–2010. Default values have also been developed for the average durations of each type of severe weather event in each area (3). These defaults should be sufficient for most analyses; however, analysts are free to substitute more recent or more localized data when available. Urban Street Facilities An urban streets reliability evaluation requires the weather-related data identified in the following list. These data represent averages by month of year for a recent 10-year period. • Total normal precipitation (in.), • Total normal snowfall (in.), • Number of days with precipitation of 0.01 in. or more (days), • Normal daily mean temperature (˚F), and • Precipitation rate (in./h). For convenience, Exhibit 36-4 assigns names to each type of weather event, but the numerical definitions shown are used to determine the capacity- and speed-reducing effects of each event, consistent with Exhibit 10-15 in Chapter 10. Exhibit 36-4 Definitions of Freeway Facility Weather Events The default weather data should be sufficient for most analyses.

Introduction Page 36-10 Chapter 36/Travel Time Reliability Default values are available for each of these statistics for 284 locations in the U.S. based on data from 2001–2010. These defaults should be sufficient for most analyses; however, analysts are free to substitute more recent or more localized data when available. In addition, a duration of pavement runoff for a snow event is required. It is defined as the period of time after the snow stops falling that snow pack (or ice) covers the pavement. After this time period elapses, the pavement is exposed and drying begins. This time is likely a function of traffic volume, snow depth, and agency snow removal capabilities. When possible, an appropriate local value should be established for the subject facility. If not possible, Section 5, Applications, provides a default value for this input parameter. Incident Data The reliability method uses incident data to adjust the facility’s capacity to reflect the effects of shoulder or lane closures. The specific inputs used in the freeway and urban street methods are sufficiently different that they are described separately below. Freeway Facilities A freeway facility reliability analysis requires the monthly probability and average duration of certain incident types, representing the fraction of time during the study period in each month where a given incident type occurs. Incident types are defined as: no incident, shoulder closure, one lane closures, two lane closures, etc., up to the number of directional lanes on the facility minus one (i.e., full facility closures are not modeled). The number of incident scenarios depends on the cross-section of the incident segment(s), which are defined by the analyst. Up to three incident segments can be defined along the facility, which are ideally located towards the beginning, in the middle, and towards the end of the facility. This approach provides the greatest accuracy, particularly when the effects of treatments to improve facility safety (i.e., reduce the incident rate) or reduce incident duration are being evaluated as part of the analysis. For situations where incident logs in sufficient detail and duration are not available, the methodology provides a simpler, alternative method for estimating the facility incident rate. This approach requires only the following data: • Local (facility or regional freeway) crash rate per 100 million vehicle-miles traveled (VMT), • Local incident to crash rate ratio, and • Facility length. Section 5, Applications, provides default incident duration values for use when this alternative approach is used to estimate the facility incident rate. The effects of treatments to improve facility safety, incident duration, or both can also be evaluated using this alternative approach, but it should be recognized that the method’s predicted changes in reliability will be based on changes from national average conditions rather than on local conditions. Full facility closures are not modeled because neither the HCM nor facility-specific alternative tools account for the shift in demand that occurs in such an event.

Chapter 36/Travel Time Reliability Page 36-11 Introduction Urban Streets Chapter 16, Urban Street Facilities, defines segments as including portions of their bounding intersections (segments extend from the upstream intersection stop bar to downstream intersection stop bar). For the purposes of reliability analysis, it is necessary to modify this definition for the exclusive purpose of classifying collision data by segment or intersection location. For collision data purposes, the classification of whether or not a collision occurred at the intersection or on the segment is determined using the definitions given in Highway Safety Manual Section A.2.3, found in Appendix A of Volume 2 (4): “Intersection crashes include crashes that occur at an intersection (i.e., within the curb limits) and crashes that occur on the intersection legs and are intersection- related. All crashes that are not classified as intersection or intersection-related crashes are considered to be roadway segment crashes.” Base Segment and Intersection Crash Frequencies The methodology predicts non-crash incident frequency, type, and location because most agencies do not have detailed non-crash incident data for urban streets. The method predicts incident frequency as a function of the crash rate. This approach requires supplying base crash frequencies for each segment and intersection along the subject facility. These crash frequencies represent an estimate of the expected crash frequency for the segment or intersection when no work zones are present or special events occur. The estimate should include all severity levels, including property-damage-only (PDO) crashes. Crash frequencies are provided in units of crashes per year, regardless of the duration of the reliability reporting period. Crash Frequency Adjustment Factors for Work Zones and Special Events One crash frequency adjustment factor for segments and one factor for intersections must be supplied for each work zone or special event for which an alternative dataset is assembled. These factors are used to estimate the expected crash frequency when a work zone or special event is present. The appropriate factor is multiplied by the base crash frequency for the segment or intersection. The result represents the expected crash frequency in a segment or at an intersection if the work zone or special event were present for one year. The factor value should include consideration of the effect of the work zone or special event on traffic volume and crash risk. For example, the volume may be reduced due to diversion, while changes to the roadway geometry and signal operation for a work zone or special event may increase the potential for a crash. To illustrate this concept, consider a work zone that is envisioned to increase crash risk by 100% (i.e., crash risk is doubled) and to decrease traffic volume by 50% (i.e., volume is halved). In this situation, the crash frequency adjustment factor is 1.0 (= 2.0 × 0.5). The analyst’s experience with similar types of work zones or special events should be used to determine the appropriate adjustment factor value for the subject facility.

Introduction Page 36-12 Chapter 36/Travel Time Reliability Crash Frequency Adjustment Factors for Inclement Weather Inclement weather conditions can increase the likelihood of crashes. Crash frequency adjustment factors are required for the following conditions: • Rainfall, • Snowfall, • Wet pavement (not raining), and • Snow or ice on pavement (not snowing). Default values for these factors are provided in Section 5, Applications. Factors Influencing Incident Duration The time required to clear an incident depends on a number of factors, including time to detect an incident, time to respond, and time to clear the incident. Response and clearance times are weather-dependent, while clearance times are also dependent on the incident severity and location (e.g., shoulder vs. travel lanes). The following values are required: • Incident detection time, in minutes, assumed to be generally applicable; • Incident response times, in minutes, for five weather categories (dry, rainfall, snowfall, wet pavement, snow or ice on pavement); and • Incident clearance times, in minutes, by street location (segment or intersection), incident type (crash or non-crash), lane location (shoulder, one lane, two or more lanes), severity (fatal/injury or PDO), and weather condition (dry, rainfall, wet pavement, snowfall or snow/ice on pavement) (96 total values). Default values for these factors are provided in Section 5, Applications. An analyst should supply local values for these factors when the reliability analysis is testing the effects of possible traffic management measures that influence incident detection, response, or clearance. Incident Location Distribution These factors are used by the urban street incident generation procedure to assign incidents to specific locations on the facility. The following incident proportions are required: • Proportion of crash and non-crash incidents by street location (segment or intersection ) (4 total values; proportions should total 1.000 for a given street location); • Proportion of shoulder, 1 lane, and 2+ lane incidents by street location and event type (crash or non-crash) (12 total values); proportions should total 1.000 for a given street location and event type combination; a 0.000 proportion should be assigned to values involving a shoulder location if no shoulders exist on the facility; • Proportion of fatal/injury and PDO crashes by street location and lane location (12 total values); proportions should total 1.000 for a given street location and lane location combination;

Chapter 36/Travel Time Reliability Page 36-13 Introduction • Proportion of breakdown and other non-crash incidents by street location and lane location (12 total values); proportions should total 1.000 for a given street location and lane location combination. Default values for these factors are provided in Section 5, Applications. Work Zones and Special Events Work zones and special events require the use of alternative datasets that specify the demand, geometric, and traffic control conditions that exist during the work zone or special event. A schedule (start and end times each day, along with start and end dates) is also required that specifies when the work zone is in effect or when the special event takes place. Nearest City The nearest city is a required input when the analyst chooses to use defaulted weather data. The analyst selects from 101 metropolitan areas for a freeway facility analysis or from 284 locations for an urban street analysis. More locations are available for urban street analysis because this method uses a smaller set of weather data that are available for a larger set of cities. Geometrics The presence of outside (i.e., right side) shoulders is used in the urban street method for predicting incident locations. This input is specified for the facility. The default distribution of incident lane location is based on facilities with outside shoulders. This distribution is modified accordingly when shoulders are not present on the subject facility. For a shoulder to be considered “present,” it must be sufficiently wide that it can store a disabled vehicle (such that the vehicle does not block traffic flow in the adjacent traffic lane). If on-street parking is allowed, the analyst will need to determine whether its occupancy during the study period is sufficient to preclude its use as a refuge for disabled vehicles. It is judged that the proportion of on-street parking occupied would need to be less than 30% to provide reasonable assurance that there will be opportunity to move a disabled vehicle from the through lanes to an open stall. Traffic Counts Both the freeway and urban street methods estimate facility demand in a given scenario by multiplying the base dataset’s demand by the day-of-week, month-of-year, and (for urban streets) hour-of-day factors associated with the scenario’s demand pattern. These factors were described earlier. However, to apply the appropriate factor, the method needs to know what the base dataset demand represents. The freeway facility method requires a demand multiplier. If the supplied demand patterns are relative to AADT, then the demand multiplier is the base dataset demand divided by the demand reflective of AADT. If the supplied demand patterns are relative to a specific date, then the demand multiplier is the base dataset demand divided by the average demand for that date. The urban street method requires the date and time of the traffic count used in the base dataset. If the base dataset demands are computed using planning

Introduction Page 36-14 Chapter 36/Travel Time Reliability procedures, they are assumed to represent average day volumes. In this case, a date does not need to be provided by the analyst. However, the time of day for which the estimated volumes apply is still needed. Functional Class The functional class of the subject facility is used in the urban street procedure for estimating the traffic volume during each of the various scenarios that comprise the reliability reporting period. Specifically, it is used to determine the appropriate traffic volume adjustment factors for each scenario. The functional classes that are considered are: • Urban expressway, • Urban principal arterial street, and • Urban minor arterial street. An urban principal arterial street emphasizes mobility over access. It serves intra-area travel, such as that between a central business district and outlying residential areas, or that between a freeway and an important activity center. It is typically used for relatively long trips within the urban area, or through trips that are entering, leaving, or passing through the city. An urban minor arterial street provides a balance between mobility and access. It interconnects with, and augments, the urban principal arterial street system. It is typically used for trips of moderate length within relatively small geographic areas (5). Default month-of-year, hour-of-day, and day-of-week adjustment factors are provided for each functional class. These factors are described in Section 5, Applications. SCOPE OF THE METHODOLOGY The reliability methodology can be used to evaluate the following sources of unreliable travel time: • Demand fluctuations, • Weather, • Traffic incidents, • Work zones, • Special events, • Inadequate base capacity, and • Traffic control devices on urban streets. Demand fluctuations are represented in the methodology in terms of systematic and random demand variation by hour of day, day of week, and month of year. Fluctuations due to diversion are not addressed directly by the methodology, but can be optionally provided by the analyst for work zones and special events through the demand specified in an alternative dataset.

Chapter 36/Travel Time Reliability Page 36-15 Introduction LIMITATIONS OF THE METHODOLOGY Because the reliability methods are based on applying the freeway and urban streets methodologies multiple times, they inherit the limitations of those methodologies, as described in Chapters 10 and 16–18, respectively. The reliability methods have additional limitations as described below. Freeways The following are limitations of the freeway methodology: • Weather events that have a small effect on segment capacity reduction (< 4%) are currently not accounted for in the methodology. In addition, a given weather event (e.g., rain, snow) is always assumed to occur at its mean duration value. Further, only two possible start times for weather events are considered. Sun glare is not accounted for. • The method assumes that incident occurrence and traffic demand are independent of weather conditions, although all are indirectly tied through the specification of demand, incident, and weather probabilities on a calendar basis. • Incidents can only occur on three possible segments: the first segment, the segment at the facility midpoint, and the last segment. The timing of the incident is either at the start of a study period or at its midpoint. Finally, only three possible incident durations are considered, which are the 25th, 50th, and 75th percentiles of the incident duration distribution. • The methodology does not include the effect of managed lanes on reliability, as the HCM freeway facility method currently does not address managed lanes. Urban Streets In general, the urban street reliability methodology can be used to evaluate the performance of most urban street facilities. However, the methodology does not address some events or conditions that that occur on some streets and influence their operation, including: • Truck pick-up and delivery (double parking), • Signal malfunction, • Railroad crossing, • Railroad and emergency vehicle preemption, • Signal plan transition, and • Fog, dust storms, smoke, high winds, or sun glare. Lane or shoulder blockage due to truck pick-up-and-delivery activities in downtown urban areas can be considered incident-like in terms of the randomness of their occurrence and the temporal extent of the event. The dwell time for these activities can range from 10 to 20 min (6). A signal malfunction occurs when one or more elements of the signal system are not operating in the intended manner. These elements include vehicle

Introduction Page 36-16 Chapter 36/Travel Time Reliability detectors, signal heads, and controller hardware. A failure of one or more of these elements typically results in poor facility operation. A railroad crossing the facility at a mid-segment location effectively blocks traffic flow while the train is present. Train crossing time can be lengthy (i.e., typically 5 to 10 min), and can result in considerable congestion that can extend for one or more subsequent analysis periods. Railroad preemption occurs when a train crosses a cross-street leg of a signalized intersection. The signal operation is disrupted to safely clear the tracks. Signal coordination may be disrupted for several cycles following train clearance. When a new timing plan is invoked, the controller goes through a transition from the previous plan to the new plan. The transition period can last several cycles, during which traffic progression is significantly disrupted. Some weather conditions that restrict driver visibility or degrade vehicle stability are not addressed by the methodology. These conditions include fog, dust storms, smoke, and high winds.

Chapter 36/Travel Time Reliability Page 36-17 Concepts 2. CONCEPTS As travel time reliability methods are new to the HCM, reliability concepts do not appear in Volume 1. Therefore, this section summarizes key reliability concepts, including discussing why an analyst might want to evaluate a facility’s reliability, presenting suggested performance measures and typical values for some common measures, identifying potential data sources for a reliability analysis, and interpreting the results of a reliability analysis. OBJECTIVES FOR RELIABILITY ANALYSIS An important first step in any analysis is defining why the analysis is being performed, including defining the key questions or issues, identifying performance measures that help answer those questions, and establishing a basis of comparison for interpreting the analysis results. Reliability analysis is no different. Examples of potential objectives of a reliability analysis include: • Tracking the reliability of a set of facilities in a jurisdiction or region over time for the purposes of prioritizing facilities for potential operational or physical treatments. • Diagnosing the primary causes of the reliability problems on a given facility so that an improvement program can be developed for the facility. • Evaluating the effects of a particular treatment or improvement on a facility once it has been implemented. More broadly, travel time reliability analysis can be used to improve the operation, planning, prioritization, and programming of transportation system improvement projects in the following applications: long range transportation plans (LRTPs), transportation improvement programs (TIPs), corridor or area- wide plans, major investment studies, congestion management, operations planning, and demand forecasting. The Use Cases portion of Section 5, Applications, describes these potential applications in greater detail. PERFORMANCE MEASURES The reliability methodology produces two types of performance measures: 1. Distributions of the performance measures produced by the HCM facility methodologies. 2. Variability and reliability measures based on characteristics of the travel time distribution. Distributions of HCM Facility Performance Measures The reliability methodology produces distributions of HCM facility measures that represent their variation during the reliability reporting period. These distributions include percentiles (e.g., 50th percentile speed) and the probability of achieving a particular LOS. For freeway facilities, distributions can be produced for such measures as facility speed, travel time, and average density. For urban streets, distributions can be produced for travel time, travel speed, and spatial stop rate, among others. Reliability analysis can be used to improve the operation, planning, prioritization, and programming of transportation system improvement projects.

Concepts Page 36-18 Chapter 36/Travel Time Reliability Performance Measures Derived from the Travel Time Distribution The travel time distribution can be used to derive a variety of performance measures that describe different aspects of reliability. These include: • Percentile-based measures, such as the 95th percentile travel time; • On-time measures, such as the percent of trips completed within a defined travel time threshold; • Failure measures, such as the percent of trips that exceed a travel time threshold; and • Statistical descriptors of the distribution, such as standard deviation and kurtosis. Exhibit 36-5 illustrates how various reliability performance measures can be derived from the travel time distribution. Some of these measures include: • Planning time, the travel time a traveler would need to budget to ensure an on-time arrival 95% of the time; • Buffer time, the extra travel time a traveler would need to budget, compared to the average travel time, to ensure an on-time arrival 95% of the time; and • Misery time, the average of the highest 5% of travel times (approximating a 97.5% travel time) minus the free-flow travel time, representing a near- worst-case condition. To facilitate comparisons of facilities, these measures can be converted into length-independent indexes by dividing the base travel time measure by the free- flow travel time. For example, the misery index is defined as the misery time divided by the free-flow travel time. The most common index measure is the travel time index (TTI), which is the ratio of the actual travel time on a facility to the theoretical travel time if traveling at free-flow speed. When used to describe Exhibit 36-5 Derivation of Reliability Performance Measures from the Travel Time Distribution

Chapter 36/Travel Time Reliability Page 36-19 Concepts the travel time distribution, TTIs are often given as a stated percentile travel time (50th, 80th, and 95th are widely used), or as a mean TTI, when mean travel time is used in the numerator. The 95th percentile TTI is also known as the planning time index (PTI). Analysts can also define a policy index, which is similar to the TTI, but replaces free-flow speed with a target speed for the facility. This target speed can represent a desired minimum operating speed for the facility (typically chosen as a speed just above breakdown), or can represent an approximation of free-flow speed for use in compiling and comparing results nationally. A related measure is the reliability rating, the percentage of trips (or VMT) serviced at a TTI below a defined congestion threshold. Performance Measures for Reliability Analysis There are many possible performance measures for quantifying different aspects of the travel time reliability distribution. The following performance measures are among the more useful measures for quantifying differences in reliability between facilities and for evaluating alternatives to improve reliability. Measures Describing Typical (Average) Conditions Typical (or average) conditions are the conditions evaluated by a standard HCM freeway or urban street facility analysis. Useful measures for these conditions include: • Travel time (minutes). Travel time is a versatile measure, as it can be monitored over time (for trend analysis), monetized (when calculating benefits), and used in the calculation of other measures (e.g., TTI, delay). Facility lengths usually remain the same over time, allowing apples-to- apples comparisons of travel times estimated for a facility in different years or under different circumstances. • 50th percentile TTI (unitless). This measure can be used for trend analysis and to demonstrate changes in performance resulting from an operational strategy, capacity improvement, or change in demand. Because TTI is unitless, it allows facilities to be compared to each other (e.g., for project prioritization purposes, or to compare individual facility results to national values, as discussed in the next subsection). The mean TTI can also be used for these purposes; this measure will typically have somewhat higher values than the 50th percentile TTI due to the influence of rare, very long travel times in the distribution. • Annual delay (veh-h and p-h). Annual delay represents the average vehicle- or person-hours of travel (VHT, PHT) that occurs minus that which would occur under free-flow conditions. Delay is useful because economic analyses have a long history of monetizing delay.

Concepts Page 36-20 Chapter 36/Travel Time Reliability Measures Describing Unreliability When one measures or predicts travel times over a long period of time (e.g., a year), a distribution of travel times results. The following are useful measures for describing (a) travel time variability or (b) the success or failure of individual trips in meeting a target travel time or speed: • Planning time index (unitless). This measure is useful for estimating how much extra time travelers must budget to ensure an on-time arrival and for describing near-worst-case conditions on urban facilities. • 80th percentile TTI (unitless). This measure has been found to be more sensitive to operational changes than the PTI (4), which makes it useful for comparison and prioritization purposes. • Failure/on-time measures (percentage). The percentage of trips with space mean speeds above (on-time) or below (failure) one or more target values (e.g., 35, 45, and 50 mi/h). These measures address how often trips succeed or fail in achieving a desired travel time or speed. • Reliability rating (percentage). The percentage of trips experiencing a TTI less than 1.33 for freeways and 2.50 for urban streets. These thresholds approximate the points beyond which travel times become much more variable (unreliable). The difference in threshold TTI values is due to differences in how free-flow speed is defined for freeways compared to urban streets, as TTI is measured relative to free-flow speed. • Semi-standard deviation (unitless). A one-sided standard deviation, with the reference point at free-flow speed instead of the mean. It provides the variability distance from free-flow conditions. • Standard deviation (unitless). The standard statistical measure. • Misery index (unitless). This measure is useful as a descriptor of near- worst-case conditions on rural facilities. In many cases, as illustrated in the example problems in Section 6, an analyst may wish to evaluate several of these measures to obtain the most complete picture of travel time reliability. However, as a single measure that reflects the traveler point-of-view by stating the potential for unreliable travel, the reliability rating is recommended to be reported as part of any HCM-based reliability analysis. TYPICAL TRAVEL TIME VARIABILITY VALUES Exhibit 36-6 provides percentile ranks of TTI, mean TTI, and PTI for a sampling of U.S. freeways and urban streets compiled by SHRP 2 Project L08 (1). The data are values from 2-h a.m. peak, midday, and p.m. peak periods. The process and data used to create this exhibit are described in Section 1 of Chapter 37, Travel Time Reliability: Supplemental. The databases used to develop this table are relatively small and it is unknown whether a larger database would produce similar percentile values. Although the table is intended as an aid to analysts in comparing a given facility’s performance to that of other U.S. facilities, caution is needed when

Chapter 36/Travel Time Reliability Page 36-21 Concepts comparing a facility’s operation to that of those shown in these exhibits, as the analyst’s facility may have different characteristics than the sample of facilities. These data are derived from field measurements. Note that the urban street values of TTI and PTI are calculated using a base travel speed, defined as the 85th percentile speed during off-peak conditions, rather than a free-flow speed. This is because the field-measured travel times include the effects of traffic control devices under low-volume conditions, whereas the HCM definition of free-flow speed specifically omits the effects of traffic control devices. As an example of how to read Exhibit 36-6, assume that one has a measured PTI for a freeway for the a.m. peak period. The PTIs of the selected freeways included in Exhibit 36-6 ranged from 1.53 to 3.92 during the a.m. peak period. Half of these facilities had PTIs less than 1.53, while only 5% of them had PTIs greater than 3.92 (i.e., 95% had PTIs less than 3.92). Percentile Rank Freeways Urban Streets TTI Mean TTI PTI TTI Mean TTI PTI AM PEAK PERIOD Worst 5% 1.95 2.08 3.92 1.35 1.36 1.84 Worst 10% 1.72 1.93 3.55 1.28 1.31 1.71 Worst 15% 1.54 1.83 3.17 1.26 1.29 1.66 Worst 20% 1.28 1.48 2.61 1.26 1.29 1.57 Worst 50% 1.09 1.17 1.53 1.20 1.23 1.41 MIDDAY Worst 5% 1.21 1.46 3.16 1.35 1.42 1.86 Worst 10% 1.17 1.42 2.85 1.33 1.38 1.63 Worst 15% 1.16 1.32 2.41 1.32 1.35 1.63 Worst 20% 1.14 1.30 1.92 1.31 1.34 1.60 Worst 50% 1.06 1.12 1.32 1.22 1.24 1.45 PM PEAK PERIOD Worst 5% 1.76 1.99 3.54 1.56 1.60 2.10 Worst 10% 1.70 1.86 3.26 1.49 1.56 1.88 Worst 15% 1.61 1.71 2.93 1.41 1.52 1.83 Worst 20% 1.35 1.57 2.77 1.41 1.49 1.78 Worst 50% 1.17 1.31 1.85 1.25 1.28 1.49 Source: Derived from values given in Chapter 37, Section 1. Entries are the lowest value for a category. Note: TTI = travel time index (50th percentile travel time divided by base travel time). Mean TTI = mean travel time index (mean travel time divided by base travel time). PTI = planning time index (95th percentile travel time divided by base travel time). For freeways, the base travel time is the free-flow travel time. For urban streets, the base travel time corresponds to the 85th percentile highest speed observed during off-peak hours. Exhibit 36-7 through Exhibit 36-9 illustrate the distribution of TTI and PTI from the sample of freeways and urban streets. It can be seen from this exhibit that a greater range of unreliable conditions is observed on freeways, compared to urban streets, as measured by the spread between the most reliable and least reliable facilities included in the dataset. An HCM-estimated TTI can be converted to a field-measured TTI by multiplying the HCM TTI by the field-measured free-flow speed and dividing by the HCM free-flow speed. Exhibit 36-6 Rankings of Selected U.S. Facilities by TTI, Mean TTI and PTI

