Incorporating Travel Time Reliability into the Highway Capacity Manual (2014)

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233 Objective This example problem illustrates the following process: 1. Calculating reliability statistics for a freeway facility using the minimum required data for the analysis; 2. Identifying key reliability problems on the facility; and 3. Diagnosing the causes (e.g., demand, weather, incidents) of reliability problems on the facility. Site The study freeway facility is a 12.5-mi portion of eastbound I-40 between Durham and Raleigh, North Carolina, bounded by NC-55 to the west and NC-54 to the east (see Figure I.1). The eastbound direction is most heavily used by commuters on weekdays, with a peak hour of 5 to 6 p.m. The posted speed limit is 65 mph. A weaving section near the downstream end of the facility creates a recurring bottleneck. Minimum Required Data Inputs The data listed below are required to perform a reliability analysis of a freeway facility. Additional desirable data are also identified, but this example problem assumes that the addi- tional desirable data are not available. Instead, this example illustrates the use of defaults and lookup tables to substitute for the desirable data. • Data required for a 2010 Highway Capacity Manual (HCM2010) (Transportation Research Board of the National Academies 2010) freeway facility analysis (Chapter 10): 44 Facility volumes by 15-min analysis periods (time slices) for a single day’s peak period 44 Desirable: single day’s peak period facility travel times for calibrating a traditional HCM2010 operations analysis model for the facility 44 Facility geometry and controls by analysis segment and by analysis period (if controls vary by analysis period) for the study period (if controls or geometry vary by time of day, day of week, or month of year); • Data required to estimate demand variability: 44 Annual average daily traffic (AADT), directional factor (D), and peak period demand profiles (K-factors) 44 Desirable: archived peak period mainline volume counts for previous year; • Data required to estimate incident frequencies: 44 Collision reports for the prior 3-year period 44 Desirable: detailed incident logs including frequency, duration, and location of incidents for a similar period; • Data required to estimate weather frequencies: 44 Weather reports for at least the prior 3-year period 44 Desirable: 10-year weather data from a nearby weather station; and • Optional extra data for calibrating estimates: 44 Facility travel times (or spot speeds) and volumes by 15-min analysis periods (time slices) for the target study period (peak periods, days of weeks, months of year, and so forth). Computational Steps This example problem proceeds through the following steps: 1. Scoping the bounds of the reliability analysis: a. Establishing the analysis purpose, scope, and approach b. Selecting an appropriate study period c. Selecting an appropriate reliability reporting period d. Selecting appropriate reliability performance measures and thresholds of acceptable performance; 2. Coding the HCM facility operations analysis: a. Identifying the sources of unreliability to be analyzed b. Coding base conditions c. Coding alternative data sets, if any; A p p e n D I x I Example Problem: Existing Freeway Reliability

234 3. Estimating the demand variability profile; 4. Estimating severe-weather frequencies; 5. Estimating incident frequencies; 6. Generating scenarios and the probabilities of their occurrence; 7. Applying the HCM2010 freeway facility analysis method; 8. Performing quality control and error checking and deter- mining inclusion thresholds; 9. Calculating performance measures; and 10. Interpreting results. Step 1. Scoping the Bounds of the Reliability Analysis Although most professional engineers and planners are already well trained in scoping a traditional highway capacity analysis, travel time reliability introduces some extra considerations that are not part of a traditional capacity analysis: • Selecting an appropriate study period for reliability (hours of day) and an appropriate reliability reporting period (days of week, months of year); • Selecting appropriate reliability performance measures according to the agency’s reliability objectives and the facil- ity type; and • Selecting thresholds of acceptable performance. A reliability analysis has much greater data and computational demands than a traditional HCM operations analysis. There- fore, it should be tightly scoped to ensure the analyst has the resources to complete the analysis. Furthermore, a loosely scoped analysis that provides more days and hours than needed runs the risk of diluting the reliability results by mixing in too many hours or days of free-flow conditions into the analysis. Purpose To focus the analysis, it is important to identify the purpose for performing the reliability analysis. In this example, the purpose of performing the reliability analysis of existing con- ditions is to • Determine if the facility is experiencing significant reliabil- ity problems; and Source: © 2013 Google. Figure I.1. Study freeway facility bottleneck during peak demand levels.