Concepts Page 36-22 Chapter 36/Travel Time Reliability Note: TTI = travel time index (50th percentile travel time divided by base travel time). PTI = planning time index (95th percentile travel time divided by base travel time). For freeways, the base travel time is the free-flow travel time. For urban streets, the base travel time corresponds to the 85th percentile highest speed observed during off-peak hours. Note: TTI = travel time index (50th percentile travel time divided by base travel time). PTI = planning time index (95th percentile travel time divided by base travel time). For freeways, the base travel time is the free-flow travel time. For urban streets, the base travel time corresponds to the 85th percentile highest speed observed during off-peak hours. Exhibit 36-7 TTI and PTI Distribution on U.S. Freeways and Urban Streets (AM Peak Period) Exhibit 36-8 TTI and PTI Distribution on U.S. Freeways and Urban Streets (Midday Period)

Chapter 36/Travel Time Reliability Page 36-23 Concepts Note: TTI = travel time index (50th percentile travel time divided by base travel time). PTI = planning time index (95th percentile travel time divided by base travel time). For freeways, the base travel time is the free-flow travel time. For urban streets, the base travel time corresponds to the 85th percentile highest speed observed during off-peak hours. DATA ACQUISITION Although default values are provided for many of the variables that affect facility reliability (see Section 5, Applications), the preceding section illustrates that reliability (as measured by TTI or PTI) can vary widely, depending on the characteristics of a particular facility. Therefore, analysts are encouraged to use local values representative of local demand, weather, and incident patterns when the data are available. In addition, analysts must supply local values for work zones and special events if they wish to account for these effects in a reliability analysis. This subsection identifies potential sources of these data. Demand Patterns The best potential source of demand pattern data is from a permanent traffic recorder (PTR) located along the facility. Alternatively, an analyst may be able to use data from a PTR located along a similar facility in the same geographic area. Many state departments of transportation produce compilations of data from their PTRs and provide demand adjustment factors by time of day, day of week, and month of year by facility and area type. The analyst is reminded that measured volumes are not necessarily reflective of demands. As was illustrated in Exhibit 3-8 (page 3-9), upstream bottlenecks may limit the amount of volume that reaches a PTR or other observation point. Weather The National Climatic Data Center (NCDC) provides rainfall, snow, and temperature statistics for thousands of locations through its website (7) and average precipitation rate data in the Rainfall Frequency Atlas (8). The more Exhibit 36-9 TTI and PTI Distribution on U.S. Freeways and Urban Streets (PM Peak Period)

Concepts Page 36-24 Chapter 36/Travel Time Reliability detailed hourly weather data needed for a freeway facility analysis is available from larger airport weather stations and can be obtained from the NCDC website or other online sources (e.g., 3). A weather station that a transportation agency has installed along the study facility may also be able to provide the required data, if the agency stores and archives the data collected by the station. It should be kept in mind that a 10-year weather dataset is desirable, to capture rare but highly impactful weather events. Finally, analysts should consider the location of the facility relative to the weather station, because elevation differences, proximity to large bodies of water, and other factors that create microclimates may result in certain types of weather events (e.g., snow, fog) occurring with significantly different probabilities on the facility than at the weather station. Incidents Freeways A significant level of effort is required to extract information about the numbers and average durations of each incident type from the annual incident logs maintained by roadway agencies, even in data-rich environments. Furthermore, certain incident types—particularly shoulder incidents—can be significantly underreported in incident logs (1). Thus the direct approach of estimating incident probabilities is reserved for those very rare cases where the incident logs are complete and accurate over the entire reliability reporting period. An alternative approach is to estimate the facility incident rate from its predicted crash rate and assume that the number of incidents in a given study period is Poisson distributed (9, 10). Details of the process are described in Chapter 37, Travel Time Reliability: Supplemental. Urban Streets The expected crash frequency can be computed using the predictive method in Chapter 12 of the 2010 Highway Safety Manual (HSM) (4). If this method cannot be used, then a three-year crash history for the subject segment or intersection can be used to estimate its expected crash frequency. Crashes that occur when work zones and special events are present should be removed from the crash data. In this situation, the expected crash frequency is computed as the count of crashes during times when work zones and special events are not present divided by the time period when work zones and special events are not present. Thus, if there were 15 crashes reported during a recent three-year period and 5 of these crashes occurred during a six-month period when a work zone was present, then the expected crash frequency is estimated as 4.0 crashes per year (= [15 – 5]/[3 – 0.5]). A technique for determining whether a crash is a segment- or intersection-related crash is described in Appendix A to Part C of the 2010 HSM (4).

Chapter 36/Travel Time Reliability Page 36-25 Concepts Work Zones A schedule of long-term work zones should be obtained from the roadway operating agency, indicating the days and times when the work zone will be in effect and the portions of the roadway that will be affected. Work zones that vary in intensity (e.g., one lane closed on some days and two lanes closed on others) or that affect different segments at different points in time will need to be provided as separate alternative datasets. When available, detailed traffic control plans for each work zone should be consulted to determine the starting and ending locations of lane closures, along with any reductions in the posted speed. When detailed plans are not available, the agency’s standard practices for work zone traffic control can be consulted to determine the likely traffic control that would be implemented, given the project’s characteristics. Special Events Special events are short-term events, such as major sporting events, concerts, and festivals that produce intense traffic demands on a facility for limited periods of time. Special traffic control procedures may need to be implemented to accommodate the traffic demands. The analyst should identify whether any events that occur in or near the study area warrant special treatment. If so, a schedule for the event (dates, starting times, typical durations) should be obtained. Some types of events also have varying intensities that will require separate treatment (e.g., a sold-out baseball game against a rival, compared to a lower-attendance midweek game). Recurring events may have developed special traffic control procedures; if so, these plans should be consulted to identify any changes required from base conditions. Alternative datasets will be needed for each combination of special event venue and event intensity. INTERPRETING RESULTS Identifying Reliability Problems In a perfect world, every freeway and urban street facility would be perfectly reliable. They would have mean TTIs and PTIs of 1.00 or better. However, since operating a “perfectly” reliable facility is not a realistic standard, an agency must distinguish between less than perfect—but still acceptable—reliability, and unacceptable reliability. This is obviously a very individual choice that each agency must make between unachievable perfection and achievable performance. This section provides guidance on the factors and criteria that a transportation agency may wish to consider in making its selection, but the final decision is ultimately up to the agency. Criterion #1: How Does Reliability Compare to Agency Congestion Management Policy? If the agency has a policy of delivering a certain minimum speed or maximum travel time on its freeways or urban streets, or a maximum acceptable delay per signal or per mile, this information can be used to either modify the computation of the reliability statistics, or the reliability statistics can be translated into delays so that failures to meet agency policy can be more quickly identified.

Concepts Page 36-26 Chapter 36/Travel Time Reliability Minimum Speed Policy If the agency has a minimum acceptable facility speed policy, this information can be used to compute the reliability statistics instead of the free- flow speed. It is then relatively easy to determine the extent to which the facility meets the agency’s target performance level by comparing the computed reliability statistic to the target value of 1.00. The result of using the policy speed instead of the free-flow speed is to neglect travel time reliability when speeds exceed the agency’s minimum acceptable threshold. TTI (policy) = mean travel timepolicy travel time 𝑃𝑇𝐼 (policy) = 95th percentile travel timepolicy travel time where • TTI (policy) = travel time index, based on the agency’s policy (or target) travel time for the facility (unitless); • PTI (policy) = planning time index, based on the agency’s policy (or target) travel time for the facility (unitless); • Mean Travel Time = observed mean travel time for through trips on the facility over the reliability reporting period (min); • 95th Percentile Travel Time = 95th percentile highest observed through trip travel time on the facility over the reliability reporting period (min); and • Policy Travel Time = agency’s maximum acceptable travel time for through trips on the facility (min), determined by dividing the facility length by the minimum acceptable average speed for the facility and converting from hours to minutes. For example, if the agency’s congestion management policy is to deliver freeway speeds in excess of 40 mi/h, then the policy travel times are computed using the facility length divided by 40 mi/h and converting the result to minutes. Values of 1.00 or less for TTI (policy) mean that the agency’s congestion management policy is being met on average over the course of the reliability reporting period. Values greater than 1.00 mean the facility is failing to meet the agency’s policy on average. Values of 1.00 or less for PTI (policy) mean that the agency’s congestion management policy is being met at least 95% of the time for the reliability reporting period. Values greater than 1.00 mean the facility is meeting the agency’s policy less than 95% of the time. Maximum Acceptable Delay If the agency has a maximum acceptable delay standard per mile (for freeways or urban streets) or per signal (for urban streets), then the TTI and PTI can be readily converted into equivalent delay estimates for the facility and compared to the agency standard. Equation 36-1

Chapter 36/Travel Time Reliability Page 36-27 Concepts Average Delay Per Trip = 3,600 × Length 𝐹𝐹𝑆 × (𝑇𝑇𝐼 − 1) Average Delay Per Mile = 3,600 × 1 𝐹𝐹𝑆 × (𝑇𝑇𝐼 − 1) Average Delay Per Signal = 3,600 × Length 𝑁𝑆 × 𝐹𝐹𝑆 × (𝑇𝑇𝐼 − 1) where average delay is the average delay per vehicle in seconds and TTI = Travel time index, the mean travel time divided by the free-flow travel time for the facility (unitless); PTI = Planning time index, the 95th percentile travel time divided by the free-flow travel time for the facility (unitless); FFS = average facility free-flow speed, including signal delay at low volumes (mi/h); Length = facility length (mi); and NS = number of signals within study section of facility (unitless). For the 95th percentile delay per trip, per mile, and per signal, substitute PTI for TTI in Equation 36-2. These equations can be solved for TTI or PTI to determine the maximum acceptable values of these indices consistent with the agency’s maximum delay policy. Criterion #2: How Does Reliability Compare to Other Facilities? This approach is the most straightforward way to identify levels of acceptable and unacceptable reliability. The agency ranks the reliability results for a given facility against that of other facilities it operates and prioritizes improvements to its facilities with the worst reliability accordingly. Of course, this approach requires that the agency collect reliability data for its facilities so that the agency’s facility investments can be properly ranked according to need. Until an agency has assembled sufficient data on the reliability of its own facilities, it may choose to use Exhibit 36-6, which provides reliability statistics constructed for a relatively small sample of freeways and urban streets in the United States. For example, if an agency’s goal is to not have facilities in the worst 5% ranking in the sample, then their TTI goals for their freeways would be 1.97 or less and 1.53 or less for urban streets. Their PTI goals for acceptable reliability would be less than 3.60 for freeways and 1.94 for urban streets. Criterion #3: How Does Reliability Compare to HCM Level of Service? This criterion involves translating reliability results into more traditional HCM level of service results that decision-makers may be more comfortable with. This involves using the reliability results to identify what percent of time a facility is operating at an unacceptable LOS and determining a percentage of time that is unacceptable. For example, the agency’s LOS standard may be LOS D. The reliability results may show that the facility operates at LOS E or worse during 5% of the weekday peak periods over the course of a year. This may be an acceptable risk for the agency, if the costs of improvements are high to eliminate the 5% risk. Equation 36-2

Concepts Page 36-28 Chapter 36/Travel Time Reliability Translating PTI Results into HCM LOS for Freeways The PTI provides the ratio of the 95th percentile travel time to the free-flow travel time. This value can be translated into the equivalent HCM LOS by converting the PTI to equivalent mean speed, converting the speed to the equivalent density, and looking up the LOS range for the freeway: 𝑆(95%) = 𝐹𝐹𝑆 𝑃𝑇𝐼 where S(95%) = 95th percentile lowest speed for the facility, the speed which is exceeded 95% of the time on the facility over the reliability analysis reporting period (mi/h); PTI = planning time index for the facility (unitless); and FFS = facility free-flow speed (mi/h). The density is compared to the values in Exhibit 10-7 to determine if the facility will operate at an acceptable LOS at least 95% of the time. The freeway speed-flow equation (Equation 25-1) is solved for volume and divided by the 95th percentile speed to obtain the equivalent density at that speed. 𝐷𝐹(95%) = 𝑐𝑆(95%) × 𝑙𝑛[1 + 𝐹𝐹𝑆 − 𝑆(95%)]𝑙𝑛 �1 + 𝐹𝐹𝑆 − 𝑐45� where DF(95%) = facility density at a speed of S(95%) (pc/mi/ln); S(95%) = 95th percentile lowest speed for the facility over the reliability reporting period (mi/h); FFS = facility free-flow speed; and c = facility per-lane capacity (pc/h/ln). Note that the 95th percentile lowest speed must be equal to or less than the free-flow speed or there is the risk of exceeding the limits of the logarithm function. Once the density is computed, the equivalent LOS can be obtained from Exhibit 10-7. Translating PTI Results into HCM LOS for Urban Streets The PTI provides the ratio of the 95th percentile highest travel time to the free-flow travel time. This can be translated into the equivalent HCM LOS by converting the PTI to equivalent mean speed. The equivalent percent free-flow speed is simply the inverse of the PTI: 𝑆𝑅(95%) = 1/𝑃𝑇𝐼 where PTI is the planning time index for the facility and SR(95%) is the 95th percentile speed ratio (unitless): the 95th percentile slowest through trip speed on the facility (including control delay) divided by the HCM-defined free-flow speed, which by definition does not include control delay. The 95th percentile Equation 36-3 Equation 36-4 Equation 36-5

Chapter 36/Travel Time Reliability Page 36-29 Concepts speed ratio is compared to the urban street LOS criteria in Exhibit 16-4 to determine if the facility will operate at a LOS acceptable to the agency at least 95% of the time. Diagnosing the Causes of Reliability Problems Exhibit 36-10 identifies seven sources of congestion and unreliability, and shows how they interact with each other. The starting point in traditional analysis is to take a fixed capacity and a fixed volume to develop an estimate of delay, usually for “typical” conditions. However, in the field both physical capacity and demand vary because of roadway disruptions, travel patterns, and traffic control devices. These conditions not only decrease available capacity or cause volatility in demand, they also interact with each other. For example, both inclement weather and work zones can lead to an increase in incidents. Thus, diagnosing the relative contribution of different causes of unreliability involves identifying the causes individually and in combination. Depending on the purpose of the evaluation, different logical approaches may be taken for assigning the proportional responsibility to individual causes when more than one is acting in combination. Selecting a Performance Measure To identify the relative effects of different causes on the travel time reliability of the facility, it is recommended that total vehicle (or person) hours of delay summed over the entire reliability reporting period be computed. This measure of effectiveness takes into account both the severity of the event (demand surge, incident, weather) and its frequency of occurrence within the reliability reporting period. Exceptionally severe but rare events may add relatively little to the total annual delay experienced by the facility. Moderate but frequent events will often have a greater effect on total annual delay. Exhibit 36-10 Interrelationship Between Causes of Congestion and the Facility

Concepts Page 36-30 Chapter 36/Travel Time Reliability Generating a Simplified Matrix of Causes Identifying patterns of results in several thousand scenarios is impractical, so it is recommended that the analyst consolidate the many scenarios into a matrix of congestion causes along the lines of Exhibit 36-11. This is best done by combining similar scenarios that individually contribute less than 1% to annual delay. In the example shown in Exhibit 36-11, because severe weather is relatively infrequent at this site, the numerous severe weather events (rain, snow, etc.) have been consolidated into a single “bad weather” category. The results from the original analysis of multiple demand levels have similarly been consolidated into three levels (low, medium, high). Low Demand Moderate Demand High Demand Incidents Fair Weather Bad Weather Fair Weather Bad Weather Fair Weather Bad Weather Total None 596 (2%) 407 (1%) 818 (3%) 362 (1%) 6,240 (23%) 956 (4%) 9,379 (34%) 1 lane closed 2,363 (9%) 92 (<1%) 2,097 (8%) 61 (<1%) 9,102 (33%) 119 (<1%) 13,834 (51%) 2 lanes closed 194 (1%) 13 (<1%) 189 (1%) 9 (<1%) 907 (3%) 17 (<1%) 1,328 (5%) 3 lanes closed 621 (2%) 40 (<1%) 468 (2%) 23 (<1%) 1,510 (6%) 32 (<1%) 2,694 (10%) Total 3,774 (14%) 551 (2%) 3,572 (13%) 456 (2%) 17,759 (65%) 1,124 (4%) 27,236 (100%) Diagnosing Primary Causes of Unreliability The diagnosis proceeds by first examining the cells of the matrix to identify the cells with the largest annual delay values. For example, examination of the cells in Exhibit 36-11 yields the following conclusions: • The single greatest cause of annual delay on the example facility is incidents closing a single lane under high-demand conditions on fair- weather days. They account for 33% of the annual delay on the facility. • The next largest occurrence of annual delay happens under high-demand, fair-weather, no-incident conditions. They account for 23% of the annual delay on the facility. • The third and fourth largest annual delays occur when incidents close a single lane under fair-weather conditions with low-to-moderate demand conditions. Together, these scenarios account for 17% of the annual delay on the facility. • The fifth largest annual delays are accumulated when incidents close three lanes under high-demand and fair-weather conditions. Exhibit 36-12 shows that the top five cells in Exhibit 36-11 account for about 78% of the annual delay on the facility. The next step is to examine the row and column totals to see if a single cause stands out. For example, examination of the row and column totals in Exhibit 36- 11 yields the following conclusions: • The highest row or column total annual delay occurs in high-demand, fair-weather conditions. Recurring congestion is therefore a significant Exhibit 36-11 Example Matrix Allocating Annual Vehicle-Hours of Delay by Cause

Chapter 36/Travel Time Reliability Page 36-31 Concepts source of delay on this example facility. High-demand conditions account for 65% of the annual delay on the facility. • The next highest row or column total occurs when incidents close one lane on the facility. Incidents blocking a single lane account for 51% of the delay on the facility. • Bad weather is a minor cause of annual delay on the facility. Develop a Treatment Plan The conclusions from the example shown in Exhibit 36-11 suggest the following options that are likely to have the greatest effect on improving reliability in the example facility: • Measures to reduce high-demand conditions or to increase capacity to address recurring congestion on the facility show high potential for improving reliability on the facility; and • Measures to manage incidents that close a single lane show high potential for improving reliability. The diagnostic process also reveals that in this particular example, bad weather and extreme incidents (2+ lane closures), although severe when they happen, are infrequent enough to be minor contributors to total annual delay on the example facility. The particular example used here was from a state with relatively mild weather. The results would likely be different on facilities in other parts of the country. Exhibit 36-12 Example Pie Chart of Congestion Causes

Freeway Facility Methodology Page 36-32 Chapter 36/Travel Time Reliability 3. FREEWAY FACILITY METHODOLOGY OVERVIEW This section describes the methodology for evaluating the reliability of a freeway facility. It also describes extensions to the base HCM freeway facility method (Chapter 10) that are required for computing reliability performance measures. The freeway methodology is computationally intense and requires software to implement. This intensity stems from the need to create and process the input and output data associated with the hundreds to thousands of scenarios considered for a typical reliability reporting period. Due to the intensity of the calculations, the objective of this section is to introduce the analyst to the calculation process and discuss the key analytic procedures, while also highlighting important equations, concepts, and interpretations. The computational details of the methodology are provided in Chapter 37, Travel Time Reliability: Supplemental. The FREEVAL-RL computational engine provided in the Technical Reference Library in the online HCM Volume 4 represents the most detailed description of the methodology. FRAMEWORK The freeway reliability methodology includes a base dataset, a scenario generator, and a core computational procedure inherited from Chapter 10. The computational procedure predicts travel times for each scenario, which are assembled into a travel time distribution that is used to determine performance measures of interest. These components are illustrated in Exhibit 36-13. Exhibit 36-13 Freeway Reliability Methodology Framework

Chapter 36/Travel Time Reliability Page 36-33 Freeway Facility Methodology Base Dataset The base dataset contains all the required input data for the Chapter 10 freeway facility. Some data are specific to the freeway facility being studied. These include, at a minimum, all segment geometries, free-flow speeds, lane patterns, and segment types, along with base demands that are typically, but not necessarily, reflective of average (AADT) conditions. In addition, the base dataset contains the required input data to execute this chapter’s reliability methodology. These data include demand patterns, a demand multiplier, weather data, and incident data. The majority of the reliability-specific input data can be defaulted when not available locally, but the analyst is encouraged to supply facility-specific data whenever available. The Required Input Data subsection of Section 1, Introduction, describes all of the freeway-related data required for a reliability analysis. The Data Acquisition subsection of Section 2, Concepts, describes potential sources for these data. Scenario Generation The scenario generator develops a sufficiently complete set of scenarios that a freeway facility may experience during the reliability reporting period, along with their associated probabilities. “Sufficiently complete” means that the analyst may specify minimum threshold probabilities for including a scenario in the analysis. In addition, different combinations of scenarios that produce similar inputs (e.g., demand volumes on Tuesdays, Wednesdays, and Thursdays) may be combined by the analyst. These steps can reduce the number of scenarios that are evaluated—thus reducing analysis time—without significantly impacting the final results. Each scenario represents a single study period (typically several hours long) that is fully characterized in terms of demand and capacity variations in time and space. The data supplied to the scenario generator are expressed as multiplicative factors that are applied to the base demand and capacity. The scenario generation process includes the following steps: • Adjusting the base demand to reflect day-of-week and month-of-year variations associated with a given scenario; • Generating severe weather events based on their probability of occurrence in a given time of year, and adjusting capacities and free-flow speeds to reflect the effects of the weather events; • Generating various types of incidents based on their probability of occurrence and adjusting capacities to reflect their effects; and • Incorporating user-supplied information about when and where work zones and special events occur, along with any corresponding changes to the base demand or geometry. The results from the above steps are used to develop one input dataset to the Chapter 10 procedure (incorporating multiple analysis periods) for each study period in the reliability reporting period.

Freeway Facility Methodology Page 36-34 Chapter 36/Travel Time Reliability Facility Evaluation In the facility evaluation step, each scenario is provided to the core HCM freeway facility methodology for analysis. The performance measures of interest to the evaluation—in particular, travel time—are calculated for each scenario and stored. At the end of this process, a travel time distribution can be formed from the travel time results stored for each scenario. Performance Summary In the final step, travel time reliability is described for the entire reliability reporting period using various performance measures. The travel time distribution is used to quantify a range of variability and reliability metrics. SCENARIO GENERATION Traffic Demand Variation Generation The freeway reliability methodology accounts for demand variability by adjusting the traffic demands for the analysis periods included in the base study period by: 1. A demand ratio, the average demand for a given day and month (e.g., Fridays in May) relative to the average demand for a specified day and month (e.g., AADT, Mondays in January). 2. A demand multiplier, the base-period demand divided by the demand for the specified day and month used in the demoninator of the demand ratio. For example, if base-period demands are expressed as AADT, and average daily traffic (ADT) volumes for Fridays in May are 21% higher than AADT, the demand ratio for an analysis period on a Friday in May would be 1.21. The demand multiplier would be 1.00, as both the base-period demand and the demand ratio denominator are expressed as AADT. The base-period demands would be divided by the demand multiplier (1.00) and multiplied by the demand ratio (1.21) to obtain the analysis period demand for a Friday in May. If base-period demands were measured on a Thursday in August, the supplied demand ratios are relative to Mondays in January, and average demands on Thursdays in August are 32% higher than average demands on Mondays in January, the demand multiplier would be 1.32. Similarly, if average demands for Fridays in May are 39% higher than Mondays in January, the demand ratio for an analysis period on a Friday in May would be 1.39. The base period demands would be divided by the demand multiplier (1.32) and multiplied by the demand ratio (1.39) to obtain analysis period demands for Fridays in May that are 5% higher than the supplied base-period demands. Demand is varied by day of week and month of year for a maximum of 7 × 12 or 84 demand patterns that can be specified for a given year. The method assumes that variability across analysis periods is consistent throughout the study period. That is, the demand ratios are applied consistently to all of the 15- min analyis periods comprising a given scenario’s study period. (Continuing the

Chapter 36/Travel Time Reliability Page 36-35 Freeway Facility Methodology first example from above, the volumes associated with all analysis periods on Fridays in May would be multiplied by 1.21 from their base values.) If demand does not vary significantly between certain days or certain months, the analyst may choose to combine days or months together to reduce the total number of scenarios that will be generated and calculated (thus reducing the analysis time). For example, local conditions permitting, the five weekdays could be consolidated into three weekday types (Monday, Tuesday to Thursday, and Friday), and the twelve months consolidated into four seasons, resulting in 3 × 4 or 12 demand patterns. When days and months are consolidated, the corresponding demand ratios are also consolidated, using average values weighted by the number of specified weekdays in each month. The ratio of highest to lowest demand ratios for urban freeways is 1.82, based on national data shown in Exhibit 36-14 (4), indicating a strong calendar effect on demand. The analyst may use the default national data, but it is recommended for best results that the analyst supply a 7 × 12 matrix of local demand ratios for each combination of day of week and month of year. Demand variation due to work zones or special events must be entered directly by the analyst, as described later in this section. Day of Week Month Monday Tuesday Wednesday Thursday Friday Saturday Sunday January 1.00 1.00 1.02 1.05 1.17 1.01 0.89 February 1.03 1.03 1.05 1.08 1.21 1.04 0.92 March 1.12 1.12 1.14 1.18 1.31 1.13 0.99 April 1.19 1.19 1.21 1.25 1.39 1.20 1.05 May 1.18 1.18 1.21 1.24 1.39 1.20 1.05 June 1.24 1.24 1.27 1.31 1.46 1.26 1.10 July 1.38 1.38 1.41 1.45 1.62 1.39 1.22 August 1.26 1.26 1.28 1.32 1.47 1.27 1.12 September 1.29 1.29 1.32 1.36 1.52 1.31 1.15 October 1.21 1.21 1.24 1.27 1.42 1.22 1.07 November 1.21 1.21 1.24 1.27 1.42 1.22 1.07 December 1.19 1.19 1.21 1.25 1.40 1.20 1.06 Source: Cambridge Systematics et al. (11). Weather Event Generation Weather events are generated based on their probability of occurrence during a given month (or set of months, if months were aggregated during the traffic demand variability process). As shown previously in Exhibit 36-4, the method incorporates ten categories of severe weather events that have been shown to reduce capacity by at least 4%, along with a “non-severe weather” category that encompasses all other weather conditions and which generates no capacity or speed adjustment. Exhibit 36-15 shows the capacity adjustment factor (CAF) and free-flow speed adjustment factor (SAF) associated with each weather event (1) for a free- flow speed (FFS) of 70 mi/h. The weather events are defined in Exhibit 36-4, which in turn is based on Exhibit 10-15 in Chapter 10, Freeway Facilities. Note that the SAF is a function of the FFS; SAF values for other free-flow speeds are provided in the Default Values subsection of Section 5, Applications. Exhibit 36-14 Demand Ratios for Urban Freeways (ADT/Mondays in January)

Freeway Facility Methodology Page 36-36 Chapter 36/Travel Time Reliability Weather Event CAF SAF Medium rain 0.93 0.93 Heavy rain 0.86 0.92 Light snow 0.96 0.87 Light-medium snow 0.91 0.86 Medium-heavy snow 0.89 0.84 Heavy snow 0.78 0.83 Severe cold 0.92 0.93 Low visibility 0.90 0.94 Very low visibility 0.88 0.92 Minimal visibility 0.90 0.92 Non-severe weather 1.00 1.00 Source: Kittelson & Associates et al. (1). Notes: CAF = capacity adjustment factor, SAF = free-flow speed adjustment factor. As described previously in the Required Input Data subsection of Section 1, Introduction, the analyst may use default weather data from any of 101 U.S. metropolitan areas, based on 2001–2010 weather records. Alternatively, the analyst may supply a 12-month by 11-weather-event matrix (132 total values) of local probabilities of each weather event, along with average durations (in minutes) for each severe event (10 total values). Weather events are assumed to occur either at the start or in the middle of the study period, with equal probability, thus generating a maximum of 11 weather events x 2 start times, or 22 weather patterns. All the segments on the facility are assumed to be affected by the weather event at the same time. Traffic Incident Generation Incidents are generated based on their probability of occurrence in a given month. As described previously in the Required Input Data subsection, the analyst may use default incident probabilities, may supply a facility-specific incident or crash rate, or may supply a 12-month by 6-incident-category matrix (72 total values) of local probabilities of each incident type, along with three possible durations (in minutes) of each incident type (18 total values). (The default duration values assume 25th, 50th, and 75th percentile durations, based on national data.) The method makes the following assumptions about a given incident: • The incident start time occurs either at the start or in the middle of the study period, with equal probability. • One of the three possible incident durations for a given incident type is selected, with equal probability. • The incident location is the first segment, middle segment, or last segment of the facility, with equal probability. Thus there are a maximum of 2 start times × 3 durations × 3 locations × 5 incident severities = 90 patterns with an incident. There is also 1 “no incident” pattern, resulting in a total of 91 possible incident patterns. Exhibit 36-16 shows the CAFs associated with each incident type, derived from Exhibit 10-17 in Chapter 10. The values shown in the exhibit reflect the remaining capacity per open lane. For example, a 2-lane closure incident on a 6-lane directional facility results in a loss of two full lane capacities, in addition to Exhibit 36-15 Weather Effects on Capacity and Speed (70 mi/h Free-flow Speed) Note that incident duration is defined as the length of time that the shoulder or one or more lanes are blocked. This may be different than the time to clear the incident. Incident severity reflects the maximum number of lanes blocked.

Chapter 36/Travel Time Reliability Page 36-37 Freeway Facility Methodology maintaining only 75% of the remaining four open lanes’ capacities. The end result is that only three lanes worth (50%) of the facility’s original six-lane capacity is maintained, consistent with Exhibit 10-17. No information is available about the effect of incidents on free-flow speed, so this effect is not modeled. As explained previously in the Incident Data subsection of Section 1, Introduction, full-facility closures are not modeled. Notes: Values represent remaining capacity per open lane, accounting for both any closed lanes and the loss of capacity in the lanes remaining open. N/A = not applicable: the method does not permit full-facility closures. Work Zones and Special Events Only significant, scheduled work zones and special events are considered in the scenario generator. The analyst provides the work zone or special event schedule and characteristics (e.g., shoulder work, single lane closure). In addition, if significant changes in traffic demand are anticipated during the work zone or special event, the appropriate demand values must also be provided. Capacity effects of work zones are taken primarily from the existing literature, including the HCM. Exhibit 36-17 shows example CAFs computed from Exhibit 10-14. Exhibit 36-17 assumes a work-zone FFS of 55 mi/h, which corresponds to a base capacity of 2,250 pc/h/ln. The values in the exhibit correspond to the per lane CAF for the open lanes. Capacity effects of special events must be entered by the analyst, as those are highly facility- and event-specific. Directional Lanes 1 Lane Closed 2 Lanes Closed 3 Lanes Closed 2 0.62 N/A N/A 3 0.64 0.64 N/A 4 0.67 0.64 0.60 Source: Computed from Exhibit 10-14, assuming a work zone FFS of 55 mi/h. Note: Values represent remaining capacity per open lane, accounting for both any closed lanes and the loss of capacity in the lanes remaining open. N/A = not applicable: the method does not permit full-facility closures. Scenario Dataset Generation The scenario generator assumes that recurring and all non-recurring congestion events are independent of each other. There is very little supporting empirical data that enable the development of predictive models of (for example) incident types by weather condition, or incidents and work zones. Therefore, the probability of a combination of two events is assumed to be equal to the product of their individual probabilities. The total number of scenarios that will emerge cannot be predicted a priori since only a subset of combinations of demand and capacity variations due to the non-recurring events will occur. An upper bound on the number of scenarios can be estimated, however. Neglecting the presence of work zones and special Exhibit 36-16 Incident Effects on Capacity Directional Lanes No Incident Shoulder Closed 1 Lane Closed 2 Lanes Closed 3 Lanes Closed 4 Lanes Closed 2 1.00 0.81 0.70 N/A N/A N/A 3 1.00 0.83 0.74 0.51 N/A N/A 4 1.00 0.85 0.77 0.50 0.52 N/A 5 1.00 0.87 0.81 0.67 0.50 0.50 6 1.00 0.89 0.85 0.75 0.52 0.52 7 1.00 0.91 0.88 0.80 0.63 0.63 8 1.00 0.93 0.89 0.84 0.66 0.66 Exhibit 36-17 Example Work Zone Effects on Capacity for Lane Closure Scenarios

Freeway Facility Methodology Page 36-38 Chapter 36/Travel Time Reliability events, and assuming 12 demand pattern scenarios, 22 weather scenarios, and 91 incident scenarios, it is possible to generate up to 24,000 scenarios for a facility. In reality, many of the combinations do not exist or are negligible (e.g., snow in the summer in most places) and the actual number of scenarios generated is a fraction of this upper bound. The scenario generator computes the fractional number of study periods each scenario is applicable to and divides that number by the number of study periods contained within the reliability reporting period to estimate each scenario’s probability. Exhibit 36-18 shows examples of scenario allocations developed by the scenario generator for a specific set of input values. The attributes listed in the exhibit provide a full specification of a given scenario. Scenario Number De- mand Pattern Scenario Prob- ability Weather Incident Incident Duration Weather Duration Event Type Start Time Type Duration Start Time Seg- ment 1 7 0.6346% Normal N/A None N/A N/A N/A N/A N/A 10 7 0.3872% Normal N/A Shoulder Closed Average Mid SP First N/A N/A 100 4 0.2640% Medium Rain Mid SP None N/A N/A N/A N/A 45 min 621 10 0.0360% Medium Rain Start SP Shoulder Closed Long Start SP Last 45 min 45 min 2269 4 0.00025% Light Snow Mid SP 3 Lanes Closed Short Mid SP Mid 60 min 135 min Note: N/A = not applicable, SP = study period. FACILITY EVALUATION Evaluation Process Each scenario produced by the scenario generator is analyzed using the Chapter 10 freeway facility methodology. Variations in input and output values between scenarios are effectively due to three types of adjustments: • Demand adjustments by day of week and month of year (or aggregations of these time periods), expressed in terms of demand ratios and multipliers that are applied to the analysis period demands specified for the base scenario. Demand adjustments may also be directly specified by the analyst for work zones and special events. • Capacity adjustments due to weather, incidents, work zones, and special events. Those are expressed in terms of capacity losses due to lane closures, CAFs applied to specific segments because of incidents or work zones, and CAFs applied to the entire facility because of severe weather events. Capacity adjustments may also be directly specified by the analyst for special events. • Free-flow speed variability due to weather conditions. This is expressed in terms of SAFs applied facility-wide for the duration of the weather event. The Chapter 10 methodology produces a variety of performance measures which are stored separately for each analysis period for each scenario. Each 15- min analysis period provides a building block for developing the travel time distribution. Exhibit 36-18 Example Scenario Attributes Generated by the Scenario Generator

Chapter 36/Travel Time Reliability Page 36-39 Freeway Facility Methodology Freeway Facilities Methodological Enhancements This section summarizes enhancements to the HCM 2010 freeway facilities method presented in Chapter 10 that have been implemented to make the method “reliability-ready.” Details of these enhancements are provided in Chapter 37, Travel Time Reliability: Supplemental. Concurrent SAF and CAF Implementation on HCM Segments To remain in general compliance with the HCM 2010 freeway facilities methodology, the speed prediction model (Equation 25-1) is revised. For basic segments, the new model replaces the base FFS with an adjusted FFS incorporating the appropriate SAF for the prevailing weather conditions. 𝑆 = (𝐹𝐹𝑆 × 𝑆𝐴𝐹) + �1 − 𝑒𝑙𝑛�(𝐹𝐹𝑆×𝑆𝐴𝐹)+1−𝐶∗𝐶𝐴𝐹45 �× 𝑣𝑝𝐶×𝐶𝐴𝐹� where S = segment speed (mi/h), FFS = segment free-flow speed (mi/h), SAF = speed adjustment factor, C = original segment capacity (pc/h/ln), CAF = capacity adjustment factor, and vp = segment flow rate (pc/h/ln). Examples of the effect of SAF and CAF on the base speed–flow relationship are shown in Exhibit 36-19. The solid lines represent the base HCM curves, while the dashed and dotted lines are revised curves resulting from speed or capacity adjustments, or both. The estimated speed from Equation 36-6 can never drop below the speed at the adjusted capacity (at a density of 45 pc/mi/ln). This constraint guarantees that the predicted speed will always be at least 1 mi/h above the estimated speed at capacity. For ramp and weaving segments, the adjustments to capacity and speeds are made independently, since speed estimation for these segment types is independent of capacity. In other words, the CAF is applied to reducing the segment capacity (thus invoking the oversaturated regime earlier than usual), and SAF is applied to reducing the FFS and by extension, the estimated segment speed. Whenever the Chapter 12 or Chapter 13 methodology uses capacity or FFS, the freeway reliability methodology replaces them with (capacity × CAF) and (FFS × SAF), respectively. Equation 36-6

Freeway Facility Methodology Page 36-40 Chapter 36/Travel Time Reliability Note: FFS = free-flow speed, CAF = crash adjustment factor. Queue-Discharge Flow Rate To more realistically model queue propagation and dissipation on congested freeway facilities, the freeway reliability methodology allows the analyst to specify a capacity loss due to freeway breakdown. This factor does not exist in the original HCM 2010 method, but has been found to have a significant effect on the duration and severity of congestion. This capacity loss averages 7% during breakdown (12). Queue discharge flow rates are applied as soon as a queue develops and remain in effect until the queue has fully dissipated. Additional Performance Measures Some scenario runs are likely to generate very severe congestion when a combination of high demand, severe weather, and incidents occur. Some cases (e.g., multiple interacting bottlenecks) may be beyond the ability of a macroscopic model to analyze. In addition to providing warning flags for such occurences, the method incorporates additional performance measures to monitor those effects, including: • Total number of vehicles denied entry onto the facility when the first segment is fully queued, • Denied-entry-vehicle queue length upstream of Segment 1 in each analysis period. The method also incorporates new reliability measures to enable before-and- after comparisons across. These measures include: • Segment TTI, the average segment travel time in an analysis period divided by its corresponding free-flow travel time. Segment TTI is calculated and reported for each segment in each analysis period. Exhibit 36-19 Example Speed–Flow Curves for Basic Freeway Segments After CAF and SAF Adjustments

Chapter 36/Travel Time Reliability Page 36-41 Freeway Facility Methodology • Facility TTI, based on a weighted average of the probabilities associated with each TTI observation. Each 15-min analysis period contributes one data point to the overall facility travel time distribution. Each facility TTI observation occurs with a probability associated with its scenario. For example, if a study period scenario has a 2.4% probability associated with a 2-h study period (8 analysis periods), then each analysis period occurs with a probability of 2.4% / 8 = 0.3%. PERFORMANCE SUMMARY In this step, the stored travel time distribution is summarized for the entire reliability reporting period using various performance measures, including: • Mean TTI, • PTI, • Reliability rating, • 80th percentile TTI, • Semi-standard deviation, • Standard deviation, • Failure/On-time percentage based on a target speed, • Policy index based on a target speed, and • Misery index. See Section 2, Concepts, for definitions of these measures.

Urban Street Methodology Page 36-42 Chapter 36/Travel Time Reliability 4. URBAN STREET METHODOLOGY OVERVIEW This section describes the methodology for evaluating the reliability of an urban street facility. It also describes the extensions to the base HCM urban street facility method (Chapter 16) that are required for computing reliability performance measures. The urban street reliability methodology is computationally intense and requires software to implement. This intensity stems from the need to create and process the input and output data associated with the hundreds or thousands of scenarios considered for a typical reliability reporting period. Due to the intensity of the calculations, the objective of this section is to introduce the analyst to the calculation process and discuss the key analytic procedures, while also highlighting important equations, concepts, and interpretations. The computational details of the methodology are provided in Chapter 37, Travel Time Reliability: Supplemental. The STREETVAL computational engine provided in the Technical Reference Library in the online HCM Volume 4 represents the most detailed description of the methodology. FRAMEWORK The sequence of calculations in the reliability methodology is shown in Exhibit 36-20. There are five main steps: (a) establishing base and alternative datasets, (b) generating scenarios, (c) evaluating each scenario with the Chapter 16 operational method, (d) compiling travel times for each analysis period in the reliability reporting period, and (e) producing reliability performance measures. Exhibit 36-20 Urban Street Reliability Methodology Framework

Chapter 36/Travel Time Reliability Page 36-43 Urban Street Methodology Data Depository Every urban street reliability analysis requires a base dataset. This dataset describes the traffic demand, geometry, and signal timing conditions for the intersections and segments along the facility during the study period, when no work zones are present and no special events occur. Additional datasets are used, as needed, to describe conditions that exist when a specific work zone is present or when a special event occurs. These datasets are called the alternative datasets. One alternative dataset is used for each time period during the reliability reporting period when a specific work zone is present, a specific special event occurs, or a unique combination of these occurs during the study period. The Required Input Data subsection of Section 1, Introduction, describes all the urban street–related data required for a reliability analysis. The Data Acquisition subsection of Section 2, Concepts, describes potential sources for these data. Scenario Generation The scenario generation stage consists of four sequential procedures: (a) weather event generation, (b) traffic demand variation generation, (c) traffic incident generation, and (d) scenario dataset generation. Each procedure processes in chronologic order the set of analysis periods that comprise the reliability reporting period. This section overviews the scenario generation process; a detailed description is provided in Chapter 37, Travel Time Reliability: Supplemental. Weather Event Generation The weather event procedure generates rain and snow events during the reliability reporting period. The dates, times, types (i.e., rain or snow), and durations of severe weather events are generated. These data are used to adjust the saturation flow rate and speed of facility traffic for each analysis period. The procedure also predicts the time following each weather event that the pavement remains wet or covered by snow or ice, as the presence of these conditions has been found to have an influence on running speed and intersection saturation flow rate. Traffic Demand Variation Generation The traffic demand variation procedure identifies the appropriate traffic demand adjustment factors for each analysis period in the reliability reporting period. A set of factors accounts for systematic demand variation by hour of day, day of week, and month of year. Default values for these factors are provided in Section 5, Applications; however, local values are recommended when available. Traffic Incident Generation The traffic incident procedure generates incident dates, times, and durations. It also determines incident types (i.e., crash or non-crash), severity levels, and locations on the facility. Location is defined by the specific intersection or segment on which the incident occurs and whether the incident occurs on the Future research may indicate that additional weather types may affect arterial operation. At this point in time, available research supports assessment of rain and snow events on arterial operation.

Urban Street Methodology Page 36-44 Chapter 36/Travel Time Reliability shoulder, in one lane, or in multiple lanes. The procedure incorporates weather and traffic demand variation information from the previous procedures when generating incidents. Scenario Dataset Generation The scenario dataset generation procedure uses the results from the preceding procedures to develop one HCM dataset for each analysis period in the reliability reporting period. Each analysis period is considered to be one scenario. The base dataset is modified to reflect conditions present during a given analysis period. Traffic volumes are modified at each intersection and driveway. Saturation flow rates are adjusted at intersections influenced by an incident or a weather event. Speeds are also adjusted for segments influenced by an incident or a weather event. Dates and times represent a common basis for tracking events and conditions from one analysis period to the next. Facility Evaluation As shown in Exhibit 36-20, the facility evaluation stage consists of two tasks that are repeated in sequence for each analysis period. The analysis periods are evaluated in chronologic order. First, the dataset associated with a given analysis period is evaluated using the urban street facility (Chapter 16) method. The performance measures output by the method are archived. Second, the dataset associated with the next analysis period is modified, if necessary, based on the results of the current analysis period. Specifically, the initial queue input value for the next analysis period is set equal to the residual queue output for the current analysis period. Performance Summary The performance summary stage consists of two sequential tasks. First, the analyst identifies a specific direction of travel and the performance measures of interest. The desired performance measures are extracted from the facility evaluation archive for each analysis period in the reliability reporting period. Available measures, as defined in Chapter 17, Urban Street Segments, are: • Travel time, • Travel speed, • Stop rate, • Running time, and • Through delay. The analyst also indicates whether the performance measures of interest should be representative of the entire facility or a specific segment. The first three measures in the above list are available for facility evaluation. All five measures are available for segment evaluation. At the conclusion of this task, the collected data represent observations of the performance measures for each analysis period occurring during the reliability reporting period (or a sampled subset thereof).

Chapter 36/Travel Time Reliability Page 36-45 Urban Street Methodology Next, the selected performance measure data are summarized using the following statistics: • Average; • Standard deviation; • Skewness; • Median; • 10th, 80th, 85th, and 95th percentiles; and • Number of observations. In addition, the average base free-flow speed is always reported. It can be used with one or more of the distribution statistics to compute various variability and reliability measures, such as the travel time index and the reliability rating. ANALYSIS TECHNIQUES Work Zones and Special Events Work zones and special events influence traffic demand levels and travel patterns. To minimize the impact of work zones and special events on traffic operation, agencies responsible for managing traffic in the vicinity of a work zone or special event will often reallocate some traffic lanes or alter the signal operation to increase the capacity of specific traffic movements. These characteristics make each work zone and special event unique, and their effect on facility performance equally unique. Multiple work zones and special events can occur during the reliability reporting period. The reliability methodology incorporates work zone and special event influences in the evaluation results. However, the analyst must describe each work zone and special event using an alternative dataset. Each dataset describes the traffic demand, geometry, and signal timing conditions when the work zone is present or the special event is underway. A start date and duration is associated with each dataset. Work zone presence can have a significant effect on traffic demand levels. The extent of the effect will depend partly on the availability of alternate routes, the number of days the work zone is in operation, and the volume-to-capacity ratio of the segment or intersection approach with the work zone. When using the reliability methodology, the analyst must provide an estimate of traffic demand volumes during the work zone or special event. These estimates should reflect the effect of diversion, and can be based on past field measurements, judgment, or area-wide traffic planning models. They are recorded by the analyst in the corresponding alternative dataset. The analyst must have information about lane closures, alternative lane assignments, and special signal timing that is present during the work zone or special event. This information can be based on agency policy, or experience with previous work zones or events. The available lanes, lane assignments, and signal timing are recorded by the analyst in the corresponding alternative dataset.

Urban Street Methodology Page 36-46 Chapter 36/Travel Time Reliability Multiple Study Periods The geometric design elements, traffic control features (including signal timing plans), and directional distribution of traffic are assumed to be constant during the study period. If any of these factors varies significantly during certain periods of the day (e.g., morning peak or evening peak), then each unique period should be the focus of a separate reliability evaluation. In this regard, each unique period represents one study period. When multiple study period evaluations are undertaken for a common facility, the set of analysis period averages for each evaluation can be merged to evaluate the overall reliability. In this manner, the combined data for a given performance measure represent the distribution of interest. The various reliability measures are then quantified using this combined distribution. Alternatives Analysis Weather events, traffic demand, and traffic incident occurrence, type, and location have both systematic and random elements. To the extent practical, the reliability methodology accounts for the systematic variation component in its predictive models. Specifically, it recognizes temporal changes in weather and traffic demand during the year, month, and day. It also recognizes the influence of geographic location on weather and the influence of weather and traffic demand on incident occurrence. Models of the systematic influences are included in the methodology. They are used to predict average weather, demand, and incident conditions during each analysis period. However, the use of averages to describe weather events and incident occurrence for such short time periods is counter to the objectives of reliability evaluation. The random element of weather events, demand variation, and traffic incident occurrence introduces a high degree of variability in the collective set of analysis periods that comprise the reliability reporting period. Thus, it is important to replicate these random elements in any reliability evaluation. Monte Carlo methods are used for this purpose in the urban street reliability methodology. A random number seed is used with the Monte Carlo methods in the reliability methodology. A seed is used so that the sequence of random events can be reproduced. In fact, unique seed numbers are separately established for weather events, demand variation, and incidents. For a given set of three seed numbers, a unique combination of weather events, demand levels, and incidents is estimated for each analysis period in the reliability reporting period. One, two, or three of the seed numbers can be changed to generate a different set of conditions, if desired. For example, if the seed number for weather events is changed, then a new series of weather events is created and, to the extent that weather influences incident occurrence, a new series of incidents is created. Similarly, the seed number for demand variation can be used to control whether a new series of demand levels is created. The seed number for incidents can be used to control whether a new series of incidents is created. When evaluating alternatives, the analyst will likely use one set of seed numbers as a variance reduction technique. In this application, the same seed A Monte Carlo approach uses essentially random inputs (within realistic limits) to model a system and produce probable outcomes.