235 • Diagnose the primary causes of the reliability problems on the facility so that an improvement program can be devel- oped for the facility. Determining the Reliability Analysis Box The reliability reporting period has three dimensions: (1) the geometric limits of the facility to be evaluated (the study sec- tion), (2) the periods within the day when the analysis is to be performed (the study period), and (3) the days of the year over which reliability is to be computed and reported (the reliability reporting period). The result is a spatial–temporal cube (see Figure I.2) within which reliability is computed. The reliability box should be dimensioned so that it includes all the recurring congestion (congestion occurring under recur- ring demand conditions, in fair weather, without incidents) of interest for the analysis. This requirement favors a large reli- ability box. However, the larger the reliability box, the greater the number of instances of free-flow conditions, which will tend to mask or dilute the reliability problems. In this example, an examination of the facility over several days determined the general spatial and temporal boundaries of congestion on the facility under fair weather, nonincident conditions. The selected study period was the 6-h-long week- day afternoon peak period (2 to 8 p.m.), and the study section was a 12.5-mi facility length between NC-55 and NC-54 (cor- responding to 34 HCM analysis segments). All the instances when speeds regularly dropped below 40 mph are encom- passed within the selected study section and study period. Figure I.2 shows an example of the speed profile generated by FREEVAL-RL when an incident occurs in the furthest downstream segment on the facility. Once the study section length and study period have been selected, the next step is to determine for how many (and which) days of the year reliability will be computed (the reliability reporting period). The objective of setting the reliability reporting period is to focus the analysis on days when reliability is a concern. The reporting period should include enough days so that the probability of encountering a significant number and range of incident types is high. A minimum of 100 days is recommended for the reporting period, although a full-year analysis is preferred. Thus, for this example, weekdays for a full year were selected for the reliability reporting period. At five weekdays per week, 52 weeks plus 1 day per year, there are 261 weekdays per year (including holidays). Holidays may be excluded from the reliability reporting period if they result in lower than normal p.m. peak period demands. (In this case, holidays were not deemed to be a significant factor affecting reliability, and were therefore included in the reliability analysis.) If an agency wishes to focus on nonweather effects and avoid vacation effects, then a single season may be selected, rather than a full year. The selection of the appropriate reli- ability reporting period hinges on the agency’s purpose for the analysis. Selecting Reliability Performance Measures For instructional purposes, all the reliability performance measures shown in Table I.1 will be computed. However, for a typical application, one or two performance measures most useful to the agency’s analysis purpose are recommended to be selected. Since all performance measures are derived from the same travel time distribution, once an agency has picked one or two measures for the reliability analysis, additional measures do not bring significant new information to the results. In that sense, it is most important that an agency selects performance Figure I.2. Sample congested speed profile on I-40. Table I.1. Reliability Performance Measures to Be Evaluated Measure Definition Mean TTI Mean travel time divided by free-flow travel time Planning time index 95th percentile travel time divided by free-flow travel time 80th percentile TTI 80th percentile travel time divided by free-flow travel time Semistandard deviation One-sided standard deviation, referenced to free-flow Failure/on-time Percent of trips less than 40 mph Standard deviation Usual statistical definition Misery index Average of top 5% of travel times divided by free-flow travel time Reliability rating Percentage of vehicle miles traveled at a TTI less than 1.33