Chapter 36/Travel Time Reliability Page 36-47 Urban Street Methodology numbers are used for all evaluations. With this approach, the results from an evaluation of one alterative can be compared with those from an evaluation of the baseline condition. Any observed difference in the results can be attributed to the changes associated with the alternative (i.e., they are not due to random changes in weather or incident events among the evaluations). Confidence Intervals A complete exploration of reliability would likely entail the use of multiple, separate evaluations of the same reliability reporting period with each evaluation using a separate set of random number seeds. This approach may be particularly useful when the facility has infrequent weather events or incidents. With this approach, the evaluation is replicated multiple times and the performance measures from each replication are averaged to produce a more reliable estimate of their long-run value. The confidence interval (expressed as a range) for the average produced in this manner can be computed using the following equation. N stCI N ××= −−− 1),2/1(1 2 αα where CI1-α = confidence interval for the true average value, with a level of confidence of 1-α; t(1-α),N-1 = Student’s t-statistic for the probability of a two-sided error of α, with N-1 degrees of freedom; N = number of replications; and s = standard deviation of the subject performance measure, computed using results from the N replications. The variable α equals the probability that the true average value lies outside of the confidence interval. Values selected for “α” typically range from 0.05 (desirable) to 0.10. Selected values of Student’s t-statistic are provided in Exhibit 36-21. Number of Replications Student’s t-Statistic for Two Values of α α = 0.05 α = 0.10 3 4.30 2.92 4 3.18 2.35 5 2.78 2.13 10 2.26 1.83 15 2.14 1.76 30 2.05 1.70 Equation 36-7 Exhibit 36-21 Student’s t-Statistic

Applications Page 36-48 Chapter 36/Travel Time Reliability 5. APPLICATIONS DEFAULT VALUES This section provides default values for much of the input data used by this chapter’s reliability methodologies. Agencies are encouraged, when possible, to develop local default values based on field measurements of facilities in their jurisdiction. Local defaults provide a better means of ensuring accuracy in analysis results. Facility-specific values provide the best means. In the absence of local data, this section’s default values can be used when the analyst believes that the values are reasonable for the facility to which they are applied. Freeways Traffic Demand Variability Exhibit 36-22 and Exhibit 36-23 present default demand ratios by day of week and month of year for urban and rural freeway facilities, respectively. These ratios were derived from a national freeway dataset developed by SHRP 2 Project L03 (11). All ratios reflect demand relative to a Monday in January. Where possible, analysts should obtain local or regional estimates of demand variability, to account for facility-specific and seasonal trends on the subject facility. Day of Week Month Monday Tuesday Wednesday Thursday Friday Saturday Sunday January 1.00 1.00 1.02 1.05 1.17 1.01 0.89 February 1.03 1.03 1.05 1.08 1.21 1.04 0.92 March 1.12 1.12 1.14 1.18 1.31 1.13 0.99 April 1.19 1.19 1.21 1.25 1.39 1.20 1.05 May 1.18 1.18 1.21 1.24 1.39 1.20 1.05 June 1.24 1.24 1.27 1.31 1.46 1.26 1.10 July 1.38 1.38 1.41 1.45 1.62 1.39 1.22 August 1.26 1.26 1.28 1.32 1.47 1.27 1.12 September 1.29 1.29 1.32 1.36 1.52 1.31 1.15 October 1.21 1.21 1.24 1.27 1.42 1.22 1.07 November 1.21 1.21 1.24 1.27 1.42 1.22 1.07 December 1.19 1.19 1.21 1.25 1.40 1.20 1.06 Source: Derived from data in Cambridge Systematics et al. (11). Note: Ratios represent demand relative to a Monday in January. Day of Week Month Monday Tuesday Wednesday Thursday Friday Saturday Sunday January 1.00 0.96 0.98 1.03 1.22 1.11 1.06 February 1.11 1.06 1.09 1.14 1.35 1.23 1.18 March 1.24 1.19 1.21 1.28 1.51 1.37 1.32 April 1.33 1.27 1.30 1.37 1.62 1.47 1.41 May 1.46 1.39 1.42 1.50 1.78 1.61 1.55 June 1.48 1.42 1.45 1.53 1.81 1.63 1.57 July 1.66 1.59 1.63 1.72 2.03 1.84 1.77 August 1.52 1.46 1.49 1.57 1.86 1.68 1.62 September 1.46 1.39 1.42 1.50 1.78 1.61 1.55 October 1.33 1.28 1.31 1.38 1.63 1.47 1.42 November 1.30 1.25 1.28 1.35 1.59 1.44 1.39 December 1.17 1.12 1.14 1.20 1.43 1.29 1.24 Source: Derived from data in Cambridge Systematics et al. (11). Exhibit 36-22 Default Urban Freeway Demand Ratios (ADT/Mondays in January) Exhibit 36-23 Default Rural Freeway Demand Ratios (ADT/Mondays in January)

Chapter 36/Travel Time Reliability Page 36-49 Applications Note: Ratios represent demand relative to a Monday in January. Weather Events Weather event probabilities by month of each weather event for 101 U.S. metropolitan areas are provided in the (ordinarily hidden) “Weather_DB” tab of the FREEVAL-RL spreadsheet, available in the online HCM Volume 4. Average durations, in hours, of each weather event for the same metropolitan areas are provided in the (ordinarily hidden) “W_DUR” spreadsheet tab. Incident Probabilities and Durations Exhibit 36-24 provides mean distributions of freeway incidents by severity. Exhibit 36-25 provides default incident durations by incident type. Incident Type Shoulder Closed 1 Lane Closed 2 Lanes Closed 3+ Lanes Closed 75.4% 19.6% 3.1% 1.9% Source: Kittelson & Associates et al. (1). Incident Type Month Shoulder Closed 1 Lane Closed 2 Lanes Closed 3 Lanes Closed 4 Lanes Closed 25th percentile 17 20 39 47 47 50th percentile 32 34 53 69 69 75th percentile 47 48 67 91 91 Source: Kittelson & Associates et al. (1). Capacity Adjustment Factors and Speed Adjustment Factors Exhibit 36-26 provides default CAFs and SAFs by weather type and facility free-flow speed. Note that changes in CAFs and SAFs related to decreasing visibility in the exhibit may be counterintuitive as these are based on a single site (see Exhibit 10-15 in Chapter 10). Weather Type Capacity Adjustment Factors Speed Adjustment Factors 55 mi/h 60 mi/h 65 mi/h 70 mi/h 75 mi/h 55 mi/h 60 mi/h 65 mi/h 70 mi/h 75 mi/h Medium rain 0.94 0.93 0.92 0.91 0.90 0.96 0.95 0.94 0.93 0.93 Heavy rain 0.89 0.88 0.86 0.84 0.82 0.94 0.93 0.93 0.92 0.91 Light snow 0.97 0.96 0.96 0.95 0.95 0.94 0.92 0.89 0.87 0.84 Light-medium snow 0.95 0.94 0.92 0.90 0.88 0.92 0.90 0.88 0.86 0.83 Medium-heavy snow 0.93 0.91 0.90 0.88 0.87 0.90 0.88 0.86 0.84 0.82 Heavy snow 0.80 0.78 0.76 0.74 0.72 0.88 0.86 0.85 0.83 0.81 Severe cold 0.93 0.92 0.92 0.91 0.90 0.95 0.95 0.94 0.93 0.92 Low visibility 0.90 0.90 0.90 0.90 0.90 0.96 0.95 0.94 0.94 0.93 Very low visibility 0.88 0.88 0.88 0.88 0.88 0.95 0.94 0.93 0.92 0.91 Minimal visibility 0.90 0.90 0.90 0.90 0.90 0.95 0.94 0.93 0.92 0.91 Non-severe weather 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Notes: Speeds given in column heads are free-flow speeds. Weather types are defined in Exhibit 36-4. Exhibit 36-24 Default Freeway Incident Severity Distributions Exhibit 36-25 Default Freeway Incident Durations (min) Exhibit 36-26 Default CAFs and SAFs by Weather Condition

Applications Page 36-50 Chapter 36/Travel Time Reliability Urban Streets The urban street default values have been derived from the best available research and data at the time of writing. Some of these values are based on the findings of several research projects and others are based on an aggregation of data from several agency databases. In contrast, some default values have a less substantial basis. In some instances, the values are based partly on experience and judgment. Regardless, analysts are encouraged to update the default values whenever possible using data representative of local conditions. It is recognized that, in some jurisdictions, updates to the incident-related default values may not be possible until transportation agencies maintain more complete urban street incident records. Traffic Demand Variability Default hour-of-day, day-of-week, and month-of-year traffic demand adjustment factors are listed in Exhibit 36-27 through Exhibit 36-29, respectively. These factors should be replaced with data from permanent traffic count stations whenever available for streets that are similar to the subject facility and located near it. The functional classes were defined in the Required Input Data section. Hour Expressway Principal Arterial Minor Arterial Starting Weekday Weekend Weekday Weekend Weekday Weekend Midnight 1 a.m. 2 a.m. 3 a.m. 4 a.m. 5 a.m. 6 a.m. 7 a.m. 8 a.m. 9 a.m. 10 a.m. 11 a.m. Noon 1 p.m. 2 p.m. 3 p.m. 4 p.m. 5 p.m. 6 p.m. 7 p.m. 8 p.m. 9 p.m. 10 p.m. 11 p.m. 0.010 0.006 0.004 0.004 0.007 0.025 0.058 0.077 0.053 0.037 0.037 0.042 0.045 0.045 0.057 0.073 0.087 0.090 0.068 0.049 0.040 0.037 0.029 0.019 0.023 0.015 0.008 0.005 0.005 0.009 0.016 0.023 0.036 0.045 0.057 0.066 0.076 0.073 0.074 0.075 0.075 0.071 0.063 0.051 0.043 0.037 0.032 0.023 0.010 0.006 0.005 0.005 0.009 0.030 0.054 0.071 0.058 0.047 0.046 0.050 0.053 0.054 0.063 0.069 0.072 0.077 0.062 0.044 0.035 0.033 0.026 0.021 0.023 0.014 0.010 0.006 0.006 0.010 0.017 0.024 0.035 0.046 0.056 0.054 0.071 0.071 0.072 0.073 0.073 0.073 0.063 0.052 0.044 0.038 0.033 0.026 0.010 0.006 0.004 0.002 0.002 0.007 0.023 0.067 0.066 0.054 0.051 0.056 0.071 0.066 0.060 0.062 0.063 0.075 0.070 0.053 0.044 0.035 0.033 0.019 0.028 0.023 0.021 0.008 0.005 0.005 0.011 0.018 0.030 0.048 0.054 0.057 0.074 0.071 0.069 0.067 0.071 0.068 0.067 0.056 0.049 0.040 0.035 0.024 Source: Hallenbeck et al. (13). Day Demand Ratio Sunday Monday Tuesday Wednesday Thursday Friday Saturday 0.87 0.98 0.98 1.00 1.03 1.15 0.99 Source: Hallenbeck et al. (13). Exhibit 36-27 Default Urban Street Hour-of- Day Demand Ratios (ADT/AADT) Exhibit 36-28 Default Urban Street Day-of- Week Demand Ratios (ADT/AADT)

Chapter 36/Travel Time Reliability Page 36-51 Applications Month Expressway Principal Arterial Minor Arterial January February March April May June July August September October November December 0.802 0.874 0.936 0.958 1.026 1.068 1.107 1.142 1.088 1.069 0.962 0.933 0.831 1.021 1.030 0.987 1.012 1.050 0.991 1.054 1.091 0.952 0.992 0.938 0.881 0.944 1.016 0.844 1.025 1.060 1.150 1.110 1.081 1.036 0.989 0.903 Source: Hallenbeck et al. (13). Weather Events Average weather statistics for 2001–2010 by month for 284 U.S. locations are provided in the STREETVAL computational engine available in the online HCM Volume 4. More recent weather data can be obtained from the National Climatic Data Center (7, 8). Exhibit 36-30 provides other weather-related default values. Input Data Item Default Value Pavement runoff duration for snow event 0.5 h Demand change factor for dry weather 1.00 Demand change factor for rain event 1.00 Demand change factor for snow event 0.80 The three “demand change factors” account for a change in traffic demand due to weather conditions. The demand volume is multiplied by the demand change factor corresponding to the weather associated with an analysis period. A factor less than 1.0 corresponds to a reduction in demand. Research indicates that urban street traffic demand tends to drop 15% to 30% when it is snowing (14). These motorists likely altered the start time of their commute, or just stayed home, to avoid the bad weather. In the absence of local data, a default value of 0.80 may be used for snow events. The research is less clear on the effect of rain on traffic demand. The effect of rain may vary depending on the trip purpose and the annual frequency of rain events in the vicinity of the subject facility. A default factor value of 1.0 is recommended for rain events. No adjustment to demand is made for dry weather. Incidents Exhibit 36-31 provides incident-related default values for urban streets. The crash frequency adjustment factor represents the ratio of hourly crash frequency during the weather event divided by the hourly crash rate during clear, dry hours. It is computed using one or more years of historic weather data and crash data for the region in which the subject facility is located. The adjustment factor for a specific weather condition is computed from (a) the number of hours for which the weather condition exists for the year and (b) the count of crashes during those hours. An hourly crash frequency for the weather condition fcwea is computed by dividing the crash count by the number of hours. Using a similar technique, the hourly crash frequency is computed for dry Exhibit 36-29 Default Urban Street Month- of-Year Demand Ratios (ADT/AADT) Exhibit 36-30 Urban Street Weather-Related Default Values

Applications Page 36-52 Chapter 36/Travel Time Reliability pavement hours fcdry. The crash adjustment factor for the weather condition is computed as the ratio of the two frequencies (i.e., CAFwea = fcwea / fcdry). The crash adjustment factor includes consideration of the effect of the weather event on traffic volume (i.e., volume may be reduced due to bad weather) and on crash risk (i.e., wet pavement may increase the potential for a crash). For example, if rainfall is envisioned to increase crash risk by 200% and to decrease traffic volume by 10%, then the crash frequency adjustment factor for rainfall is 2.70 (= 3.0 × 0.9). Input Data Element Default Values Crash frequency adjustment factor for weather conditions Rainfall: 2.0 Wet pavement (not raining): 3.0 Snowfall: 1.5 Snow or ice on pavement (not snowing): 2.75 Incident detection time 2.0 min (all weather conditions) Incident response time Clear, dry: 15.0 min Rainfall: 15.0 min Wet pavement (not raining): 15.0 min Snowfall: 20.4 min Snow or ice on pavement (not snowing): 20.4 min Incident clearance time See Exhibit 36-32 Incident distribution See Exhibit 36-33 and Exhibit 36-34 Source: Kittelson & Associates, et al. (1). Incident duration is computed as the sum of the incident detection time, response time, and clearance time. The incident detection time represents the time period starting with the occurrence of the incident and ending when the response officials are notified of the incident. A default value of 2.0 min is recommended for this variable. Incident response time represents the time period starting from the receipt of incident notification by officials to the time the first response vehicle arrives to the scene of the incident. It is likely that this time will vary among jurisdictions and facilities, depending on the priority placed on street system management and the connectivity of the street system. A default value of 15 min is used for all weather conditions, except when snow is on the pavement. When there is snowfall, or snow or ice on the pavement, the default value is 20.4 min. Incident clearance time is the time from the arrival of the first response vehicle to the time when the incident and service vehicles no longer directly affect travel on the roadway. This time varies by incident location, type, and severity. Default clearance times are provided in Exhibit 36-32. The default distributions for segments and intersections are the same in this exhibit. The reason segments and intersections are differentiated is because the method allows the analyst to provide different clearance times for segments and intersections when local values are available. The default incident type distribution time is provided in Exhibit 36-33 and Exhibit 36-34. Research indicates that this distribution varies by incident location, type, and severity. The first table provides the distribution for urban streets with shoulders. The second table provides the distribution for urban streets without shoulders. The joint proportion in the last column of each exhibit represents the product of the proportions for each of the preceding incident categories. Exhibit 36-31 Urban Street Incident Default Values

Chapter 36/Travel Time Reliability Page 36-53 Applications Street Location Event Type Lane Location Severitya Clearance Time by Weather Condition (min) Dry Rain- fall Wet Pavement Snow or Iceb Segment Crash One lane 2+ lanes Shoulder FI PDO FI PDO FI PDO 56.4 39.5 56.4 39.5 56.4 39.5 42.1 28.6 42.1 28.6 42.1 28.6 43.5 29.7 43.5 29.7 43.5 29.7 76.7 53.7 76.7 53.7 76.7 53.7 Non- crash One lane 2+ lanes Shoulder Breakdown Other Breakdown Other Breakdown Other 10.8 6.7 10.8 6.7 10.8 6.7 5.6 2.4 5.6 2.4 5.6 2.4 5.7 2.8 5.7 2.8 5.7 2.8 14.7 9.1 14.7 9.1 14.7 9.1 Signalized Intersection Crash One lane 2+ lanes Shoulder FI PDO FI PDO FI PDO 56.4 39.5 56.4 39.5 56.4 39.5 42.1 28.6 42.1 28.6 42.1 28.6 43.5 29.7 43.5 29.7 43.5 29.7 76.7 53.7 76.7 53.7 76.7 53.7 Non- crash One lane 2+ lanes Shoulder Breakdown Other Breakdown Other Breakdown Other 10.8 6.7 10.8 6.7 10.8 6.7 5.6 2.4 5.6 2.4 5.6 2.4 5.7 2.8 5.7 2.8 5.7 2.8 14.7 9.1 14.7 9.1 14.7 9.1 Source: Kittelson & Associates, et al. (1). Notes: (a) FI: fatal or injury crash; PDO: property-damage-only crash. (b) Applies to snowfall and to snow or ice on pavement (but not snowing). Street Location Event Type Pro- portion Lane Location Pro- portion Severitya Pro- portion Joint Proportion Segment Crash 0.358 1 lane 2+ lanes Shoulder 0.335 0.163 0.502 FI PDO FI PDO FI PDO 0.304 0.696 0.478 0.522 0.111 0.889 0.036 0.083 0.028 0.030 0.020 0.160 Non- crash 0.642 1 lane 2+ lanes Shoulder 0.849 0.119 0.032 Breakdown Other Breakdown Other Breakdown Other 0.836 0.164 0.773 0.227 0.667 0.333 0.456 0.089 0.059 0.017 0.014 0.007 Total: 1.000 Signalized Intersection Crash 0.310 1 lane 2+ lanes Shoulder 0.314 0.144 0.542 FI PDO FI PDO FI PDO 0.378 0.622 0.412 0.588 0.109 0.891 0.037 0.061 0.018 0.026 0.018 0.150 Non- crash 0.690 1 lane 2+ lanes Shoulder 0.829 0.141 0.030 Breakdown Other Breakdown Other Breakdown Other 0.849 0.151 0.865 0.135 0.875 0.125 0.486 0.086 0.084 0.013 0.018 0.003 Total: 1.000 Source: Kittelson & Associates, et al. (1). Note: (a) FI = fatal or injury crash, PDO = property-damage-only crash, Other = not breakdown (e.g., debris). Exhibit 36-32 Default Urban Street Incident Clearance Times Exhibit 36-33 Default Urban Street Incident Distribution with Shoulder Presence

Applications Page 36-54 Chapter 36/Travel Time Reliability Street Location Event Type Pro- portion Lane Location Pro- portion Severitya Pro- portion Joint Proportion Segment Crash 0.358 1 lane 2+ lanes 0.837 0.163 FI PDO FI PDO 0.304 0.696 0.478 0.522 0.091 0.209 0.028 0.030 Non- crash 0.642 1 lane 2+ lanes 0.881 0.119 Breakdown Other Breakdown Other 0.836 0.164 0.773 0.227 0.473 0.093 0.059 0.017 Total: 1.000 Signalized Intersection Crash 0.310 1 lane 2+ lanes 0.856 0.144 FI PDO FI PDO 0.378 0.622 0.412 0.588 0.100 0.165 0.018 0.026 Non- crash 0.690 1 lane 2+ lanes 0.859 0.141 Breakdown Other Breakdown Other 0.849 0.151 0.865 0.135 0.503 0.089 0.084 0.013 Total: 1.000 Source: Kittelson & Associates, et al. (1). Note: (a) FI = fatal or injury crash, PDO = property-damage-only crash, Other = not breakdown (e.g., debris). USE CASES Travel time reliability measures can be applied to a number of planning and roadway operating agency activities, including the ones listed in Exhibit 36-35: Application Use Cases for Travel Time Reliability Long Range Transportation Plan Transportation Improvement Program Corridor or Area Plans Major Investment Studies Congestion Management Operations Planning • Identifying existing facilities not meeting reliability standards. • Identifying future facilities not meeting reliability standards. • Generating alternatives to address reliability problems. • Evaluating reliability benefits of improvement alternatives. • Prioritizing operational improvements and traditional capacity improvements. • Evaluating the probability of achieving acceptable reliability and/or LOS. Long-range Planning: Demand Forecasting • Modeling choice between tolled and untolled facilities. • Improving modeling of destination, time of day, mode, and route choice. Each of these applications has several potential uses for travel time reliability. Reliability may be assessed for existing or future facilities to identify current problem spots and future deficiencies in system operation. Reliability may provide additional performance measures used to generate and evaluate alternatives. Reliability may supplement conventional measurements for prioritizing improvement projects. Planning has traditionally focused on capacity improvements and has been relatively insensitive to the reliability improvements that come with operations improvements. Thus, reliability can become an important new measure to better identify improvement alternatives, evaluate their benefits, and more accurately prioritize them in relation to conventional capacity improvements. Exhibit 36-34 Default Urban Street Incident Distribution Without Shoulder Presence Exhibit 36-35 Use Cases of Travel Time Reliability

Chapter 36/Travel Time Reliability Page 36-55 Applications Reliability also adds another dimension of information on facility performance that can aid travel demand models to better predict the conditions under which people will choose to pay a toll for more reliable service. Reliability will enable better destination, time of day, mode, and route choice models. Use Case #1: Detecting Existing Deficiencies This use case for reliability methods in the HCM involves monitoring conditions on a facility, identifying unacceptable performance, and detecting the primary causes of unreliable facility operation. This use case involves selecting the appropriate study period, performance measures, and thresholds of acceptance; calibrating the HCM operations models; and expanding limited data to a full reliability dataset. Use Case #2: Forecasting Future Problems This use case evaluates future reliability conditions on a facility, including: • Expanding average annual (daily, peak period, or peak hour) volumes (forecasted demand) to the full variety of study period demands. • Estimating facility travel times by time slice within the full study period. • Comparing future to existing performance and identifying “significant” changes in performance. The forecasting questions that Case 2 addresses include: 3. How to forecast weather: a. Use of Monte Carlo or expected value techniques to forecast the frequency of future weather events. b. Number of years that the forecast must be carried into the future to obtain a reasonably likely set of scenarios. 4. How to forecast incident frequency: a. Use of Monte Carlo or expected-value techniques. b. Number of future years that must be forecast to obtain a reasonably likely set of scenarios. c. Predicting the effect of capacity improvements, demand changes, and Active Traffic Demand Management (ATDM) improvements on crash frequencies. 5. Dealing with congestion overflows (e.g., over the entry link, over the last analysis period) when computing performance measures and comparing to existing conditions. 6. Calibrating this chapter’s forecasted reliability for future conditions to field-measured reliability under existing conditions (for data-rich agencies). Use Case #3: Generating Alternatives This use case identifies alternative operational and capacity improvements for addressing reliability problems, including selecting operational and capacity

Applications Page 36-56 Chapter 36/Travel Time Reliability improvements that are likely to best address the identified primary causes of reliability problems on the facility. This case requires that the analyst: 1. Determine that a reliability problem exists (see Use Case #6), 2. Diagnose the causes of the reliability problem, and 3. Identify promising treatment options for addressing the problem. As part of the diagnostic process, the analyst needs to be able to identify the facility’s primary causes of unreliability and then identify two or three possible courses of action to address those causes. This approach requires guidance linking causes of unreliability to cost-effective solutions that can be considered. Use Case #4: Reliability Benefits of Alternatives This use case computes the reliability effects of alternative operational and capacity improvements for addressing reliability problems, including traditional capacity improvements as well as more innovative ATDM measures. While Use Case #3 was primarily about diagnosis, Use Case #4 focuses on evaluating candidate treatment options. The analyst fleshes out possible treatments, estimates their effectiveness, and estimates their costs. This analysis requires procedures and parameters for computing the effects of capacity, operational, and ATDM improvements on existing or predicted reliability. Once an agency has performed enough of these analyses, it can probably develop its own Case #3 diagnosis chart with locally specific treatment options. Use Case #5: Prioritizing Improvements This use case applies reliability performance measures in combination with other performance measures to prioritize investments in operational and capacity improvements. Estimating the relative values of mean travel time improvements and travel time reliability improvements are included in this case. While this chapter’s methodology provides results for only one facility at a time, agencies putting together a regional program will want to combine the results of individual facility analyses (freeways and urban streets) into a prioritized table. In essence, the issue is how to weight the relative benefits of reliability improvements versus more-traditional capacity improvements. How much is average travel time worth to the agency and the public, compared to 95th percentile travel time or some other measure of reliability? Use Case #6: Achieving Acceptable Performance This use case estimates the probability of failure or the probability of achieving acceptable performance. Performance may be reported as achieving a minimum acceptable LOS. This use defines and determines acceptable and unacceptable reliability performance. As such, it is a critical input to the diagnostic process of Use Case #3. No diagnosis is needed when it is determined that no reliability problem exists. However, if Use Case #6 determines that a problem exists, then Use Case #3 is used to diagnose the causes and identify promising treatment options.

Chapter 36/Travel Time Reliability Page 36-57 Applications Use Case #6 shares much with Case #5, but it introduces a new concept, acceptability or failure. The numerical results produced in Use Case #5 are compared to some standard—a national, state, or agency-specific standard of acceptable performance. This use case introduces the concept of defining a standard both as a minimum acceptable performance level (such as LOS or PTI) and the probability of failing to achieve that level (i.e., probability of failure). The standard is thus defined in two dimensions, a value, and a probability of exceeding that value. Use Case #5 deals with numerical outputs that are compared relative to each other (relativistic evaluation). In contrast, Use Case #6 compares the numerical outputs to an absolute standard (failure analysis). Use Case #7: Modeling Choice This use case applies HCM reliability methods in support of the development and calibration of a route choice model that can distinguish the differing levels of reliability between a tolled and untolled facility. The HCM reliability method is applied repeatedly at different levels of demand to develop one or more formulas for predicting how travel time variance varies with demand by facility type. This approach is particularly useful for developing route choice models that trade-off the greater reliability of tolled roads against less reliable untolled roads. The resulting demand/reliability equations then become inputs to a demand model’s route choice (toll versus non-toll) algorithm. Use Case #8: Improved Demand Modeling This use case applies HCM methods to develop volume/reliability curves by facility type for use in a demand modeling environment to estimate reliability and to improve destination, time of day, mode choice, and route choice models. USE OF ALTERNATIVE TOOLS There will be cases where a finer temporal sensitivity to dynamic changes in the system will be required for a reliability analysis than can be provided by the typical 15-min analysis period used by HCM methods. This situation may occur when evaluating traffic-responsive signal timing, traffic adaptive control, dynamic ramp metering, dynamic congestion pricing, or measures affecting the prevalence or duration of incidents with less than 10-min durations. There may also be scenarios and configurations that the HCM cannot address, such as complex merging and diverging freeway sections. For such situations it is possible to apply this chapter’s conceptual framework for evaluating travel time reliability to alternative analysis tools. The same conceptual approach of generating scenarios, assigning scenario probabilities, evaluating scenario performance, and summarizing the results applies when using alternative analysis tools, such as microsimulation, to estimating the reliability effects of operations improvements. Before embarking on the use of alternative tools for reliability analysis, the analyst should consider the much greater analytical demands imposed by a reliability analysis following this chapter’s conceptual analysis framework.

Applications Page 36-58 Chapter 36/Travel Time Reliability Thousands of scenarios may need to be analyzed using the alternative tool in addition to the number of replications per scenario required by the tool itself to establish average conditions. Extracting and summarizing the results from numerous applications of the alternative tool may be a significant task. If a microscopic simulation tool is used, some portions of this chapter’s analysis framework that were fit to the HCM’s 15-min analysis periods, and tailored to the HCM’s speed-flow curves, will no longer be needed. Specifically: • Scenarios may be defined differently and may be of longer or shorter duration than those used in HCM analysis. • Incident start times and durations will no longer need to be rounded to the nearest 15-min analysis period. • Weather start times and durations will no longer need to be rounded to the nearest 15-min analysis period. • Demand will no longer need to be held constant for the duration of the 15-min analysis period. • The freeway and urban street peak hour factors used to identify the peak 15-min flow rate within the hour would no longer be applied. They would be replaced with the analysis tool’s built-in randomization process. • The urban street randomization factor for 15-min demands would no longer be applicable. It would be replaced with the analysis tool’s built-in randomization process. • This chapter’s recommended urban street saturation flow rate adjustments, freeway capacity adjustment factors, and free-flow speed adjustment factors for weather events and incidents would have to be converted by the analyst to the microsimulation model equivalents: desired speed distribution and desired headway distribution. Acceleration and deceleration rates would also be affected for some weather events. • This chapter’s recommended freeway speed–flow curves for weather events and incidents would be replaced with adjustments to the model’s car-following parameters, such as desired FFS, saturation headway, and start-up lost time. Unlike incidents, which the tool’s car-following logic can take care of, weather is modeled by adjusting the car-following parameters through weather adjustment factors before running the scenarios. Application guidance and typical factors are provided in the FHWA’s Traffic Analysis Toolbox (15). If a less-disaggregate tool is used (e.g., mesoscopic simulation analysis tool, dynamic traffic assignment tool, demand forecasting tool), then many of this chapter’s adaptations of the conceptual analysis framework to the HCM may still be appropriate or may need to be further aggregated. The analyst should consult the appropriate tool documentation and determine what further adaptations of the conceptual analysis framework might be required to apply the alternative tool to reliability analysis.

Chapter 36/Travel Time Reliability Page 36-59 Example Problems 6. EXAMPLE PROBLEMS Problem Number Description Application 1 2 3 4 5 6 7 Freeway facility reliability under existing conditions Freeway facility reliability with a geometric treatment Freeway facility reliability with incident management Freeway facility reliability with a safety treatment Freeway facility reliability with demand management Urban street reliability under existing conditions Urban street reliability strategy evaluation Operational analysis Planning analysis Planning analysis Planning analysis Planning analysis Operational analysis Planning analysis The example problems in this section demonstrate the application of the freeway facility (Example Problems 1–5) and urban street (Example Problems 6– 7) reliability methods. They illustrate the general process of applying the methods that is described in this chapter, but also incorporate details about selected calculations that are drawn from Chapter 37, Travel Time Reliability: Supplemental. An additional freeway example problem is found in Chapter 37. EXAMPLE PROBLEM 1: RELIABILITY EVALUATION OF AN EXISTING FREEWAY FACILITY This example problem uses the same 6-mi facility used in Example Problem 1 in Chapter 10. For completeness, the schematic of the facility (Exhibit 10-25) is repeated below in Exhibit 36-37. The facility consists of 11 segments with the properties indicated in Exhibit 36-38. Other facility characteristics are identical to those given in Chapter 10’s Example Problem 1, except that the study period in this example has been extended from 75 to 180 min. Segment No. 1 2 3 4 5 6 7 8 9 10 11 Segment type B ONR B OFR B B or W B ONR R OFR B Segment length (ft) 5,280 1,500 2,280 1,500 5,280 2,640 5,280 1,140 360 1,140 5,280 No. of lanes 3 3 3 3 3 4 3 3 3 3 3 Note: B = basic freeway segment, W = weaving segment, ONR = on-ramp (merge) segment, OFR = off-ramp (diverge) segment, R = overlapping ramp segment. This and the following four example problems illustrate: 1. Calculating a variety of reliability statistics for a freeway facility using the minimum required data, 2. Identifying key reliability problems on the facility, and 3. Testing a number of operational, design, and safety strategies intended to enhance the facility’s reliability. Exhibit 36-36 List of Example Problems An additional freeway example problem is found in Chapter 37. Exhibit 36-37 Example Problem 1: Freeway Facility Schematic Exhibit 36-38 Example Problem 1: Freeway Facility Segment Properties

Example Problems Page 36-60 Chapter 36/Travel Time Reliability Input Data This example illustrates the use of defaults and lookup tables to substitute for desirable, but difficult to obtain, data. Minimum facility inputs for the example problem include the following. Facility Geometry All of the geometric information about the facility normally required for an HCM freeway facility analysis (Chapters 10–13) is also required for a reliability analysis. These data are supplied as part of the base dataset. Study Parameters These parameters specify the study period, the reliability reporting period, and the date represented by the traffic demand data used in the base dataset. The study period in this example is 4 p.m. to 7 p.m., which covers the p.m. peak hour and shoulder periods. This period is selected for reliability analysis because it is when recurring congestion is typically present in the study direction of this facility. The reliability reporting period is set as all weekdays in the calendar year. (For simplicity in this example, holidays have not been removed from the reliability reporting period.) The demand data are reflective of AADT. Base Demand Demand flow rates (in vehicles per hour) are supplied for each 15-minute analysis period in the base dataset. Care should be taken to make sure that demand data are measured upstream of any queued traffic. If necessary, demand can be estimated as the sum of departing volume and the change in the queue size at a recurring bottleneck, as described in the Oversaturated Segment Evaluation section of Chapter 25, Freeway Facilities: Supplemental. Exhibit 36-39 provides the twelve 15-min demand flow rates required for the entire 3-h study period. Analysis Period Demand Entry Flow Rate On- Ramp 1 On- Ramp 2 On- Ramp 3 Off- Ramp 1 Off- Ramp 2 Off- Ramp 3 1 3,095 270 270 270 180 270 180 2 3,595 360 360 360 270 360 270 3 4,175 360 450 450 270 360 270 4 4,505 450 540 450 270 360 270 5 4,955 540 720 540 360 360 270 6 5,225 630 810 630 270 360 450 7 4,685 360 360 450 270 360 270 8 3,785 180 270 270 270 180 180 9 3,305 180 270 270 270 180 180 10 2,805 180 270 270 270 180 180 11 2,455 180 180 180 270 180 180 12 2,405 180 180 180 180 180 180 Incident Data Detailed incident logs are not available for this facility, but local data are available about the facility’s crash rate: 150 crashes per 100 million vehicle-miles travelled (VMT). Furthermore, an earlier study conducted by the state that the facility is located in found that an average of 7 incidents occur for every 1 crash. Exhibit 36-39 Example Problem 1: Demand Flow Rates (veh/h) by Analysis Period in the Base Dataset

Chapter 36/Travel Time Reliability Page 36-61 Example Problems Computational Steps Base Dataset Analysis The Chapter 10 freeway facility methodology is applied to the base dataset to make sure that the specified facility boundaries and study period are sufficient to cover any bottlenecks and queues. In addition, because incident data are being supplied in the form of a facility crash rate, the VMT associated with the base dataset is calculated so that incident probabilities can be calculated in a subsequent step. In this case, 71,501 VMT occur on the facility over the 3-h base study period. The performance measures normally output by the Chapter 10 methodology are compiled for each combination of segment and analysis period during the study period and stored for later use. In particular, the facility operates just under capacity, with a maximum demand-to-capacity (d/c) ratio of 0.99 in segments 7–10. Incorporating Demand Variability Exhibit 36-40 provides demand ratios relative to AADT by month and day, derived from a permanent traffic recorder on the facility. Because the demand ratios are based on AADT and because the base dataset demands represent AADT demands, the demand multiplier is 1.00. Month Monday Tuesday Wednesday Thursday Friday January 1.015 0.971 1.018 1.018 1.022 February 1.030 1.020 1.029 1.016 0.995 March 1.098 1.105 1.105 1.113 1.142 April 1.143 1.105 1.105 1.105 1.132 May 1.132 1.113 1.113 1.113 1.132 June 1.120 1.088 1.088 1.089 1.125 July 1.128 1.096 1.088 1.088 1.120 August 1.120 1.088 1.092 1.089 1.134 September 1.066 1.058 1.058 1.058 1.078 October 1.085 1.060 1.060 1.058 1.091 November 1.053 1.060 1.058 1.060 1.047 December 1.031 1.023 1.022 1.022 1.030 An inspection of these demand patterns finds two distinct weekday patterns: (a) Tuesdays, Wednesdays, and Thursdays have similar volumes across a given month, as do (b) Mondays and Fridays. Furthermore, traffic demands are relatively similar across seasons: December–February (winter), March–May (spring), June–August (summer), and September–November (fall). Therefore, the analyst may choose to consolidate the 5 days × 12 months = 60 demand patterns into a smaller set of 2 × 4 = 8 demand patterns, which will greatly reduce the computation time later in the process. The individual demand ratios within each aggregation are averaged to develop an overall aggregated demand ratio (ignoring small differences in the number of days per month). For example, an aggregated demand ratio for Mondays and Fridays in the fall would be determined by averaging the six individual Monday and Friday demand ratios for September, October, and November, resulting in an aggregated demand ratio of 1.070. For a scenario involving a study period on a Monday in October, the base dataset demands would be multiplied by the demand ratio of 1.070 and Exhibit 36-40 Example Problem 1: Demand Ratios Relative to AADT

Example Problems Page 36-62 Chapter 36/Travel Time Reliability divided by the demand multiplier of 1.00, resulting in a 7% increase in the base dataset volumes across all analysis periods for that scenario. The probability of any given demand pattern is the ratio of the number of days (or hours) in a pattern to the total number of days (or hours) in the reliability reporting period. For example, the demand pattern representing Mondays and Fridays in the fall includes 26 weekdays. There are 261 weekdays in the reliability reporting period, thus the probability of this demand pattern is 26 / 261 or approximately 10%. Incorporating Weather Variability In the absence of facility-specific weather data, the default weather data for the metropolitan area closest to the facility are used. Because the demand data were condensed from twelve months to four seasons in the previous step, the probabilities and average durations of each type of weather event are also condensed into four seasons by averaging the monthly values. In the absence of local data, the default CAF and SAF values given in Exhibit 36-26 for each weather event for a FFS of 60 mi/h are used. These values are applied in a later step to each scenario involving a severe weather event. Exhibit 36-41 summarizes the probabilities of each weather event by season, while Exhibit 36-42 summarizes the CAF, SAF, and event duration values associated with each weather event. Weather Event Probability (%) Weather Event Winter Spring Summer Fall Medium rain 0.80 1.01 0.71 0.86 Heavy rain 0.47 0.81 1.33 0.68 Light snow 0.91 0.00 0.00 0.00 Light-medium snow 0.29 0.00 0.00 0.00 Medium-heavy snow 0.04 0.00 0.00 0.00 Heavy snow 0.00 0.00 0.00 0.00 Severe cold 0.00 0.00 0.00 0.00 Low visibility 0.97 0.12 0.16 0.34 Very low visibility 0.00 0.00 0.00 0.00 Minimal visibility 0.44 0.10 0.00 0.03 Non-severe weather 96.09 97.95 97.80 98.08 Weather Event CAF SAF Average Duration (min) Medium rain 0.93 0.95 40.2 Heavy rain 0.88 0.93 33.7 Light snow 0.96 0.92 93.1 Light-medium snow 0.94 0.90 33.4 Medium-heavy snow 0.91 0.88 21.7 Heavy snow 0.78 0.86 7.3 Severe cold 0.92 0.95 0.0 Low visibility 0.90 0.95 76.2 Very low visibility 0.88 0.94 0.0 Minimal visibility 0.90 0.94 145 Non-severe weather 1.00 1.00 N/A Note: N/A = not applicable. Exhibit 36-41 Example Problem 1: Weather Event Probabilities by Season Exhibit 36-42 Example Problem 1: CAF, SAF, and Event Duration Values Associated with Weather Events

Chapter 36/Travel Time Reliability Page 36-63 Example Problems Incorporating Incident Variability For an existing freeway facility such as this one, it is desirable to have detailed incident logs that can be used to develop monthly or seasonal probabilities of various incident severities. However, in this case, incident logs of sufficient detail are not available. Therefore, the alternative method of using local crash rates and ratios of incidents to crashes, in combination with default values, is used to estimate incident probabilities and severities. This process is described in the Freeway Incident Prediction section of Chapter 37, Travel Time Reliability: Supplemental. In summary, the expected number of incidents during a study period under a specified demand pattern is the product of the crash rate, the local incident to crash ratio, the demand volume during the study period, and the facility length. Continuing with the example of the demand pattern associated with Mondays and Fridays in the fall, the crash rate is 150 crashes per 100 million VMT and the ratio of incidents to crashes is 7 (from the input incident data), the base study period VMT is 71,501 (from the Base Dataset Analysis step), and the demand ratio is 1.070 and the demand multiplier is 1.00 (from the Incorporating Demand Variability step). Then, the expected number of incidents is (150 × 10-8) × 7 × 71,501 × (1.07 / 1.00) = 0.803 incidents per 3-h study period. Estimating the time-based probability of a specific incident type requires data on the fraction of all incidents of that type and their average duration. In the absence of local data, the default values from Exhibit 36-24 and are used. For example, from Exhibit 36-24, 75% of all incidents nationally are shoulder-closure incidents. Because full-facility closures (i.e., all 3 lanes in the case of this facility) are not modeled by the reliability method, the probability of a 3+ lane closure is combined with that of a 2-lane closure, resulting in a 5% probability of a 2-lane closure. The average duration of shoulder-closure incidents is 32 min. The time-based probability of a shoulder closure incident for this demand pattern is given in Chapter 37 (Equation 37-5) as: 𝑃𝑠𝑐,𝑓𝑎𝑙𝑙,𝑀/𝐹 = 1 − 𝑒−(𝑛𝑓𝑎𝑙𝑙,𝑀/𝐹𝑔𝑠𝑐)(𝑡𝑠𝑐/𝑡𝑠𝑝) where Psc,fall,M/F = time-based probability of a shoulder closure incident for the “fall, Monday and Friday” demand pattern, nfall,M/F = expected number of incidents per study period for the “fall, Monday and Friday” demand pattern, gsc = proportion of all incidents that are shoulder-closure incidents, tsc = average duration of a shoulder-closure incident (min or h), and tsp = study period duration (min or h). Therefore, with 0.803 incidents expected per study period for this demand pattern, 75% of which are shoulder-closure incidents, a 32-min average duration

Example Problems Page 36-64 Chapter 36/Travel Time Reliability for shoulder-closure incidents, and a 180-min study period duration, the probability of a shoulder-closure incident for this demand pattern is: 𝑃𝑠𝑐,𝑓𝑎𝑙𝑙,𝑀/𝐹 = 1 − 𝑒−(0.803 ×0.75)(32/180) = 0.1015 Exhibit 36-43 presents the full matrix of incident probabilities by severity and demand pattern obtained by applying this equation to all combinations of incidents and demand patterns. Incident Time-based Probability Demand Pattern No Incident Shoulder Closure One Lane Closed Two Lanes Closed Winter, M/F 86.32% 9.71% 2.85% 1.12% Winter, Tu/W/Th 86.39% 9.66% 2.84% 1.12% Spring, M/F 84.90% 10.70% 3.16% 1.24% Spring, Tu/W/Th 85.18% 10.51% 3.10% 1.22% Summer, M/F 84.97% 10.65% 3.14% 1.24% Summer, Tu/W/Th 85.43% 10.33% 3.04% 1.20% Fall, M/F 85.68% 10.15% 2.99% 1.18% Fall, Tu/W/Th 85.90% 10.00% 2.94% 1.16% Notes: M = Monday, Tu = Tuesday, W = Wednesday, Th = Thursday, F = Friday. Scenario Generation Now that the probabilities of various demand patterns, severe weather events, and incident types have been determined, the scenario generator creates the one operational scenario for each possible combination of pattern and event, along with the scenario’s overall probability and its operational (i.e., demand and capacity) characteristics. The resulting combinations of operational scenarios and their relative probabilities are illustrated in Exhibit 36-44. An example of how these probabilities are calculated is now given for the demand pattern representing Mondays and Fridays in the fall. For this demand pattern, the sum of the time-based probabilities for all incidents is 14.32%, from Exhibit 36-43. Similarly, the sum of the time-based probabilities of all severe weather events in the fall is 1.92%, from Exhibit 36-41. Since the freeway reliability methodology assumes independence between the events, the joint probability of a combination of events is simply the product of the individual events’ probability. As an illustration, some of the relevant base probabilities are calculated for Mondays and Fridays in the fall. Note that this demand pattern occurs for 10% of the days in the reliability reporting period, as determined earlier. Then: • P (Monday/Friday fall demand, no incident, non-severe weather) = 0.10 × 0.8568 × 0.9808 = 8.40% • P (Monday/Friday fall demand, no incident, severe weather) = 0.10 × 0.8568 × (1 – 0.9808) = 0.16% • P (Monday/Friday fall demand, incident, non-severe weather) = 0.10 × (1 – 0.8568) × 0.9808 = 1.40%, and • P (Monday/Friday fall demand, incident, severe weather) = 0.10 × (1 – 0.8568) × (1 – 0.9808) = 0.03% Exhibit 36-43 Example Problem 1: Incident Time-based Probabilities by Demand Pattern

Chapter 36/Travel Time Reliability Page 36-65 Example Problems As a check, these probabilities add up to 10%, after accounting for rounding errors. The “Study Period and Detailed Scenario Generation” procedure given in Chapter 37 is applied to create the final set of the scenarios. This procedure ensures consistency between the stated duration of events (weather or incidents) and their probability. For example, most of the time in a “demand and incident only” scenario consists of “demand only” time (i.e., the portion of a “demand and incident scenario” without an incident). The unadjusted probability for the “demand and incident scenario” therefore represents the probability that an incident will occur at any point during the study period, while the adjusted probability represents the probability that an incident is present during a specific 15-min analysis period. In this case, this process yields a total of 1,928 operational scenarios incorporating all variations in demand, weather, and incidents, as shown in the “no exclusion” column of Exhibit 36-45. Scenario Description Number of Scenarios Percentage of Scenarios No Exclusion 0.01% Inclusion Threshold No Exclusion 0.01% Inclusion Threshold Demand-only variations 8 8 0.4% 1.3% Demand and weather variations 72 60 3.7% 10.0% Demand and incident variations 336 336 17.4% 55.8% Demand, weather, and incidents 1,512 198 78.4% 32.9% TOTAL 1,928 602 100% 100% Summer, M/F DP 7 Fall, Tu/W/ThWinter, M/F Winter, Tu/W/Th Spring, M/F Spring, Tu/W/Th Demand and Incident Only Demand and Weather Only Demand, Weather, and Incident DemandOnly Summer, Tu/W/Th Fall, M/F: Probability = 10% Exhibit 36-44 Example Problem 1: Probabilities of Combinations of Demand, Weather, and Incidents Exhibit 36-45 Example Problem 1: Number and Types of Generated Scenarios

Example Problems Page 36-66 Chapter 36/Travel Time Reliability The method allows the analyst to discard very-low-probability scenarios by applying an inclusion threshold. This approach entails a risk of missing some of the very severe scenarios (e.g., multiple lane closures in a snow storm) that fall below the inclusion threshold; however, these scenarios may also be so rare that they do not occur every year (or only every few years). If low-probability scenarios are discarded, the probabilities of all discarded scenarios are proportionally reassigned to the remaining scenarios. This main reason for choosing this approach is to significantly reduce the number of scenarios evaluated using the Chapter 10 freeway facilities methodology and the corresponding analysis time. If the analysis time is not an issue, then there is no need to discard scenarios. Exhibit 36-45 shows the number of scenarios that would be generated if a 0.01% probability threshold were applied; it can be seen that the number of scenarios to be evaluated would drop by more than two-thirds. In summary, a detailed scenario will contain the following attributes, many of which are converted into a set of adjustments to free-flow speed, capacity, and possibly demand. The following items represent the minimum information needed to characterize a detailed scenario: • Scenario number • Adjusted scenario probability • Demand pattern number • Whether a weather event is present and if so: o Type of the weather event (rain, snow, low visibility, etc.) o Duration of the weather event (average duration only) o Start time of the weather event (either at the beginning or halfway in the study period) • Whether an incident is present and if so: o Severity of the incident (shoulder closure, single or multiple lane closures) o Duration of the incident event (25th, 50th, and 75th percentile of default distribution) o Start time of the incident event (either at the beginning or halfway in the study period) o Location on the incident on facility (3 locations, on first, last, and midpoint segments) • Whether a combination of weather and incident events are present (combinations of the above two conditions) Applying the Chapter 10 Procedure Each scenario is converted into a matrix of adjusted demands, segment capacities, free-flow speeds, and number of open lanes that are applied to the base database values for the specific segments and analysis periods. The input data for each scenario are then provided one scenario at a time to the Chapter 10

Chapter 36/Travel Time Reliability Page 36-67 Example Problems freeway facilities method, which generates an average travel time for each analysis period within the scenario’s defined study period, along with the other performance measures that the Chapter 10 method produces. After all of the scenarios have been analyzed, a VMT-weighted probability value is applied to each scenario travel time. The resulting distribution of travel times can then be used to generate a variety of reliability performance measures. Results and Discussion Exhibit 36-46 provides key reliability performance measure results for this example problem, based on a scenario inclusion threshold of 0.01%, involving a total of 602 scenarios. The exhibit provides the results for just the base conditions (representing a standard HCM freeway facilities analysis for conditions representative of AADT demands) along with the results from running all 602 scenarios, covering 7,224 analysis periods. Exhibit 36-47 shows the generated probability and cumulative distributions of TTI for this example problem. Reliability Performance Measure Value for Base Scenario Value from all Scenarios Percent Difference Mean facility TTI (corresponding speed, mi/h) 1.04 (57.7) 1.21 (49.7) +16% PTI (corresponding speed, mi/h) Unavailable 1.65 (36.4) N/A Maximum observed facility TTI (speed, mi/h) 1.09 (55.0) 37.1 (1.6) +3300% Misery Index (corresponding speed, mi/h) Unavailable 3.00 (20.0) N/A Reliability Rating Unavailable 85.0% N/A Average VHD per analysis period 4.0 21.9 +443% Average VHD due to recurring congestion Unavailable 9.3 N/A Average VHD due to non-recurring congestion Unavailable 12.6 N/A Notes: N/A = not applicable, VHD = vehicle-hours of delay. (a) Probability Distribution Function (b) Cumulative Distribution Function These results demonstrate that focusing on a single study period tends to provide an incomplete and biased picture of facility performance over the course of the reliability reporting period. When only a single study period is analyzed, none of the reliability statistics can be computed, and the impact of incidents and weather are typically not taken into account. For an operating agency, knowing Exhibit 36-46 Example Problem 1: Summary Reliability Performance Measure Results Exhibit 36-47 Example Problem 1: VMT- weighted TTI Probability and Cumulative Distribution Functions