236 measures consistently across different reliability analyses, allowing agency staff and stakeholders to begin developing an understanding of these metrics. In this example, the agency could pick the mean travel time index (TTI) so that average performance could be evaluated (the mean is useful for computing total benefits later). As an indicator of reliability, the agency could pick the 80th percen- tile TTI or the planning time index (PTI). Selecting Thresholds of Acceptable Performance Ideally, an agency has already developed its own thresholds of acceptable reliability performance based on locally collected data. However, in this case, the agency responsible for the free- way has not yet assembled sufficient data on the reliability of its own facilities to have confidence in setting its own standards. Consequently, two standards of performance will be evaluated in this example problem as part of the reliability assessment. The first standard will be determined by comparing the per- formance of the I-40 facility to other facilities in the SHRP 2 Project L08 data set. For example, the operating agency may select a performance threshold to be more reliable than the worst 10% of U.S. urban freeway facilities studied for this proj- ect. Thus, if the mean TTI for the facility is computed to be greater than 1.93, then the facility’s reliability will be consid- ered unacceptable. Similarly, if the computed PTI exceeds 3.55, that will also be considered unacceptable. The second standard is set based on the agency’s conges- tion management goal of operating its freeways at 40 mph or better during the majority of the peak periods within the year. This particular standard requires that a modified travel time performance index, called the policy index, be computed that uses the agency’s 40-mph target speed in place of the free-flow speed. =PI mean travel time travel time at 40 mph Since the agency’s goal is for the mean annual peak period speed on the facility to be 40 mph or higher, then if the policy index exceeds 1.00, the reliability of the facility will be consid- ered unacceptable. Step 2. Coding the HCM Facility Operations Analysis Selecting Reliability Factors for Evaluation The major causes of travel time reliability problems are demand surges, weather, incidents, special events, and work zones. Eval- uating all possible causes of reliability puts a significant strain on analytical resources, so it is recommended that rarer causes of unreliability be excluded from the reliability analysis. In addition, the purpose of the analysis may suggest that some causes can be bundled together. The study facility in this case is large, and adjacent special event generators do not significantly affect operations during the selected study period (most events are on weekends). Con- sequently, the effects of special events do not need to be evalu- ated separately and can be bundled in with other causes of surges in demand. Similarly, work zones are not planned dur- ing weekday peak periods on the facility in the analysis year, so work zones can be excluded from the reliability analysis. Coding Base Conditions The base HCM analysis input file (the seed file) was coded for the selected study section and study period using the proce- dures and guidance contained in HCM2010 Chapters 10 to 13. Demands, geometries, and free-flow speed were obtained for a single, typical, fair weather, nonincident, nonholiday, weekday p.m. peak period (2 to 8 p.m.). Figure I.3 shows the geometry of the study section of the facility. Table I.2 shows a portion of the input entries for the seed file. Mainline volumes were obtained from side-fire radar sta- tions spaced roughly 1.5 mi apart. Ramp volumes were counted for 2 weeks using portable tube counters. A typical fair-weather weekday when daily traffic was close to the AADT was selected from the 2-week count period. Default values of 5% trucks, 0% recreational vehicles, and 0% buses were used to account for heavy vehicles. There were no extended grades in excess of 2% for longer than 0.5 mi on the facility (see HCM2010, p. 11–15), and the facility has a generally level vertical profile, so a general ter- rain category of level was used to characterize the vertical geometry of the facility. Segment lengths and number of lanes were obtained by field inspection or Google aerial photos. Lane widths are a standard 12 ft. The free-flow speed was estimated using HCM2010 Equation 11-1. Coding Alternative Data Sets As there is no need to account for special events or work zones, no alternative data sets need to be created. If there had been a need for them, they would have been developed in the same way as the base data set, with appropriate modifications to the input data to reflect changes in demand, geometry, and traffic control. Step 3. Estimating the Demand Variability Profile The total number of scenarios that must be evaluated signifi- cantly affects the processing time and the time required by the