Example Problems Page 36-68 Chapter 36/Travel Time Reliability that 85% of the facility’s VMT during the p.m. peak period operates at a speed of 45 mi/h or higher is an important benchmark. It is also clear that much of the facility’s delay is due to demand variability and the effect of weather and incidents. It is worthwhile considering whether using a scenario inclusion threshold of 0.01% substantially affected the reliability performance measure results. When all 1,928 scenarios are evaluated, the mean TTI remains at 1.21, the PTI increases from 1.65 to 1.67, the misery index increases from 3.00 to 3.04, and the reliability rating decreases from 85.04% to 84.85%. None of these changes would be expected to materially change any conclusions or comparisons. EXAMPLE PROBLEM 2: GEOMETRIC TREATMENT In this example, the freeway facility from Example Problem 1 is widened by a lane in segments 7–11. These segments operated close to capacity in the base scenario and were definitely over capacity in scenarios with severe weather or incident conditions. The revised geometry also improves the operation of weaving segment 6 as no lane changes are required of traffic entering at on-ramp 2. Exhibit 36-48 provides a schematic of the freeway facility. Data Inputs All the input data used in Example Problem 1 remain unchanged, except of course for the number of lanes on the facility. The only other exception is the consideration of having a three-lane-closure incident scenario in the four-lane section of the facility. From Exhibit 36-24, the probability of a 2-lane closure in this portion of the facility is 3.1%, while the probability of a 3-lane closure is 1.9%. Results and Discussion As a result of the lane additions, and the emergence of an additional set of scenarios with 3 lane closures, the total number of possible scenarios increases from 1,928 in Example Problem 1 to 2,192 here. Using a scenario inclusion threshold of 0.01% changes the number of scenarios from 602 in Example Problem 1 to 650 here. Exhibit 36-48 Example Problem 2: Freeway Facility Schematic

Chapter 36/Travel Time Reliability Page 36-69 Example Problems Reliability Performance Measure Value for Base Scenario Value from all Scenarios Percent Difference Mean facility TTI (corresponding speed, mi/h) 1.03 (58.3) 1.09 (55.0) +6% PTI (corresponding speed, mi/h) Unavailable 1.16 (51.7) N/A Maximum observed facility TTI (speed, mi/h) 1.04 (57.7) 37.6 (1.6) +3500% Misery Index (corresponding speed, mi/h) Unavailable 2.04 (29.4) N/A Reliability Rating Unavailable 97.4% N/A Average VHD per analysis period 3.2 8.9 +179% Average VHD due to recurring congestion Unavailable 2.8 N/A Average VHD due to non-recurring congestion Unavailable 6.1 N/A Notes: N/A = not applicable, VHD = vehicle-hours of delay. The results of this example problem again confirm the value of a time- extended facility analysis. Had the analyst relied only on the seed file results from one representative day, the mean TTI would have decreased from 1.04 in the base case to 1.03 in the improved case, or conversely the speed would have been predicted to increase from 57.7 to 58.3 mi/h—barely a perceptible change, and certainly not significant enough to recommend the major improvement. On the other hand, the mean TTIs across the reliability reporting period decreases from 1.21 to 1.09, corresponding to a speed improvement from 49.7 to 55.0 mi/h—more than a 10% increase and perhaps enough to justify the improvement, once non-reliability-related factors are taken into account. Similar results occur for most other performance measures. One lesson learned from this exercise is that benefits derived from capacity improvements could be substantially understated if based only on operations on a typical day. The geometric improvement implemented in this example problem provided a good “performance buffer” for severe weather and incident events that reduce the facility’s capacity. EXAMPLE PROBLEM 3: INCIDENT MANAGEMENT TREATMENT This example problem illustrates the analysis of a non-construction alternative that focuses on improved incident management strategies. In this example, the size of the motorist response fleet is increased and communication is improved between the various stakeholders (e.g., traffic management center, emergency responders, and motorist response fleet), allowing incidents to be cleared faster than before. Data Inputs All the input data used in Example Problem 1 remain unchanged, except for the assumed incident duration and standard deviation. The default incident duration values given in Exhibit 36-25 are modified as shown in Exhibit 36-50, based on the analyst’s review of a peer agency’s incident management program. Note that these durations have been created for the purposes of this example problem and do not necessarily reflect the results one would obtain in a real- world situation. Exhibit 36-49 Example Problem 2: Summary Reliability Performance Measure Results

Example Problems Page 36-70 Chapter 36/Travel Time Reliability Incident Type Month Shoulder Closed 1 Lane Closed 2 Lanes Closed 25th percentile 14 16 28 50th percentile 26 27 39 75th percentile 38 38 50 Results and Discussion The key congestion and reliability statistics for this example problem are summarized in Exhibit 36-51. The total number of possible scenarios decreases from 1,928 in Example Problem 1 to 1,664 here, while using a scenario inclusion threshold of 0.01% decreases the number of scenarios from 602 to 442. This result occurs because more combinations of demand, weather, and incidents have probabilities less than 0.01%. Reliability Performance Measure Value for Base Scenario Value from all Scenarios Percent Difference Mean facility TTI (corresponding speed, mi/h) 1.04 (57.7) 1.17 (51.3) +13% PTI (corresponding speed, mi/h) Unavailable 1.61 (37.3) N/A Maximum observed facility TTI (speed, mi/h) 1.09 (55.5) 32.2 (1.86) +2850% Misery Index (corresponding speed, mi/h) Unavailable 2.47 (24.3) N/A Reliability Rating Unavailable 87.3% N/A Average VHD per analysis period 4.0 17.7 +340% Average VHD due to recurring congestion Unavailable 9.6 N/A Average VHD due to non-recurring congestion Unavailable 8.1 N/A Notes: N/A = not applicable, VHD = vehicle-hours of delay. The facility’s operations generally show some slight operational improvements—for example, a drop in the PTI from 1.65 to 1.61—compared to Example Problem 1. The largest improvement is in the misery index, which improves from 3.00 (20 mi/h) to 2.47 (24.4 mi/h), a 20% improvement. It appears that the proposed treatment, while not necessarily impacting average operations, would have a positive effect on reducing the severity of extreme cases combining both weather and incident effects. The analyst should also bear in mind that within the Chapter 10 freeway facility methodology, all incident durations must be entered in multiples of 15 minutes. As a result, the impact of the reduced incident duration time may not be fully captured by the model structure. However, a traditional HCM analysis would not have captured any effect: as seen by comparing the results of base scenario from Example Problems 1 and 3, the base scenario results are the same. Only by incorporating the effects of incidents on travel time, as this chapter’s reliability method does, can the effectiveness of incident management treatments on a facility be evaluated. EXAMPLE PROBLEM 4: SAFETY TREATMENT This example problem illustrates the analysis of safety-related treatments that reduce the likelihood of incidents occurring. In this case, a road safety audit has identified a package of potential safety improvements along the facility; this example problem evaluates the combined effect of these improvements on reliability. Exhibit 36-50 Example Problem 3: Assumed Freeway Incident Durations (min) Exhibit 36-51 *Example Problem 3: Summary Reliability Performance Measure Results

Chapter 36/Travel Time Reliability Page 36-71 Example Problems Data Inputs All the input data used in Example Problem 1 remain unchanged, except for the assumed incident probabilities given in Exhibit 36-43. These incident probabilities are modified as shown in Exhibit 36-52, based on the analyst’s review of a peer agency’s results following the implementation of a similar package of treatments. Note that these incident probabilities have been created for the purposes of this example problem and do not necessarily reflect the results one would obtain in a real-world situation. Incident Probability Demand Pattern No Incident Shoulder Closure One Lane Closed Two Lanes Closed Winter, M/F 92.20% 5.56% 1.61% 0.63% Winter, Tu/W/Th 92.25% 5.53% 1.60% 0.63% Spring, M/F 91.38% 6.14% 1.78% 0.70% Spring, Tu/W/Th 91.54% 6.03% 1.75% 0.68% Summer, M/F 91.42% 6.11% 1.77% 0.69% Summer, Tu/W/Th 91.69% 5.93% 1.72% 0.67% Fall, M/F 91.84% 5.82% 1.68% 0.66% Fall, Tu/W/Th 91.96% 5.73% 1.66% 0.65% Notes: M = Monday, Tu = Tuesday, W = Wednesday, Th = Thursday, F = Friday. Results and Discussion The key congestion and reliability statistics for this example problem are summarized in Exhibit 36-61. The total number of possible scenarios remains 1,928, while using a scenario inclusion threshold of 0.01% decreases the number of scenarios from 602 to 424. This result occurs because more combinations of demand, weather, and incidents have probabilities less than 0.01%. Reliability Performance Measure Value for Base Scenario Value from all Scenarios Percent Difference Mean facility TTI (corresponding speed, mi/h) 1.04 (57.7) 1.16 (51.0) +12% PTI (corresponding speed, mi/h) Unavailable 1.61 (37.3) N/A Maximum observed facility TTI (speed, mi/h) 1.09 (55.5) 37.1 (1.6) +3300% Misery Index (corresponding speed, mi/h) Unavailable 2.53 (23.8) N/A Reliability Rating Unavailable 87.7% N/A Average VHD per analysis period 4.0 17.4 +333% Average VHD due to recurring congestion Unavailable 10.0 N/A Average VHD due to non-recurring congestion Unavailable 7.4 N/A Notes: N/A = not applicable, VHD = vehicle-hours of delay. Similar to Example Problem 3, it appears that average facility operations improve slightly compared to Example Problem 1. While the PTI drops slightly from 1.65 to 1.61, the misery index improves by 18% from 3.00 (20 mi/h) to 2.53 (23.8 mi/h) and the VHD drops by 20% from 21.9 to 17.4. The reliability rating improves from 85.0 to 87.7%. As was the case in Example Problem 3, a traditional HCM analysis would not have captured any effect from the safety treatment, as the base scenario results of Example Problems 1 and 4 are the same. Exhibit 36-52 Example Problem 4: Incident Probabilities by Demand Pattern Exhibit 36-53 Example Problem 4: Summary Reliability Performance Measure Results

Example Problems Page 36-72 Chapter 36/Travel Time Reliability EXAMPLE PROBLEM 5: DEMAND MANAGEMENT STRATEGY In this example problem, demand management techniques are used to shift peak-hour demand to the shoulder periods. By reducing peak-period demand, a capacity buffer is provided that can possibly absorb some of the capacity- reducing effects of severe weather and incidents. Data Inputs All the input data used in Example Problem 1 remain unchanged, except for the traffic demands given in Exhibit 36-39. These traffic demands are modified as shown in Exhibit 36-52 (flattening the peak), based on the analyst’s assumptions about the effectiveness of the demand management strategy. Note that these changes in demand have been created for the purposes of this example problem and do not necessarily reflect the results one would obtain in a real-world situation. Analysis Period Demand Entry Flow Rate On- Ramp 1 On- Ramp 2 On- Ramp 3 Off- Ramp 1 Off- Ramp 2 Off- Ramp 3 1 3,405 297 297 297 198 297 198 2 3,595 360 360 360 270 360 270 3 3,758 324 405 405 243 324 243 4 3,829 383 459 383 230 306 230 5 3,964 432 576 432 288 288 216 6 3,919 473 608 473 203 270 338 7 4,217 324 324 405 243 324 243 8 4,164 198 297 297 297 198 198 9 3,966 216 324 324 324 216 216 10 3,703 238 356 356 356 238 238 11 3,535 259 259 259 389 259 259 12 3,236 242 242 242 242 242 242 The VMT remains 71,501, the same as in Example Problem 1, but more demand occurs in the shoulder periods than before and less demand in the peak period. Exhibit 36-55 illustrates the change in demand by analysis period. In Example Problem 1, the demand during analysis period 6 was approximately 8,900 VMT, while the new demand as a result of the demand-management strategies is approximately 6,800 VMT. Exhibit 36-54 Example Problem 5: Demand Flow Rates (veh/h) by Analysis Period in the Base Dataset

Chapter 36/Travel Time Reliability Page 36-73 Example Problems Results and Discussion Exhibit 36-58 summarizes the key congestion and reliability statistics for Example Problem 5. The total number of possible scenarios remains the same as in Example Problem 1 (1,928 with no scenario exclusion and 602 using a 0.01% scenario inclusion threshold). Reliability Performance Measure Value for Base Scenario Value from all Scenarios Percent Difference Mean facility TTI (corresponding speed, mi/h) 1.04 (57.7) 1.12 (53.6) +8% PTI (corresponding speed, mi/h) Unavailable 1.29 (46.5) N/A Maximum observed facility TTI (speed, mi/h) 1.09 (55.5) 33.1 (1.8) +2900% Misery Index (corresponding speed, mi/h) Unavailable 2.69 (23.5) N/A Reliability Rating Unavailable 95.3% N/A Average VHD per analysis period 4.0 12.5 +211% Average VHD due to recurring congestion Unavailable 2.9 N/A Average VHD due to non-recurring congestion Unavailable 9.6 N/A Notes: N/A = not applicable, VHD = vehicle-hours of delay. On average, the facility shows significant operational improvements compared to Example Problem 1. The improvement is not as great as that of Example Problem 2 (the geometric treatment), but is more significant than the improvements from the incident management and safety treatments evaluated in Example Problems 3 and 4, respectively. In particular, both the PTI and the VHD show significant improvements over the 3-h study period, and the misery index also improves. Treatment Comparisons A side-by-side summary of the treatments’ effect in the five example problems on a number of performance measures is given in Exhibit 36-57. Exhibit 36-55 Example Problem 5: Comparison of VMT Demand by 15-min Analysis Periods Exhibit 36-56 Example Problem 5: Summary Reliability Performance Measure Results

Example Problems Page 36-74 Chapter 36/Travel Time Reliability Several observations emerge from this comparison: • The lane-add treatment had the strongest effect on performance. The added lane essentially serves as a buffer that helps absorb the shock of capacity-reducing incident or weather events. Since this is a bottleneck treatment that addresses a recurring congestion problem, the share of delay due to non-recurring events increased. • Demand management had the second most beneficial effect on the absorption of the recurring congestion problem. • Both the incident management and safety treatments produced similar positive effects compared to the base condition. The interesting difference is that because the incident duration (and standard deviation) was reduced in the incident management case, that treatment yielded a slightly lower misery index than the safety treatment. The misery index is pegged to the most severe cases a user can expect on the facility. In contrast, the safety treatment reduced the overall probability of crashes and incidents. As a result, delays due to non-recurring congestion had the smallest share of VHD with this treatment. • Safety treatments and incident management strategies affect the tail of travel time distribution. The misery index experienced the greatest improvement under these treatments. In contrast, the demand management treatment affects the peak of the travel time distribution. The PTI and mean TTI showed substantial improvements under the demand management strategy. • In all cases, the treatment benefits far exceeded those that would have been estimated using a traditional HCM analysis that only considers recurring congestion effects during a single study period. • A host of other treatments related to Active Traffic Demand Management can be tested using this chapter’s reliability methodology, as long as their impacts can be converted into adjustments to free-flow speed, capacity, traffic demand, or a combination of these. • An important limitation of the analysis presented in these examples is the assumption that travel demand is insensitive to severe weather or incident conditions. It is likely under such scenarios that travelers may Exhibit 36-57 Example Problem 5: Treatment Summary Comparison Reliability Performance Measure Ex am pl e P ro bl em 1 Ba se C on di tio n Ex am pl e P ro bl em 2 G eo m et ric T re at m en t Ex am pl e P ro bl em 3 In ci de nt M an ag em en t Ex am pl e P ro bl em 4 Sa fe ty T re at m en t Ex am pl e P ro bl em 5 D em an d M an ag em en t Mean TTI across all scenarios 1.21 1.09 1.17 1.16 1.12 Facility mean speed (mi/h) 49.7 55.0 51.3 51.7 53.6 PTI 1.65 1.16 1.61 1.61 1.29 Reliability rating (%) 85.0% 97.4% 87.3% 87.3% 95.3% Misery Index 3.00 2.04 2.47 2.53 2.69 Mean VHD in a 3-h study period 263 108 213 209 150 % VHD due to non-recurring effects 57% 68% 46% 43% 77%

Chapter 36/Travel Time Reliability Page 36-75 Example Problems alter their route, departure time, or mode, or may cancel their trip altogether. While the methodology accommodates user-defined changes in demand associated with weather or incidents that capability was not used in these example problems. EXAMPLE PROBLEM 6: EXISTING URBAN STREET RELIABILITY Objective This example problem illustrates: • The steps involved in calculating reliability statistics for an urban street facility using the minimum required data for the analysis, • Identifying the key reliability problems on the facility, and • Diagnosing the causes (e.g., demand, weather, incidents) of reliability problems on the facility. Site The selected site for this example problem is an idealized 3-mi-long principal arterial street located in Lincoln, Nebraska. The street is a two-way, four-lane, divided roadway with shoulders. There are seven signalized intersections that are spaced uniformly at 0.5-mi intervals along the street. The posted speed limit on the major street and the minor streets is 35 mi/h. A portion of this street is shown in Exhibit 36-58. The distances shown are the same for the other segments of the facility. Also shown in Exhibit 36-58 are the traffic movement volumes for each intersection and access point on the facility. Each intersection has the same volume, and each access point has the same volume. Intersection geometry and signal timing is described in a subsequent section. 200 1,000 10 100 500 50 50 500 100 10 1,000 200 80 1,050 100 80 100 100 80 100 1,050 80Signal Access Point 1 2 Signal 2,640 ft SignalSegment 1 AP1 AP2 600 ft 600 ft 3 2,640 ft Signal N Segment 2 AP3 AP4 600 ft 600 ft Exhibit 36-58 Example Problem 6: Urban Street Facility

Example Problems Page 36-76 Chapter 36/Travel Time Reliability Required Input Data This section describes the input data needed for both the reliability methodology and the core HCM urban streets methodology. The dataset that describes conditions where no work zones or special events are present is known as the base dataset. Other datasets used to describe work zones or special events are called alternative datasets. Reliability Methodology Input Data Exhibit 36-59 lists the input data needed for an urban street reliability evaluation. The agency does not collect traffic volume data on a continual basis, so the factors and ratios that describe demand patterns will be defaulted. Traffic counts for one representative day are provided by the analysis and used as the basis for estimating volume during other hours of the year. Lincoln, Nebraska, is one of the communities for which a 10-year summary of weather data is provided, so the default weather data will be used. Incident data are available locally as annual crash frequencies by intersection and street segment. It was determined that the effect of work zones or special events on reliability would not be considered in the evaluation. HCM Urban Street Methodology Input Data This subsection describes the data gathered to develop the base dataset. The base dataset contains all of the input data required to conduct an urban street facility analysis using the methodologies described in HCM Chapters 16 through 18. Alternative datasets are not needed because the effects of work zones and special events are not being considered in the evaluation. Data Category Input Data Need Data Value Time periods Analysis period Study period Reliability reporting period 15 min 7–10 a.m. Non-holiday weekdays for 1 year Demand patterns Hour-of-day factors Day-of-week demand ratio Month-of-year demand ratio Demand change due to rain, snow Will be defaulted Weather Rain, snow, and temperature data by month Pavement runoff duration Will be defaulted Incidents Segment and intersection crash frequencies Crash frequency adjustment factors for work zones/special events Factors influencing incident duration Available locally (See Step 5) Not required (no work zones) Will be defaulted Work zones and special events Changes to base conditions (alternative dataset) and schedule Not required (no work zones) Nearest city Required when defaulted weather data used Lincoln, Nebraska Geometrics Presence of shoulder Yes Traffic counts Day and time of traffic counts used in base and alternative datasets Tuesday, January 4, 7–8 a.m. No alternative datasets required (no work zones) Functional class Urban street functional class Urban principal arterial Exhibit 36-59 Example Problem 6: Input Data Needs and Sources

Chapter 36/Travel Time Reliability Page 36-77 Example Problems Traffic count data for the hour beginning at 7:00 a.m. are available from a recent traffic count taken on a Tuesday, January 4. Weather conditions were clear and the pavement was dry. The traffic volumes are shown in Exhibit 36-58. They are the same at all seven intersections for this idealized example. Exhibit 36-60 provides the signal timing data for Intersection #1. The other signalized intersections have the same signal timing. Approach Eastbound Westbound Northbound Southbound Movement L T R L T R L T R L T R NEMA Movement # 5 2 12 1 6 16 3 8 18 7 4 14 Volume (veh/h) 200 1000 10 200 1000 10 100 500 50 100 500 50 Lanes 1 2 1 1 2 1 1 2 0 1 2 0 Turn Bay Length (ft) 200 0 200 200 0 200 200 0 0 200 0 0 Saturation Flow Rate (veh/h/ln) 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 Platoon Ratio 1.000 1.333 1.000 1.000 1.333 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Initial Queue (veh) 0 0 0 0 0 0 0 0 0 0 0 0 Speed Limit (mi/h) -- 35 -- -- 35 -- -- 35 -- -- 35 -- Detector Length (ft) 40 40 -- -- 40 40 -- 40 40 -- Lead/Lag Left-Turn Phase Lead -- Lead -- Lead -- Lead -- Left Turn Mode Prot. -- Prot. -- Pr/Pm -- Pr/Pm -- Passage Time (s) 2.0 -- 2.0 -- 2.0 2.0 2.0 2.0 Minimum Green (s) 5 -- 5 -- 5 5 5 5 Change Period (Y+Rc) (s) 3.0 4.0 3.0 4.0 3.0 4.0 3.0 4.0 Phase Splits (s) 20.0 35.0 20.0 35.0 20.0 25.0 20.0 25.0 Max. Recall off -- off -- off off off off Min. Recall off -- off -- off off off off Dual Entry no yes no yes no yes no yes Simultaneous Gap Out yes yes yes yes yes yes yes yes Dallas Phasing no no no no no no no no Reference Phase 2 Offset (s) 0 or 50 Notes: L = left turn, T = through, R = right turn, Prot. = protected, Pr/Pm = permissive-protected. See Chapter 18 for definitions of signal timing variables. At each signalized intersection, there are left- and right-turn bays on each of the two major-street approaches, left-turn bays on each of the minor-street approaches, and two through lanes on each approach. Two unsignalized access points exist between each signal. The posted speed limit for the major street and the minor streets is 35 mi/h. The traffic signals operate in coordinated-actuated mode at a 100-s cycle. The offset for the eastbound through phase alternates between 0 and 50 s at successive intersections to provide good two-way progression. The peak hour factor is 0.99, 0.92, 0.93, 0.94, 0.95, 0.96, and 0.97 at intersections #1 through #7, respectively. Analysis Replications The urban street reliability method uses a Monte Carlo approach to generate variables describing weather events, incidents, and random demand fluctuations for each scenario in the reliability reporting period. One variation of this approach is to use an initial random number seed. The use of a seed number ensures that the same random number sequence is used each time a set of scenarios are generated for a given reliability reporting period. Any positive integer can be used as a seed value. Each set of scenarios is called a replication. Exhibit 36-60 Example Problem 6: Intersection #1 Signal Timing Data A Monte Carlo approach is used when there is some randomness in the value of a variable due to unknown influences and known influences by other variables that also have some randomness such that it is difficult to accurately determine the frequency (or probability) of the subject variable’s value.

Example Problems Page 36-78 Chapter 36/Travel Time Reliability Because events (e.g., a storm, a crash) are generated randomly in the urban street method, the possibility exists that highly unlikely events could be overrepresented or underrepresented in a given set of scenarios. To minimize any bias these rare events may cause, the set of scenarios should be replicated and evaluated two or more times. Each time the set of scenarios are created, the inputs should be identical, except that a different set of random number seeds is used. Then, the performance measures of interest from the evaluation of each set of scenarios are averaged to produce the final performance results. Five replications were found to provide sufficient precision in the predicted reliability measures for this example problem. The seed numbers in the following list were selected by the analyst for this example problem. The first replication used seed numbers 82, 11, and 63. The second replication used numbers 83, 12, and 64. This pattern continues for the other three replications. • Weather event generator: 82, 83, 85, 87, 89 • Demand event generator: 11, 12, 14, 16, 18 • Incident event generator: 63, 64, 66, 68, 70 The random number sequence created by a specific seed number may be specific to the software implementation and computer platform employed in the analysis. As a result, evaluating the same dataset and seed number in different software or on a different platform may result in different results than shown here. Each result, though different, will be equally valid. Computational Steps This example problem proceeds through the following steps: 1. Establish the purpose, scope, and approach. 2. Code datasets. 3. Estimate weather events. 4. Estimate demand volumes. 5. Estimate incident events. 6. Generate scenarios. 7. Apply the Chapter 16 analysis method. 8. Conduct quality control and error checking. 9. Interpret results. Step 1: Establish the Purpose, Scope, and Approach Define the Purpose The agency responsible for this urban street wishes to perform a reliability analysis of existing conditions to determine if the facility is experiencing significant reliability problems. They also want to diagnose the primary causes of any identified reliability problems on the facility so that an improvement strategy can be developed. Multiple analysis replications are needed to determine the confidence interval for the final performance results.

Chapter 36/Travel Time Reliability Page 36-79 Example Problems Define the Reliability Analysis Box The results from a preliminary evaluation of the facility were used to define the general spatial and temporal boundaries of congestion on the facility under fair weather, non-incident conditions. A study period consisting of the weekday morning peak period (7 a.m. to 10 a.m.) and a study area consisting of the 3-mi length of facility between intersections #1 and #7 encompasses all of the recurring congestion. The reliability reporting period is desired to include all weekdays, excluding major holidays, over the course of a year. The analysis period will be 15 min in duration. Select Reliability Performance Measures Reliability will be reported using the following performance measures: mean TTI, 80th percentile TTI, 95th percentile TTI (PTI), reliability rating, and total delay (in vehicle-hours) for the reliability reporting period. Step 2: Code Datasets Select Reliability Factors for Evaluation The major causes of travel time reliability problems are demand surges, weather, and incidents. It was determined that reliability problems associated with work zones and special events were not key elements of the evaluation of this specific facility. Code the Base Dataset The base dataset was developed for the selected study section and study period. This dataset describes the traffic demand, geometry, and signal timing conditions for the intersections and segments on the subject urban street facility during the study period when no work zones are present and no special events occur. The data included in this dataset are described in Chapters 16 through 18. Code the Alternative Datasets As no work zones are planned in the next year and no special events affect the facility on weekdays, only the base dataset will be required. Step 3: Estimate Weather Events This step predicts weather event date, time, type (i.e., rain or snow), and duration for each study period day in the reliability reporting period. Identify Input Data The default weather data for Lincoln, Nebraska, are a compilation of 10 years of historical data from the NCDC (7, 8) and include the following statistics: • Total normal precipitation, • Total normal snowfall, • Number of days with precipitation of 0.01 in. or more, • Normal daily mean temperature, and

Example Problems Page 36-80 Chapter 36/Travel Time Reliability • Precipitation rate. One inch of snowfall is estimated to have the water content of 0.1 in. of rain. Exhibit 36-61 shows the historical weather data for two months of the year. Weather Data January April Normal precipitation (in.)* 0.67 2.90 Normal snowfall (in.) 6.60 1.50 Days with precipitation (days) 5 9 Daily mean temperature (˚F) 22.40 51.20 Precipitation rate (in./h) 0.030 0.062 Note: *Rainfall plus water content of snow. Determine Weather Events for Each Day At this point in the analysis, weather is estimated for all days during a 2-year period. The analysis is not yet confined to the days within the reliability reporting period or the hours within the study period. The purpose of the extra calculations is to define the expected weather pattern for the study facility, which will be used in a later step to estimate incident frequencies. A Monte Carlo approach is used to decide if precipitation will occur in a given day. If yes, then a Monte Carlo approach is also used to determine the type of precipitation (i.e., rain or snow), precipitation rate, total precipitation, and start time for the current day. The details of the process are described in the Urban Street Scenario Generation section of Chapter 37, Travel Time Reliability: Supplemental. Exhibit 36-62 illustrates the results of the calculations for two non-holiday weeks in January and two non-holiday weeks in April. These results are based on the historical weather data for Lincoln, Nebraska, as shown in Exhibit 36-61. The random number values shown in the exhibit are intended to illustrate the computations within this specific table. Different values are obtained if the random number seed is changed. Only dates falling within the reliability reporting period are shown. For reliability evaluation, total precipitation is assumed to be perfectly correlated with the precipitation rate such that storms producing a large total precipitation are associated with a high precipitation rate. This relationship is replicated by estimating both values using the same random number. As can be seen from Exhibit 36-62, the computed event durations may exceed 24 h, but when the end times are set for the event, any event that ends beyond 24:00 is truncated to 24:00. Exhibit 36-61 Example Problem 6: Sample Weather Data for Lincoln, Nebraska

Chapter 36/Travel Time Reliability Page 36-81 Example Problems Date P re ci pi ta ti on R N R D P re ci pi ta ti on ? (Y es /N o) Te m pe ra tu re R N R T d M ea n T em p er at u re ( ˚F ) Sn ow /R ai n? P re ci pi ta ti on R at e R N R P d P re ci pi ta ti on R at e (i n. /h ) To ta l P re ci pi ta ti on R N R TP d To ta l P re ci pi ta ti on ( in .) P re ci pi ta ti on S ta rt R N R S d ,m St ar t of P re ci pi ta ti on E ve nt P re ci pi ta ti on D ur at io n (h ) Ti m e W et A ft er P re ci p. ( h) D ay /N ig ht ? To ta l E ve nt D ur at io n (h ) En d of P re ci pi ta ti on En d of W et P av em en t Jan 10 0.03 Yes 0.94 30 Snow 0.83 0.54 0.83 2.08 0.23 4:30 3.88 1.22 Night 5.10 8:23 9:36 Jan 11 0.00 Yes 0.22 19 Snow 0.62 0.29 0.62 0.27 0.21 4:45 0.95 1.28 Night 2.23 5:42 6:59 Jan 12 0.30 No Jan 13 0.90 No Jan 14 0.20 No Jan 24 0.00 Yes 0.89 28 Snow 0.09 0.03 0.09 0.01 0.12 3:00 0.01 1.23 Night 1.23 3:00 4:14 Jan 25 0.53 No Jan 26 0.45 No Jan 27 0.21 No Jan 28 0.60 No Apr 4 0.64 No Apr 5 0.24 Yes 0.11 45 Rain 0.40 0.03 0.40 0.02 1.00 23:15 0.68 0.07 Night 0.75 23:56 24:00 Apr 6 0.22 Yes 0.19 47 Rain 0.31 0.02 0.31 0.01 0.08 1:45 0.34 0.92 Night 1.26 2:05 3:00 Apr 7 0.78 No Apr 8 0.39 No Apr 11 0.55 No Apr 12 0.37 No Apr 13 0.10 Yes 0.28 48 Rain 0.82 0.11 0.82 0.54 0.39 7:15 5.05 0.72 Day 5.76 12:18 13:01 Apr 14 0.78 No Apr 15 0.27 Yes 0.98 61 Rain 0.73 0.08 0.73 0.30 0.57 11:30 3.62 0.66 Day 4.28 15:07 15:47 Note: RN = random number. Determine Weather Events for Each Analysis Period The days that have weather events are subsequently examined to determine whether the event occurs during the study period. Specifically, each analysis period is examined to determine whether it is associated with a weather event. An examination of the start and end times in Exhibit 36-62 indicates that the snow on January 10 and the rain on April 13 occur during the 7:00 a.m. to 10:00 a.m. study period. Step 4: Estimate Demand Volumes This step identifies the appropriate traffic volume adjustment factors (demand ratios) for each date and time during the reliability reporting period. These factors are used during the scenario file generation procedure to estimate the volume associated with each analysis period. If the analyst does not provide demand ratios based on local data, then the default ratios provided in Section 5 Applications are used. Identify Input Data The input data needed for this step are identified in the following list. • Hour-of-day demand ratio, • Day-of-week demand ratio, • Month-of-year demand ratio, • Demand change factor for rain event, and • Demand change factor for snow event. Exhibit 36-62 Example Problem 6: Sample Generated Weather Events

Example Problems Page 36-82 Chapter 36/Travel Time Reliability The default values for these factors are obtained from Exhibit 36-27 to Exhibit 36-30. Their selection is based on the functional class of the subject facility, which is “urban principal arterial.” Determine Base Demand Ratio First, the demand ratios for the day of the traffic count are determined. The count was taken on Tuesday, January 4 during the 7:00 a.m. hour. Using the default demand ratio data from Exhibit 36-27 through Exhibit 36-29, it can be seen that: • The hour-of-day ratio for the 7:00 a.m. hour for principal arterials is 0.071, • The day-of-week ratio for Tuesdays is 0.98, and • The month-of-year ratio for principal arterials in May is 0.831. Multiplying these three factors together yields the base demand ratio of 0.0578. This ratio indicates that counted traffic volumes represent 5.78% of AADT, if this urban street’s demand pattern is similar to that of the default demand data. Determine Analysis Period Demand Ratio A similar process is used to determine the demand ratio represented by each analysis period, except that an additional adjustment is made for weather. From Exhibit 36-30, a default 1.00 demand adjustment factor is applied to analysis periods with rain and a 0.80 adjustment factor is applied to analysis periods with snow. As an example, the weather generator produced snow conditions for Monday, January 10 at 7:00 a.m. Default demand ratio data are obtained again from Exhibit 36-27 through Exhibit 36-29. The text accompanying Exhibit 36-30 states that a demand change factor of 0.80 is appropriate for snowing conditions. Therefore, the factor values in the following list are established for the evaluation. • The hour-of-day ratio for the 7:00 a.m. hour for principal arterials is 0.071, • The day-of-week ratio for Mondays is 0.98, • The month-of-year ratio for principal arterials in January is 0.831, and • Demand change factor is 0.80. Multiplying these factors together yields the demand ratio of 0.0463. This ratio indicates that the analysis period volumes represent 4.63% of AADT. Therefore, the traffic counts are multiplied by (0.0463 / 0.0578) = 0.800 to produce equivalent volumes for the hour starting at 7:00 a.m. on Monday, January 10. Exhibit 36-63 shows a selection of demand profile computations for different hours, days, months, and weather events. Each row in this exhibit corresponds to one analysis period (i.e., scenario). Although the computations are performed for all non-holiday days of the year, this table illustrates the computations for selected days when dry weather or snow are predicted. The ratio shown in the last column of this exhibit is multiplied by the traffic counts for each signalized

Chapter 36/Travel Time Reliability Page 36-83 Example Problems intersection to estimate the equivalent hourly flow rate for the associated analysis period. Date Weekday Time Weather Weather Factor Hour Factor Day Factor Month Factor Total Factor Total/Base Jan 10 Mon 7:00 Snow 0.80 0.071 0.980 0.831 0.0463 0.800 Jan 10 Mon 7:15 Snow 0.80 0.071 0.980 0.831 0.0463 0.800 Jan 10 Mon 7:30 Snow 0.80 0.071 0.980 0.831 0.0463 0.800 Jan 10 Mon 7:45 Snow 0.80 0.071 0.980 0.831 0.0463 0.800 Jan 10 Mon 8:00 Snow 0.80 0.058 0.980 0.831 0.0378 0.654 Jan 10 Mon 8:15 Snow 0.80 0.058 0.980 0.831 0.0378 0.654 Jan 10 Mon 8:30 Dry 1.00 0.058 0.980 0.831 0.0472 0.817 Jan 10 Mon 8:45 Dry 1.00 0.058 0.980 0.831 0.0472 0.817 Jan 10 Mon 9:00 Dry 1.00 0.047 0.980 0.831 0.0383 0.662 Jan 10 Mon 9:15 Dry 1.00 0.047 0.980 0.831 0.0383 0.662 Jan 10 Mon 9:30 Dry 1.00 0.047 0.980 0.831 0.0383 0.662 Jan 10 Mon 9:45 Dry 1.00 0.047 0.980 0.831 0.0383 0.662 Apr 6 Wed 7:00 Dry 1.00 0.071 1.000 0.987 0.0701 1.212 Apr 6 Wed 7:15 Dry 1.00 0.071 1.000 0.987 0.0701 1.212 Apr 6 Wed 7:30 Dry 1.00 0.071 1.000 0.987 0.0701 1.212 Apr 6 Wed 7:45 Dry 1.00 0.071 1.000 0.987 0.0701 1.212 Apr 6 Wed 8:00 Dry 1.00 0.058 1.000 0.987 0.0572 0.990 Apr 6 Wed 8:15 Dry 1.00 0.058 1.000 0.987 0.0572 0.990 Apr 6 Wed 8:30 Dry 1.00 0.058 1.000 0.987 0.0572 0.990 Apr 6 Wed 8:45 Dry 1.00 0.058 1.000 0.987 0.0572 0.990 Apr 6 Wed 9:00 Dry 1.00 0.047 1.000 0.987 0.0464 0.802 Apr 6 Wed 9:15 Dry 1.00 0.047 1.000 0.987 0.0464 0.802 Apr 6 Wed 9:30 Dry 1.00 0.047 1.000 0.987 0.0464 0.802 Apr 6 Wed 9:45 Dry 1.00 0.047 1.000 0.987 0.0464 0.802 Step 5: Estimate Incident Events The procedure described in this step is used to predict incident event dates, times, and durations. It also determines each incident event’s type (i.e., crash or non-crash), severity level, and location on the facility. The procedure uses weather event and demand variation information from the two previous steps as part of the incident prediction process. Crash frequency data are used to estimate the frequency of both crash-related incidents and non-crash-related incidents. For an urban street reliability evaluation, incidents are categorized as being: • Segment-related, or • Intersection-related. These two categories are mutually exclusive. Identify Input Data Incident Frequency Data. Three-year average crash frequencies are determined from locally available crash records for each segment and intersection along the facility. These averages are shown in Exhibit 36-64. The frequency of non-crash incidents is estimated from the crash frequency data in a subsequent step. Non- crash incident frequency is not an input quantity due to the difficulty agencies have in acquiring non-crash incident data. Exhibit 36-63 Example Problem 6: Sample Demand Profile Calculations

Example Problems Page 36-84 Chapter 36/Travel Time Reliability Location Crash Frequency (cr/yr) Segment 1-2 (intersections 1 to 2) 15 Segment 2-3 (intersections 2 to 3) Segment 3-4 (intersections 3 to 4) Segment 4-5 (intersections 4 to 5) Segment 5-6 (intersections 5 to 6) Segment 6-7 (intersections 6 to 7) 16 17 18 19 20 Intersection 1 32 Intersection 2 33 Intersection 3 Intersection 4 Intersection 5 Intersection 6 Intersection 7 34 35 36 37 38 Work Zone/Special Event Crash Frequency Adjustment Factors. Work zones and special events are not being considered in this example; therefore, these crash frequency adjustment factors do not need to be provided. Weather Event Crash Frequency Adjustment Factors. The default crash frequency adjustment factors given in Exhibit 36-31 are used. Incident Duration Factors. The default incident detection and response times given in Exhibit 36-31 and the default clearance times given in Exhibit 36-32 are used. Incident Distribution. The default incident distribution given in Exhibit 36-33 for urban street facilities with shoulders is used. Compute Equivalent Crash Frequency for Weather This step converts the average crash frequencies (supplied as input data) into the equivalent crash frequencies for each weather type. First, the input crash frequency data for segments and intersections are converted into an equivalent crash frequency for each of the following weather conditions: clear and dry, rainfall, wet pavement (not raining), and snow or ice on pavement (not snowing). This conversion is based on the number of hours during a 2-year period that a particular weather condition occurs and the crash adjustment factor corresponding to each weather condition. For this example problem, the number of hours in a year with particular weather condition is determined from the default weather data for Lincoln, Nebraska. The equivalent crash frequency when every day is dry for street location i is computed using the following equation. Variable definitions are given in Exhibit 36-65. spspsfsfwpwprfrf istr istr NhCAFNhCAFNhCAFNhCAFNh NyFc Fc ++++ = dry )( dry),( 760,8 weaistrweaistr CAFFcFc dry),(),( = Exhibit 36-65 illustrates the computations of the equivalent crash frequencies by weather type for two segments and three intersections. The calculations are similar for the other segments and intersections. Exhibit 36-64 Example Problem 6: Locally Available Crash Frequency Data This equation and the equations that follow are explained in Section 5, Urban Street Scenario Generation, in Chapter 37.

Chapter 36/Travel Time Reliability Page 36-85 Example Problems Segments Intersections Variable Definition 1-2 2-3 1 2 3 Fcstr(i) Observed average crash frequency 15 16 65 66 67 Ny Number of years 2 2 2 2 2 Nhdry Hours of dry weather 17026.98 17026.98 17026.98 17026.98 17026.98 Nhrf Hours of rainfall 278.22 278.22 278.22 278.22 278.22 Nhwp Hours of wet pavement 104.33 104.33 104.33 104.33 104.33 Nhsf Hours of snowfall 64.61 64.61 64.61 64.61 64.61 Nhsp Hours of snow/ice on pavement 45.86 45.86 45.86 45.86 45.86 Crash adjustment factors for… CAFrf Rainfall 2.0 2.0 2.0 2.0 2.0 CAFwp Wet pavement 3.0 3.0 3.0 3.0 3.0 CAFsf Snowfall 1.5 1.5 1.5 1.5 1.5 CAFsp Snow/ice on pavement 2.75 2.75 2.75 2.75 2.75 Calculated crash frequencies for… Fcstr(i),dry Dry weather 14.50 15.47 30.94 31.91 32.88 Fcstr(i),rf Rainfall 29.01 30.94 61.89 63.82 65.75 Fcstr(i),wp Wet pavement 43.51 46.41 92.83 95.73 98.63 Fcstr(i),sf Snowfall 21.76 23.21 46.41 47.86 49.32 Fcstr(i),sp Snow/ice on pavement 39.89 42.54 85.09 87.75 90.41 Note: Hours of dry, rainfall, wet pavement, snowfall, and snow/ice on pavement sums to 17,520 h (2 yr). Establish Crash Adjustment Factors for Work Zones or Special Events This step is skipped because work zones and special events are not being considered for this evaluation. Determine Whether an Incident Occurs This step goes through each of the 24 hours of each day that is represented in the reliability reporting period. For each hour, it is determined if an incident occurs. If an incident occurs, then its duration is also determined. Finally, for each incident identified in this manner, it is determined whether some portion (or all) of the incident occurs during a portion of the study period. Weather-Adjusted Incident Frequencies. First, for a given hour in a given day, the weather event data are checked to see which weather condition (dry, rainfall, snowfall, wet pavement and not raining, or snow/ice on pavement and not snowing) was generated for that hour. The expected incident frequencies for street locations (i.e., segments and intersections) Fistr(i),wea(h,d) are determined from: (1) the corresponding crash frequency for the given weather condition Fcstr(i),wea (from a previous step) and (2) a factor pcstr,wea relating total crashes to total incidents for the given weather condition (from the default values in the third column of Exhibit 36-33). If a special event or work zone was present on the given hour and day, the expected incident frequency is then multiplied by the segment or intersection (as appropriate) crash adjustment factor CAFstr specified by the analyst for special events and work zones. The following equation is used: weastr weaistr strdhweaistr pc Fc CAFFi , ),( ),(),( = For example, weather was dry on Wednesday, April 6 at 9:00 a.m. For segment 1-2, the equivalent crash frequency for dry weather is 14.50 crashes/yr (from Exhibit 36-65). The ratio of crashes to incidents for segments in dry weather is 0.358. There is no work zone or special event, so the crash adjustment factor is 1.0. Then: Exhibit 36-65 Example Problem 6: Computation of Crash Frequency by Weather Type

Example Problems Page 36-86 Chapter 36/Travel Time Reliability yrincidents/ 5.40 )358.0( )50.14()0.1(,21 ==− drysegFi Similarly, snow was falling on Monday, January 10 at 7:00 a.m. The equivalent crash frequency for snowfall on segment 1-2 is 21.76 cr/yr. The ratio of crashes to incidents for segments in snowy weather is 0.358. Therefore, yrincidents/ 8.60 )358.0( )76.21()0.1(,21 ==− sfsegFi Conversion to Hourly Frequencies. Next, the incident frequency Fistr(i),wea(h,d) is converted to an hourly frequency fistr(i),wea(h,d),h,d by multiplying it by the percent of annual demand represented by the hour and by dividing by the number of days in a year (expressed as a ratio of hours). The same hour-of-day fhod,h,d, day-of-week fdow,d, and month-of-year fmoy,d demand ratios used in Step 4 are used here. The following equation is used, where “8,760” represents the number of hours in a year and “24” represents the number of hours in a day. ( ) dmoyddowdhhoddhweaistrdhdhweaistr fff Fi fi ,,,, ),(),( ,),,(),( 24760,8 = The month-of-year demand ratio for April is 0.987, the day-of-week demand ratio for Wednesday is 1.00, and the hour-of-day demand ratio for 9:00 a.m. is 0.047. The incident frequency for this day and time is calculated above as 40.5 incidents per year. Therefore, the equivalent hourly incident frequency for segment 1-2 on Wednesday, April 6, at 9:00 a.m. is ( ) hincidents/ 00515.0)987.0()00.1(047.024 )760,8( )5.40( Jan10,0700,,21 =×=− drysegfi Similarly, the equivalent hourly incident frequency for segment 1-2 on Monday, January 10 at 7:00 a.m. is ( ) hincidents/ 00963.0)831.0()980.0(071.024 )760,8( )8.60( Jan12,0800,,21 =×=− sfsegfi Probability of No Incidents. Incidents for a given day, street location, incident type, and hour of day are assumed to follow a Poisson distribution: )exp(0 ,,),,(),(,),,(),(,,,,),,(),( sevlancondhweaistrdhdhweaistrdhsevlancondhweaistr pifip ×−= where p0str(i),wea(h,d),con,lan,sev,h,d = probability of no incident for a given combination of street location, weather condition, incident type, lane location, and severity for a given hour and day; fistr(i),wea(h,d),h,d = expected hourly incident frequency for a given combination of street location and weather condition for a given hour day (calculated above); and pistr,wea(h,d),con,lan,sev = proportion of incidents for a given combination of street location, weather condition, incident type, lane location, and severity for a given hour and day (from the default values given in Exhibit 36-33).