237 Section A Section B Section C Figure I.3. Geometry of facility study section. analyst to analyze the results. The number of scenarios is the product of the number of demand levels, weather levels, and incident levels selected for evaluation. Thus, any reduction in the number of unnecessary demand, weather, and incident lev- els needed for the reliability analysis will result in significant processing and evaluation time savings. An examination of local data on I-40 demand variability over the course of a year (see Table I.3) revealed that weekday demand variability over the year at the site could be adequately represented by three demand patterns (Monday to Wednesday, Thursday, and Friday) and four month types grouped by the major seasons of the year (December to February; March to May; June to August; and September to November). Thus it was possible to consolidate 60 potential demand levels (five week- day times 12 months) into 12 demand levels (three weekday patterns by four month types). Days and months with similar ratios of monthly average daily traffic (ADT) to AADT for a given demand pattern were grouped together. All entries were normalized to a Monday in January. Entries in Table I.3 are ADT demand adjustments for a given combination of day and month relative to ADT for a Monday in January. Table I.4 shows the consolidated table of demand ratios for the example problem, and Table I.5 shows the percentage time of year by season and demand pattern. Step 4. Estimating Severe-Weather Frequencies Exhibit 10-15 in HCM2010 identifies five weather types (rain, snow, temperature, wind, and visibility) with varying intensity

238 Table I.3. Demand Ratios for I-40 Case Study (ADT for Mondays in January) Month Day of Week Monday Tuesday Wednesday Thursday Friday January 1.00 1.03 1.04 1.05 1.08 February 0.94 1.01 1.04 1.09 1.14 March 1.04 1.07 1.06 1.11 1.17 April 1.07 1.09 1.10 1.16 1.22 May 1.08 1.11 1.11 1.16 1.21 June 1.08 1.09 1.07 1.14 1.18 July 1.08 1.07 1.10 1.15 1.18 August 1.05 1.05 1.06 1.09 1.16 September 1.02 1.02 1.02 1.07 1.15 October 1.05 1.05 1.07 1.11 1.16 November 0.97 1.00 1.04 1.08 1.07 December 0.97 0.96 0.99 0.92 1.01 Input Worksheet - Directional Freeway Facility Release May 9th, 2012 FREEWAY SYSTEM TITLE: I-40 SEGMENT NUMBER : 1 2 3 4 5 6 7 8 SEGMENT LABEL : S01 147S 147N S04 147N 147S S07 Davis Type (B, ONR, OFR, R, or W) B OFR OFR B ONR ONR R OFR Length (ft) 4000 1500 1500 855 1300 1280 220 1280 Number of Lanes 3 3 3 3 3 3 4 4 FF Speed (Mi/hr) 70 70 70 70 70 70 70 70 Segment Demand (vph) 3,427 3,427 3,359 3,017 3,395 4,889 4,889 4,889 Vehicle Occupancy (pass/veh) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Capacity Adjustment Factor 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Origin Demand Adjustment Factor 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Destination Demand Adjustment Factor 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 FF Speed Adjustment Factor 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Lane Width (ft) 12 12 12 12 12 12 12 12 Lateral Clearance (ft) 4 4 4 4 4 4 4 4 % Trucks 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 % RV's 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Terrain level level level level level level level level Truck Passenger Car Equivalent ET 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 R.V. Passenger Car Equivalent ER 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 On-Ramp Demand (vph) 0 0 0 0 379 1,493 0 0 On-Ramp % Trucks 5 5 5 5 5 5 5 5 On-Ramp % RV's 0 0 0 0 0 0 0 0 Off-Ramp Demand(vph) 0 68 342 0 0 0 0 190 Off-Ramp % Trucks 5 5 5 5 5 5 5 5 Off-Ramp % RV's 0 0 0 0 0 0 0 0 Acc/ Dec Lane Length (ft) 300 300 300 300 800 1280 300 300 Number of Lanes on Ramp 1 1 1 1 1 1 1 1 Ramp on Left or Right (L / R) Right Right Right Right Right Left Right Right Ramp FFS (mi/hr) 45 45 45 45 45 55 45 45 Ramp Metering Rate (vph) 2100 2100 2100 2100 2100 2100 2100 2100 Ramp-to-Ramp Demand (vph) 0 0 0 0 0 0 0 0 Table I.2. Sample Freeway Input Entries for Seed File

239 Table I.4. Consolidated Demand Ratios for I-40 Case Study Season Monday– Wednesday Thursday Friday Average Winter 0.9969 1.0202 1.0765 1.0398 Spring 1.0813 1.1435 1.1989 1.0443 Summer 1.0689 1.1264 1.1767 1.0916 Fall 1.0267 1.0878 1.1281 1.1272 Average 1.0435 1.0945 1.1450 1.0744 Table I.5. Time of Year by Season and Demand Pattern Season Monday– Wednesday (%) Thursday (%) Friday (%) Average (%) Winter 13.903 4.887 5.255 24.045 Spring 15.179 4.933 4.933 25.045 Summer 15.475 5.022 5.022 25.519 Fall 15.246 5.066 5.079 25.391 Average 59.804 19.907 20.289 100.000 levels that affect the capacity of freeways. Some of these categories or intensity levels have a negligible effect on free- way capacities (4% or less effect) and are consequently neglected in the reliability analysis. Based on this criterion, rain under 0.10 in./h, temperature events above -4°F, and all wind events are consolidated into the nonsevere weather category because of their negligible effects on capacity. A 10-year weather history of National Weather Service meteo- rological aviation report data was obtained for the nearby Raleigh–Durham Airport from Weather Underground (http://www.wunderground.com/history/). The data were filtered to eliminate unknown (-9999) con- ditions. The time between reports was calculated to obtain the duration of each weather report and to account for miss- ing reports. The data were then classified into the categories defined in Table I.6. Table I.6. Presence of Weather Categories on I-40 by Percentage Time per Month Month Rain Snow Severe Cold (%) Visibility Nonsevere Weather (%) Med. (%) Heavy (%) Light (%) Light–Med. (%) Med.–Heavy (%) Heavy (%) Low (%) Very Low (%) Min. (%) January 1.97 0.00 5.91 0.00 0.00 0.00 0.00 0.00 0.00 0.00 92.12 February 2.72 0.00 0.00 0.00 0.00 0.00 0.00 2.17 0.00 0.00 95.11 March 0.51 0.00 1.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 98.48 April 0.00 0.54 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 99.46 May 1.95 1.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 96.10 June 0.51 0.51 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 98.99 July 0.50 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 99.00 August 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100.00 September 4.26 0.53 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 95.21 October 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100.00 November 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100.00 December 0.00 0.00 7.81 0.49 0.00 0.00 0.00 0.00 0.00 0.00 91.71 Year 1.03 0.34 1.23 0.04 0.00 0.00 0.00 0.18 0.00 0.00 97.18 Note: Med. = medium; Min. = minimal. The percentage of time during the reliability reporting period that each of the weather categories are present was computed by dividing the total number of minutes for each weather category observed in the prior 10 years during the reliability reporting period by the total number of minutes within the reliability reporting period (Table I.6). The total number of minutes within the reliability reporting period for the 10-year period of weather observations (939,600 min) was computed for this example by multiplying the 6-h study period per day by 60 min per hour by 261 weekdays per year (five weekdays per week times 52 weeks per year plus 1 day) by 10 years. In cases for which multiple weather categories are present (e.g., poor visibility during a snow event), the most severe condition (the one most affecting capacity) is assumed to control, and the event is assigned to that weather category.

240 Entries are minutes of identified weather type divided by total minutes of weekday study periods (in this example, weekdays, 6-h p.m. peak) for that month. Monthly and annual percentages total to 100% for each month and for the full year. Weather categories with less than 0.1% probability for a given month in the 10-year weather history were dropped from further consideration to manage the number of scenarios. Based on this criterion, severe cold, medium-heavy and heavy snow, and very low and minimal visibility were dropped, and the probabilities of all remaining categories renormalized to add up to 100%. The final set of six weather categories and intensity levels selected for this example problem are shown in Table I.7 along with their estimated probabilities. Seasonal weather probabilities are assumed to apply iden- tically to all demand patterns within the season, and weather is assumed to be independent of demand pattern within the season. Step 5. Estimating Incident Frequencies Exhibit 10-17 in HCM2010 identifies the capacity effects of five incident types (shoulder disablement, shoulder accident, one lane blocked, two lanes blocked, and three lanes blocked). The shoulder disablement category was dropped for this exam- ple problem because its capacity effects are 1% for facilities with three or more lanes, such as the facility in this example. The HCM analysis method, like all methods limited to a single facility, cannot produce meaningful results for com- plete facility closures, since any methodology confined to a single