Chapter 36/Travel Time Reliability Page 36-87 Example Problems Exhibit 36-66 demonstrates the determination of incidents for Segment 1-2 on April 6 for the 9:00 a.m. hour. Exhibit 36-67 does the same for January 10 for the 7:00 a.m. hour. Incident Type Incident Proportion Hourly Incident Frequency exp (-fi × pi) Random Number Incident ? Crash 1 lane Fatal/Injury 0.036 0.00515 0.99981 0.90019 No Crash 1 lane PDO 0.083 0.00515 0.99957 0.38078 No Crash 2 lane Fatal/Injury 0.028 0.00515 0.99986 0.90860 No Crash 2 lane PDO 0.030 0.00515 0.99984 0.06081 No Crash Shoulder Fatal/Injury 0.021 0.00515 0.99990 0.82183 No Crash Shoulder PDO 0.016 0.00515 0.99918 0.34916 No Non-crash 1 lane Breakdown 0.456 0.00515 0.99766 0.99900 Yes Non-crash 1 lane Other 0.089 0.00515 0.99954 0.59842 No Non-crash 2 lane Breakdown 0.059 0.00515 0.99970 0.69323 No Non-crash 2 lane Other 0.017 0.00515 0.99991 0.08131 No Non-crash Shoulder Breakdown 0.014 0.00515 0.99993 0.13012 No Non-crash Shoulder Other 0.007 0.00515 0.99996 0.44620 No Notes: Incident proportions total 100%. PDO = property damage only. Random numbers have been selected to illustrate this particular step of the computations. They are not necessarily the same results that would be achieved in a full run of the procedure. Incident Type Incident Proportion Hourly Incident Frequency exp (-fi × pi) Random Number Incident ? Crash 1 lane Fatal/Injury 0.036 0.00963 0.99965 0.21041 No Crash 1 lane PDO 0.083 0.00963 0.99920 0.83017 No Crash 2 lane Fatal/Injury 0.028 0.00963 0.99973 0.58437 No Crash 2 lane PDO 0.030 0.00963 0.99971 0.80487 No Crash Shoulder Fatal/Injury 0.021 0.00963 0.99981 0.35441 No Crash Shoulder PDO 0.016 0.00963 0.99846 0.64888 No Non-crash 1 lane Breakdown 0.456 0.00963 0.99562 0.40513 No Non-crash 1 lane Other 0.089 0.00963 0.99914 0.98428 No Non-crash 2 lane Breakdown 0.059 0.00963 0.99943 0.61918 No Non-crash 2 lane Other 0.017 0.00963 0.99983 0.13712 No Non-crash Shoulder Breakdown 0.014 0.00963 0.99987 0.30502 No Non-crash Shoulder Other 0.007 0.00963 0.99993 0.33279 No Note: Incident proportions total 100%. PDO = property damage only. Random numbers have been selected to illustrate this particular step of the computations. They are not necessarily the same results that would be achieved in a full run of the procedure. If more than one incident occurs at the same time and location, then the more serious incident is considered in the methodology. During an incident, the methodology requires that at least one lane remain open in each direction of travel on a segment and on each intersection approach. If the number of lanes blocked by an incident is predicted to equal the number of lanes available on the segment or intersection approach, then one lane is maintained open and the remaining lanes are blocked. For example, if the segment has two lanes in the subject travel direction and an incident occurs and is predicted to block two lanes, then the incident is modeled as blocking only one lane. Determine Incident Duration If the result of the previous step indicates that an incident occurs in a given segment or intersection during a given hour and day, the incident duration is then determined randomly from a gamma distribution using the average Exhibit 36-66 Example Problem 6: Incident Determination for April 6, 9:00 a.m., for Segment 1-2 Exhibit 36-67 Example Problem 6: Incident Determination for January 10, 7:00 a.m., for Segment 1-2

Example Problems Page 36-88 Chapter 36/Travel Time Reliability incident duration and the standard deviation of incident duration as inputs. These values are supplied as input data. The duration is used in a subsequent step to determine which analysis periods are associated with an incident. The incident duration is rounded to the nearest quarter hour for 15-min analysis periods. This rounding is performed to ensure the most representative match between event duration and analysis period start/end times. This approach causes events that are shorter than one-half the analysis period duration to be ignored (i.e., they are not recognized in the scenario generation process). Exhibit 36-66 shows that a non-crash, 1-lane, breakdown incident was generated for segment 1-2 on April 6 starting at the 9:00 a.m. hour. Exhibit 36-68 shows the inputs into the incident duration calculation and the result. As with other computations in this example problem involving random numbers, different values are obtained if the random number seed is changed. Variable Value Location Segment 1-2 Incident type Non-Crash Number of lanes involved 1-lane Incident severity Breakdown Weather Dry Incident detection time (min) 2.0 Incident response time, dry weather (min) 15.0 Incident clearance time (min) 10.8 Average incident duration (min) 27.8 Standard deviation of incident duration (min) 22.2 Average incident duration (h) 0.463 Standard deviation of incident duration (h) 0.371 Random number 0.57455 Gamma function alpha parameter (mean2/variance) 1.5625 Gamma function beta parameter (variance/mean) 0.2965 Duration (h) 0.433 Rounded duration (nearest 15 min) (h) 0.50 Incident start time 9:00 Incident end time 9:30 Determine Incident Location If an incident occurs at a segment or intersection during a given hour and day, then its location is determined in this step. For intersections, the location is one of the intersection legs. For segments, the location is one of the two segment travel directions. In the case of the incident identified on Segment 1-2 at 9:00 a.m. on April 6, the two directions of the segment have equal traffic volumes (see Exhibit 36-58) and therefore have equal probability of having the incident occur. This time, the scenario generator randomly assigned the incident to the westbound direction (identified as being associated with NEMA phase 6 at the intersection). Exhibit 36-68 Example Problem 6: Sample Calculation of Incident Duration

Chapter 36/Travel Time Reliability Page 36-89 Example Problems Identify Analysis Period Incidents The preceding steps of the incident estimation procedure are repeated for each hour of each day in the reliability reporting period. During this step, the analysis periods associated with an incident are identified. Specifically, each hour of the study period is examined to determine whether it coincides with an incident. If an incident occurs, then its event type, lane location, severity, and street location are identified and recorded. Each subsequent analysis period coincident with the incident is also recorded. Step 6: Generate Scenarios This step uses the results from Steps 3 to 5 to create one scenario for each analysis period in the reliability reporting period. The base dataset coded in Step 2 represents the “seed” file from which the new scenarios are created. As discussed previously, each analysis period is considered to be one scenario. There are 3,120 analysis periods in the reliability reporting period (= 4 analysis periods/hours × 3 hours/day × 5 days/week × 52 weeks/year ×1 year/reporting period). Thus, there are 3,120 scenarios. Each scenario created in this step includes the appropriate adjustments to segment running speed and intersection saturation flow rate associated with the weather events or incidents that are predicted to occur during the corresponding analysis period. If an analysis period has an incident, the number of lanes is reduced, the saturation flow rate is adjusted for affected intersection lanes, and a free-flow speed adjustment factor is applied to the affected lanes in the segment. If an analysis period has rainfall, snowfall, wet pavement, or snow/ice on the pavement then the saturation flow rate is adjusted for all intersections, the free- flow speed is adjusted for all segments, and the left-turn critical headways are adjusted for all intersections. The traffic demand volumes in each dataset are adjusted for monthly, weekly, and hourly variations. Step 7: Apply the Chapter 16 Analysis Method The analysis methodology for urban street facility evaluation is applied to each scenario generated in the previous step. This methodology is based on that described in the HCM 2010. However, this methodology includes an additional procedure that so the methodology can be used to evaluate segments that experience sustained spillback during the analysis period. At the conclusion of this step, the delay and queue length for each intersection, as well as the speed and travel time for each segment, is computed for each scenario. Step 8: Conduct Quality Control and Error Checking It is difficult to quality control thousands of scenarios, so it is recommended that the analyst focus on error checking and quality control on the base dataset. The results should be error-checked to the analyst’s satisfaction to ensure that it accurately represents real-world congestion on the facility under recurring demand conditions with no incidents and under dry weather conditions. The same criteria for error checking should be used as for a conventional HCM analysis, but with the recognition that any error in the base dataset will be

Example Problems Page 36-90 Chapter 36/Travel Time Reliability crucial, because it will be reproduced thousands of times by the scenario generator. The total delay for each scenario should be scanned to identify the study periods likely to be associated with exceptionally long queues. For a given study, period, the final queue on each entry intersection approach for the last analysis period should not be longer than the corresponding initial queue for the first analysis period. The study period duration should be increased (i.e., started earlier, ended later) such that this condition is satisfied. Ideally, the study period is sufficiently long that these reference initial and final queues both equal zero. An efficient approach for making this check is to start by evaluating the scenario with the largest total delay. Step 9: Interpret Results This step examines the reliability results for the existing facility. These results are listed in Exhibit 36-69. Although both travel directions have the same volume and capacity, several of the values in this exhibit vary slightly by travel direction due to the use of Monte Carlo methods. Measure Eastbound Westbound Vehicle-miles traveled a 2260 2257 Number of scenarios a 3120 3120 Base free-flow travel time, s b 262.9 262.9 Mean TTI b 1.69 1.64 80th percentile TTI 1.57 1.56 95th percentile TTI (PTI) 2.98 2.61 Reliability rating 93.2 94.1 Total delay (veh-h) b 72.0 Notes: (a) This statistic represents a total for the reliability reporting period. (b) This statistic represents an average of the value for each scenario (i.e., an average value for all scenarios). The vehicle-miles traveled (VMT) is computed for each scenario and added for all scenarios in the reliability reporting period. This statistic describes overall facility utilization for the reliability reporting period. The travel time indices shown in Exhibit 36-69 were computed by finding the average (i.e., mean), 80th, and 95th percentile travel times for a given direction of travel across all scenarios and dividing by the facility’s base free-flow speed. Since hourly demands, geometry, weather, and signal timings are identical in both directions, the differences between the indices illustrate the effects of random variation in incidents and 15-min demands for the two directions. The reliability rating describes the percent of VMT on the facility associated with a TTI less than 2.5. A facility that satisfies this criterion during a given scenario is likely to provide a LOS D or better for that scenario. The reliability ratings shown in the exhibit indicate than more than 90% of the vehicle-miles of travel on the facility are associated with LOS D or better. The total delay (in vehicle-hours) combines the delay-per-vehicle and volume of all intersection lane groups at each intersection during a scenario. This statistic increases with an increase in volume or delay. It is the only statistic of those listed in Exhibit 36-69 that considers the performance of all traffic movements (i.e., the other measures consider just the major-street through Exhibit 36-69 Example Problem 6: Reliability Performance Measure Results

Chapter 36/Travel Time Reliability Page 36-91 Example Problems movement). Hence, it is useful for quantifying the overall change in operation associated with a strategy. When considered on a scenario-by-scenario basis, this statistic can be used to identify those scenarios with extensive queuing on one or more “entry” approaches (i.e., the cross-street intersection approaches and the major-street approaches that are external to the facility). Exhibit 36-70 shows the travel time distribution for the facility’s eastbound travel direction. That for the westbound direction has a similar shape. The longer travel times tend to be associated with poor weather. The longest travel times coincide with one or more incidents and poor weather. The reliability methodology was repeated several times to examine the variability in the reliability performance measures. Each replication used the same input data, with the exception that the three random numbers were changed for each replication. Exhibit 36-71 shows the predicted average and 95th percentile travel times for the eastbound travel direction based on five replications. The last four rows of Exhibit 36-71 show the statistics for the sample of five observations. The 95th percentile confidence interval was computed using Equation 36-7. The confidence interval for the average travel time is 432.2 to 441.1 s, which equates to ±1.36% of the overall average travel time. Similarly, the confidence interval for the 95th percentile travel time is ±3.16% of the average of the 95th percentile travel times. This confidence interval is larger than that of the average travel time because the 95th percentile travel time tends to be influenced more by the occurrence of incidents and poor weather. As suggested by the formulation of Equation 36-7, the confidence interval can be reduced in width by increasing the number of replications. Exhibit 36-70 Example Problem 6: Eastbound Travel Time Distribution 0 200 400 600 800 1000 1200 31 0 36 6 42 2 47 8 53 4 59 0 64 6 70 2 75 8 81 4 87 0 Travel Time, s Fr eq ue nc y

Example Problems Page 36-92 Chapter 36/Travel Time Reliability Replication Average Travel Time (s) 95th Percentile Travel Time (s) 1 443.7 783.8 2 441.4 787.5 3 432.8 758.4 4 439.3 740.0 5 433.7 772.9 Average 438.2 768.5 Standard deviation 4.79 19.6 95th% confidence interval 432.2–444.1 (±1.36%) 744.4–792.8 (±3.16%) The contribution of demand, incidents, and weather to total vehicle-hours of delay (VHD) during the reliability reporting period is used to determine the relative contributions of each factor to the facility’s reliability. The annual VHD takes into account both the severity of the event and its likelihood of occurrence. VHD is computed by identifying the appropriate category for each scenario and adding the estimated VHD for each scenario in this category. The results are summed for all scenarios in each category in the reliability reporting period. They are presented in Exhibit 36-72 and Exhibit 36-73. The categories have been condensed to facilitate the diagnosis of the primary causes of reliability problems on the urban street. Demand has been grouped into two levels. All foul weather and incident scenarios have been grouped into a single category each. Total Delay by Demand and Weather (veh-h) Low Demand High Demand Fair Weather Foul Weather Fair Weather Foul Weather Total No Incidents 52,957 6,337 120,393 5,025 184,713 Incidents 5,865 23 22,714 11,437 40,038 Total 58,822 6,360 143,107 16,462 224,751 Low Demand High Demand Fair Weather Foul Weather Fair Weather Foul Weather Total No Incidents 23.6% 2.8% 53.6% 2.2% 82.2% Incidents 2.6% 0.0% 10.1% 5.1% 17.8% Total 26.2% 2.8% 63.7% 7.3% 100.0% An examination of the cell values in Exhibit 36-73 yields the conclusion that the single most significant cause of annual delay on the urban street example is high demand, accounting for 53.6% of annual delay during fair weather with no incidents. Incidents or bad weather collectively account for 22.9% of annual delay on the facility (17.8% + 7.3% + 2.8% – 5.1% – 0.0%). EXAMPLE PROBLEM 7: URBAN STREET STRATEGY EVALUATION Objective This example problem illustrates an application of the reliability methodology for alternatives analysis. The objective is to demonstrate the utility of reliability information when evaluating improvement strategies. The strategies considered in this example involve changes to the urban street’s geometric design or its signal operation. These changes are shown to have an impact on traffic operation and safety, both of which can influence reliability. Exhibit 36-71 Example Problem 6: Confidence Interval Calculation for Eastbound Direction Exhibit 36-72 Example Problem 6: Annual VHD by Cause Exhibit 36-73 Example Problem 6: Percentage of Annual VHD by Cause

Chapter 36/Travel Time Reliability Page 36-93 Example Problems Site The same urban street described in Example Problem 6 is used in this example problem. Required Input Data The same types of required input data described in Example Problem 6 are used here. The conditions described in Example Problem 6 are used as the starting point for evaluating each of three strategies that have been identified as having the potential to improve facility reliability. One base dataset is used to describe the “existing” facility of Example Problem 6, while one base dataset is associated with each strategy, resulting in a total of four base datasets. Specific changes to the Example Problem 6 base dataset required to represent each strategy are described later. The three strategies are as follows: 1. Shift 5 s from the cross-street left-turn phase to the major-street through phase. 2. Change the major-street left-turn mode from protected-only to protected-permitted. 3. Eliminate major-street right-turn bays and add a second lane to major- street left-turn bays. These strategies were formulated to address a capacity deficiency for the major-street through movements at each intersection. This deficiency was noted as part of the analysis described in Example Problem 6. The change associated with each strategy was implemented at each of the seven intersections on the street. For this example problem, the changes needed to implement the strategies require changes only to the base datasets. However, it should be noted that some strategies may require changes to the reliability methodology input data, the HCM urban streets methodology input data, or both. Computational Steps This example problem proceeds through the following steps: 1. Establish the purpose, scope, and approach. 2. Code datasets. 3. Generate scenarios. 4. Apply the Chapter 16 analysis method. 5. Interpret results. Step 1: Establish the Purpose, Scope, and Approach Define the Purpose The agency responsible for this urban street wishes to perform a reliability analysis of existing conditions to determine which of the three strategies offers the greatest potential for improvement in facility reliability.

Example Problems Page 36-94 Chapter 36/Travel Time Reliability Define the Reliability Analysis Box The results from a preliminary evaluation of the facility were used to define the general spatial and temporal boundaries of congestion on the facility under fair weather, non-incident conditions. A study period consisting of the weekday morning peak period (7 a.m. to 10 a.m.) and a study area consisting of the 3-mi length of facility between intersections #1 and #7 encompasses all of the recurring congestion. The reliability reporting period is desired to include all weekdays, excluding major holidays, over the course of a year. The analysis period will be 15 min in duration. Select Reliability Performance Measures Reliability will be reported using the following performance measures: mean TTI, 80th percentile TTI, 95th percentile TTI (PTI), reliability rating, and total delay (in vehicle-hours) for the reliability reporting period. Step 2: Code Datasets Code the Base Dataset The first base dataset represents existing conditions and is identical to the base dataset described in Example Problem 6. This base dataset was modified as follows to create a new base dataset (three in all) for each strategy being evaluated: • The signal timing parameters for the Strategy 1 base dataset were modified at each intersection to reduce the phase splits for the minor- street left-turn movements by 5 s and to increase the phase splits for the major-street through movements by 5 s. • The signal timing parameters for the Strategy 2 base dataset were modified at each intersection to change the major street left turn mode from protected-only to protected-permitted. Furthermore, Chapter 12 of the Highway Safety Manual (4) indicates that intersection crash frequency increases by 11% on average when this change is made. Therefore, the crash frequency input data for each intersection was increased to reflect this change. • The geometric parameters for the Strategy 3 base dataset were modified at each intersection to eliminate the major-street right-turn bays and to add a second lane to the major-street left-turn bays. Furthermore, Chapter 12 of the Highway Safety Manual (4) indicates that intersection crash frequency increases by 9% for this change. Therefore, the crash frequency input data for each intersection was increased to reflect this change. Code the Alternative Datasets As no work zones are planned in the next year and no special events affect the facility on weekdays, only the base datasets will be required.

Chapter 36/Travel Time Reliability Page 36-95 Example Problems Step 3: Generate Scenarios During this step, the reliability methodology is used to create one scenario for each analysis period in the reliability reporting period. The base datasets coded in Step 2 represent the “seed” files from which the scenarios are created associated with each strategy. As in Example Problem 6, one set of 3,120 scenarios is created for the existing facility. Additional sets of 3,120 scenarios are created for each of the three strategies. Step 4: Apply the Chapter 16 Method The analysis methodology for urban street facility evaluation is applied to each scenario generated in the previous step, as described in Example Problem 6. Step 5: Interpret Results This step examines the reliability results for the facility. Initially, the results for the existing facility are described. Then, the results for each of the three strategies are summarized and compared with those of the existing facility. The formulation of these strategies was motivated by an examination of the results for the existing facility. This examination revealed that the major-street through movements had inadequate capacity during the morning peak traffic hour for several high-volume months of the year. Results for the Existing Facility The results for the existing facility are the same as for Example Problem 6, given previously in Exhibit 36-69 through Exhibit 36-73. Results for Strategy 1 In Strategy 1, 5 s are taken from the cross-street left-turn phase split. This change increases the time available to the major-street through (i.e., coordinated) phase, and increases the through movement capacity. The results for this strategy are listed in Exhibit 36-74. The first two rows list the average values obtained from five replications. The third row lists the change in the performance measure value. The last row indicates whether the change is statistically significant. Case Travel Time (s) Total Delay (veh-h) Reliability Rating Average 95th Percentile Existing 438.2 768.5 70.7 93.2 Strategy 1 400.7 542.2 66.2 96.8 Change -37.5 -226.3 -4.5 3.6 Significant? Yes Yes Yes Yes Note: Results based on five replications. The statistics in Exhibit 36-74 indicate that the strategy produces a relatively large improvement in travel time, particularly in the 95th percentile travel time. The strategy improves reliability during the peak hour for the high-volume months, which is reflected by the increase in the reliability rating. It forecasts an increase of 3.6% in the VMT for which LOS D or better is provided. On the other hand, delay to the cross-street left-turn movements increases, which partially Exhibit 36-74 Example Problem 7: Results for Strategy 1

Example Problems Page 36-96 Chapter 36/Travel Time Reliability offsets the decrease in delay to the major-street through movements. This trade- off is reflected by a small reduction of 4.5 veh-h total delay. Results for Strategy 2 In Strategy 2, the major-street left-turn mode is changed from protected-only to protected-permitted. This change reduces the time required by the major- street left-turn phase, which increases the time available to the coordinated phase, and increases the through movement capacity. The results of the evaluation of this strategy are given in Exhibit 36-75. Case Travel Time (s) Total Delay (veh-h) Reliability Rating Average 95th Percentile Existing 438.2 768.5 70.7 93.2 Strategy 2 382.9 473.5 49.6 97.3 Change -55.3 -295.0 -21.1 4.1 Significant? Yes Yes Yes Yes Note: Results based on five replications. The statistics in Exhibit 36-75 indicate that the strategy produces a relatively large improvement in travel time, particularly in the average travel time. The strategy improves reliability during the peak hour for the high-volume months, reflected by the increase in the reliability rating. It forecasts an increase of 4.1% in the VMT for which LOS D or better is provided. The delay to the major-street through movements decreases without a significant increase in the delay to the other movements. This trend is reflected by the notable reduction of 21.1 veh-h total delay. Results for Strategy 3 In Strategy 3, the major-street right-turn bays are eliminated and second lanes are added to the major-street left-turn bays. This change reduced the time required by the major-street left-turn phase, which increased the time available to the coordinated phase, and increased the through movement capacity. The results for this strategy are listed in Exhibit 36-76. Case Travel Time (s) Total Delay (veh-h) Reliability Rating Average 95th Percentile Existing 438.2 768.5 70.7 93.2 Strategy 3 410.0 460.2 59.0 98.5 Change -28.2 -308.3 -11.7 5.3 Significant? No Yes Yes Yes Note: results based on five replications. The statistics in Exhibit 36-76 indicate that the strategy produces a relatively large improvement in travel time, particularly in the 95th percentile travel time. The strategy improves reliability during the peak hour for the high-volume months, reflected by the increase in the reliability rating. It forecasts an increase of 5.3% in the VMT for which LOS D or better is provided. Delay to the major- street through movements decreases, as reflected by the reduction of 11.7 veh-h total delay. The change in average travel time is not statistically significant because the loss of the right-turn bays shifts the location of many incidents from Exhibit 36-75 Example Problem 7: Results for Strategy 2 Exhibit 36-76 Example Problem 7: Results for Strategy 3

Chapter 36/Travel Time Reliability Page 36-97 Example Problems the bays to the through lanes. This shift causes the average travel time for Strategy 3 to vary more widely among scenarios. Summary of Findings All three strategies improved the facility’s reliability and overall operation. Strategy 1 (shift 5 s to the coordinated phase) provides some improvement in reliability of travel through the facility and some reduction in total delay in the system. Strategy 2 (protected-only to protected-permitted) provides the lowest average travel time and the lowest total delay. It also provides a notable improvement in travel reliability. Strategy 3 (eliminate right-turn lanes, increase left-turn lanes) provides the biggest improvement in reliability of travel. It also provides some overall benefit in terms of lower travel time and total delay. The selection of the best strategy should include considering the change in road user costs, as measured in terms of reliability, total delay, and crash frequency. Viable strategies are those for which the reduction in road user costs exceeds the construction costs associated with strategy installation and maintenance.

References Page 36-98 Chapter 36/Travel Time Reliability 7. REFERENCES 1. Zegeer, J., J. Bonneson, R. Dowling, P. Ryus, M. Vandehey, W. Kittelson, et al. SHRP 2 Report S2-L08-RW-1: Incorporating Travel Time Reliability into the Highway Capacity Manual. Transportation Research Board of the National Academies, Washington, D.C., forthcoming. 2. Agarwal, M., T.H. Maze, and R. Souleyrette. Impact of Weather on Urban Freeway Traffic Flow Characteristics and Facility Capacity. Center for Transportation Research and Education, Iowa State University, Ames, Aug. 2005. 3. WeatherUnderground. Weather History. http://www.wunderground.com/history/. Accessed April 2012. 4. American Association of State Highway and Transportation Officials. Highway Safety Manual, 1st Edition. Washington, D.C., 2010. 5. American Association of State Highway and Transportation Officials. A Policy on Geometric Design of Highways and Streets. Washington, D.C., 2011. 6. Habib, P.A. Transportation System Management Options for Downtown Curbside Pickup and Delivery of Freight. In Transportation Research Record 758, Transportation Research Board, National Research Council, Washington, D.C., 1980, pp. 63–69. 7. Comparative Climatic Data for the United States through 2010. National Climatic Data Center, National Oceanic and Atmospheric Administration, Asheville, North Carolina, 2011. http://www.ncdc.noaa.gov. Accessed September 21, 2011. 8. Rainfall Frequency Atlas of the U.S.: Rainfall Event Statistics. National Climatic Data Center, National Oceanic and Atmospheric Administration, Asheville, North Carolina, 2011. http://www.ncdc.noaa.gov/oa/documentlibrary/rainfall.html. Accessed September 21, 2011. 9. Khattak, A., and N. Rouphail. Incident Management Assistance Patrols: Assessment of Investment Benefits and Costs. Report FHWA/NC/2005-02, North Carolina Department of Transportation, Raleigh, 2005. 10. Skabardonis, A., K.F. Petty, R.L. Bertini, P.P. Varaiya, H. Noeimi, and D. Rydzewski. The I-880 Field Experiment: Analysis of the Incident Data. In Transportation Research Record 1603, Transportation Research Board, National Research Council, Washington, D.C., 1997, pp. 72–79.Cambridge Systematics, Inc.; Texas A&M University; University of Washington; Dowling Associates; Street Smarts; H. Levinson; and H. Rakha. Analytical Procedures for Determining the Impacts of Reliability Mitigation Strategies. SHRP 2 L03 Draft Final Report. Cambridge, Mass., February 2010. 11. Jia, A., B. Williams, and N. Rouphail. Identification and Calibration of Site- Specific Stochastic Freeway Breakdown and Queue Discharge. In Transportation Research Record: Journal of the Transportation Research Board, No. 2188, Transportation Research Board of the National Academies, Some of these references are available in the Technical Reference Library in Volume 4.

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