facility cannot predict demand rerouting to other facil- ities. Therefore, the evaluation of incidents in this example is limited to incidents that maintain at least one lane open to traffic. The facility is mostly four lanes in one direction, but there are some segments with only two or three lanes. In this example, generalized crash data were available, but reliable incident logs that indicated incident type by number of lanes closed were not. Five years of crash data were obtained for the 12.5-mi-long eastbound direction of I-40. The data indicated that this portion of I-40 experiences an average of 164.5 crashes per 100 million vehicle miles traveled (VMT). The crash rate for this facility was then expanded to inci- dents by lane and shoulder closure type by using an expansion factor. A local study comparing shoulder and lane closure incidents to reported crashes found that there were approxi- mately seven incidents involving shoulder or lane closures for every reported crash on I-40. The expected number of incidents I by month m for the facility is computed as shown in Equation I.1: CR ICR VMT seed DM 100 10 SFDM (I.1) 6 I m m( ) ( ) ( )= × × × × × where Im = expected number of incidents in month m in the subject direction of travel; CR = reported crash rate, crashes per 100 million VMT; ICR = ratio of incidents to reported crashes, incidents/crash; VMT(seed) = seed file VMT on facility in subject direction during study period, VMT; DM(m) = demand multiplier for month m; and SFDM = seed file demand multiplier, the ratio of seed file study period demand to AADT for the study period. The estimated number of incidents is split into severity types and mean durations by using the values shown in Table I.8. Finally, the probability of an incident type is computed as shown by Equation I.2: ( ) = − ( )( ) ( ) ( )− × ×, 1 (I.2)p t m e SPI m P t D t where p(t,m) = probability that incident type t is present in month m; I(m) = expected number of incidents in subject direction in month m; P(t) = proportion of incidents of type t; D(t) = mean duration of incidents of type t, min; and SP = study period duration, min. Table I.7. Estimated Percentage of Time Weather Events Present on I-40 by Season Season Medium Rain (%) Heavy Rain (%) Light Snow (%) Light–Med. Snow (%) Low Visibility (%) Normal Weather (%) Total (%) Winter 1.496 0.000 4.745 0.175 0.679 92.905 100.000 Spring 0.797 0.802 0.352 0.000 0.000 98.049 100.000 Summer 0.335 0.335 0.000 0.000 0.000 99.330 100.000 Fall 1.440 0.180 0.000 0.000 0.000 98.380 100.000 Total 1.010 0.332 1.229 0.042 0.163 97.223 100.000

241 The resulting estimated average percentage time with inci- dents present on the facility is shown in Table I.9. Results that are specific to individual demand patterns are too numerous to show here. The entries in Table I.9 represent the probability of having a given incident type in each month. The values were com- puted using a crash rate of 164.5 per 100 million VMT, a rounded crash-to-incident expansion factor of 7, and a seed VMT of 330,006 in Equation I.2. Incidents were computed using Equation I.1. Monthly and annual values total to 100% for each demand pattern. Step 6. Generating Scenarios and the Probabilities of Their Occurrence Base Scenario Development The base scenario represents a specific combination of a demand level, a weather type, and an incident type. The demand levels are specified by month and day of week rather than by volume level. This specification enables the analyst to partially account for the effects of demand on incidents, and the effects of weather on demand, by using calendar-specific weather and incident probabilities. The initial estimate of the percentage time that each scenario represents of the reliability reporting period is the product of the demand, weather, and incident type percentage times that combine to describe the scenario, as shown by Equation I.3. The assumption is that the percentage time of incidents and the percentage time of weather are a function of the calendar month and that other correlations between demand, incidents, and weather can be neglected. ( ) ( ) ( )( )= × ×PT , , PT PT PT (I.3)d w t d w d t d where PT(d,w,t) = percentage time associated with demand pattern d with weather type w and incident type t; Table I.8. Mean Duration and Distribution of Incidents by Severity Severity Shoulder Closed One Lane Closed Two Lanes Closed Three or More Lanes Closed Total Mean incidents (%) 75.4% 19.6% 3.1% 1.9% 100.0% Mean duration (min) 34.0 34.0 53.6 69.6 35.4a a Average weighted by the relative frequencies. Table I.9. Estimated Percentage of Time Incidents Present on I-40 Eastbound Month Incident Type No Incident (%) Shoulder Closed (%) One Lane Closed (%) Two Lanes Closed (%) Three Lanes Closed (%) Four Lanes Closed (%) January 66.42 23.30 7.06 1.79 1.43 0.00 February 66.36 23.34 7.08 1.79 1.43 0.00 March 65.10 24.18 7.36 1.87 1.49 0.00 April 63.79 25.05 7.66 1.94 1.56 0.00 May 63.87 25.00 7.64 1.94 1.55 0.00 June 64.53 24.56 7.49 1.90 1.52 0.00 July 64.10 24.85 7.59 1.93 1.54 0.00 August 65.30 24.04 7.32 1.86 1.48 0.00 September 65.97 23.60 7.17 1.82 1.45 0.00 October 65.04 24.22 7.38 1.87 1.50 0.00 November 66.79 23.05 6.98 1.77 1.41 0.00 December 68.56 21.86 6.59 1.67 1.33 0.00

242 PT(d) = percentage time of demand pattern d within the reliability reporting period; PT(w|d) = percentage time of weather type w associated with demand pattern d; and PT(t|d) = percentage time of incident type t associated with demand pattern d. Table I.10 shows the initial estimated scenario percentage times before the details as to starting time, location, and duration of incidents and weather have been specified. This table shows the results for only normal weather conditions. Similar computations and results are obtained for the other weather conditions. Note that the initial probabilities for all weather and incident conditions must sum to the percentage time for each demand pattern within each season. For computing percentage time of incident type t associ- ated with demand pattern d, the probabilities presented in Table I.10 are averaged and weighted by the number of days each demand pattern has in the calendar. All entries are percentage time within the reliability reporting period when the specified conditions are present on the facility. Not shown are percentages for rain, snow, and low-visibility conditions. Percentages are computed using Equation I.3 and percentages from Table I.6, Table I.8, and Table I.10. Table I.11 shows the final estimated scenario probabilities for the scenarios involving nonsevere weather. Not shown are similar tables for rain, snow, and low-visibility conditions used to derive the severe-weather column. Specifying Incident and Weather Scenario Details The incident starting time, duration, and location must be specified for incident scenarios. To ensure that a representative cross section of performance results are obtained, each inci- dent scenario involving a closure of some kind is subdivided into 18 possible subscenarios (two start times, three locations, and three durations): • Start at the beginning or the middle of the study period; • Located at the beginning, middle, or end of the facility; and • Enduring for the 25th, 50th, or 75th percentile highest duration for a given incident type. Note that some subscenario options may be prohibited. For example, if the beginning, middle, or end of the facility only has three lanes, then the three-lane closure scenario is not modeled for this condition. In this case, the subscenario is removed from the total list of scenarios, and subscenarios and the probability for the removed subscenario are assigned proportionally to the remaining subscenarios. Each of the 18 incident subscenarios is considered equally probable within the base incident scenario. Thus, each sub- scenario is given one-eighteenth the probability of the base scenario for the incident type. For example, the scenario associated with Demand Pattern 1 (Mondays to Wednesdays in winter) with nonsevere weather and a shoulder closure has a 4.00645% probability of occur- rence. Thus, the subscenario associated with the incident Table I.10. Percentage Times for Incident Scenarios in Nonsevere Weather Season Day No Incident (%) Shoulder Closure (%) One Lane Closed (%) Two Lanes Closed (%) Three Lanes Closed (%) Subtotal Nonsevere Weather (%) Subtotal Severe Weather (%) Total (%) Winter M–W 8.847 3.005 0.909 0.230 0.184 13.176 1.000 14.176 Thu 3.110 1.053 0.319 0.081 0.064 4.626 0.355 4.981 Fri 3.344 1.135 0.343 0.087 0.070 4.979 0.385 5.364 Spring M–W 9.660 3.710 1.132 0.287 0.230 15.019 0.307 15.326 Thu 3.139 1.210 0.369 0.094 0.075 4.887 0.094 4.981 Fri 3.139 1.210 0.369 0.094 0.075 4.887 0.094 4.981 Summer M–W 9.848 3.724 1.135 0.288 0.230 15.226 0.100 15.326 Thu 3.196 1.212 0.370 0.094 0.075 4.946 0.035 4.981 Fri 3.196 1.212 0.370 0.094 0.075 4.946 0.035 4.981 Fall M–W 9.702 3.468 1.053 0.267 0.213 14.704 0.239 14.943 Thu 3.224 1.155 0.351 0.089 0.071 4.889 0.092 4.981 Fri 3.232 1.161 0.353 0.089 0.072 4.907 0.074 4.981 Total All 63.637 23.255 7.073 1.794 1.434 97.194 2.806 100.000 Note: M = Monday; W = Wednesday; Thu = Thursday; Fri = Friday.

243 starting at the beginning of the study period, in the middle segment, and for an average duration will have a 4.00645%/ 18 = 0.22258% probability of occurrence. The starting time and duration must also be specified for the severe-weather scenarios (e.g., rain, snow). Weather is assumed to apply equally across the entire facility. To ensure that a representative cross section of performance results is obtained, each severe-weather scenario is subdivided into two possible subscenarios: severe weather beginning at the start of the study period and severe weather beginning in the middle of the study period. Each weather subscenario for each severe-weather base scenario is given one-half the probability of the base sce- nario for the weather type. For example, the scenario associ- ated with Demand Pattern 1 (Mondays to Wednesdays in winter), with light snow and no incident, has a 0.22294% probability of occurrence. Therefore, the subscenario associ- ated with the weather event starting at the beginning of the study period will have a 0.22294%/2 = 0.11147% probability of occurrence. Removal of Improbable and Infeasible Scenarios Theoretically, the procedure can generate up to 22,932 scenar- ios and subscenarios for the subject facility. Many of these may have exceptionally low or near-zero probability. In addition, some may be infeasible—for example, a two- or three-lane closure on a two-lane freeway segment. For this example, the improbable and zero-probability scenarios or subscenarios were removed from the reliability analysis. These exclusions translate to an inclusion threshold of near zero, meaning that all scenarios with probability greater than zero are included in the analysis. This inclusion threshold left 2,058 scenarios to be used in evaluating travel time reliability for the I-40 facility. Table I.12 shows the final scenario categorization. It should be noted that the percentages shown here are not the probabilities of occurrence. They indicate the proportion- ate number of HCM analyses that will be performed on each scenario type for the reliability analysis. This is because each 6-h study period for incident and weather scenarios contains many 15-min analysis time periods characterized by fair weather and no incident conditions. The numbers shown in Table I.12 ensure that the initial incident and weather probabilities are honored. Table I.11. Estimated Incident Scenario Probabilities After Adjustment Season Day Nonsevere Weather Weather Subtotals Total (%) No Incident (%) Shoulder Closed (%) One Lane Closed (%) Two Lanes Closed (%) Three Lanes Closed (%) Nonsevere (%) Severe (%) Winter M–W 0.008 4.006 3.637 1.373 0.871 9.896 4.28 14.176 Thu 0.027 1.404 1.274 0.481 0.305 3.491 1.49 4.981 Fri 0.018 1.513 1.374 0.519 0.329 3.753 1.61 5.364 Spring M–W 0.431 4.947 4.529 1.706 1.083 12.695 2.63 15.326 Thu 0.153 1.614 1.478 0.557 0.354 4.155 0.83 4.981 Fri 0.153 1.614 1.478 0.557 0.354 4.155 0.83 4.981 Summer M–W 0.581 6.384 4.541 1.721 1.098 14.324 1.00 15.326 Thu 0.161 2.078 1.478 0.560 0.357 4.634 0.35 4.981 Fri 0.161 2.078 1.478 0.560 0.357 4.634 0.35 4.981 Fall M–W 0.167 5.946 4.213 1.591 1.012 12.929 2.01 14.943 Thu 0.206 1.732 1.403 0.529 0.336 4.206 0.78 4.981 Fri 0.087 1.991 1.411 0.533 0.339 4.361 0.62 4.981 Total All 2.154 35.305 28.293 10.687 6.795 83.235 16.77 100.00 Table I.12. Final Scenario Categorization Scenario Type No. of Scenarios and Subscenarios Total (%) No incidents and nonsevere weather 12 0.6 No incidents and severe weather 66 3.2 Incidents and nonsevere weather 528 25.7 Incidents and severe weather 1,452 70.6 Total 2,058 100.0

244 Step 7. Applying the HCM2010 Freeway Facility Analysis Method The HCM2010 freeway facility analysis method was applied to each of the 2,058 scenarios with capacity and speed–flow curve adjustments appropriate for each scenario. The standard HCM freeway speed–flow curves are not appropriate when modeling incidents and weather. There- fore, as described in HCM2010, Chapter 37, a modified ver- sion of Equation 25-1 from Chapter 25 (Freeway Facilities: Supplemental) is used in combination with the combined capacity adjustment factors (CAFs) and speed adjustment factors (SAFs) to predict basic freeway segment performance under incident and severe-weather scenarios, as shown by Equation I.4: ( )= × + −   ( )( )× + − × ∗ ×FFS SAF 1 (I.4)S e ln FFS SAF 1 CAF45 CAFC vC p where S = segment speed, mph; FFS = segment free-flow speed, mph; SAF = segment SAF; C = original segment capacity, passenger cars per hour per lane (pcphpl); and np = segment flow rate, pcphpl. CAFs and free-flow SAFs for weather are selected for the I-40 facility based on its free-flow speed of 70 mph, as shown in Table I.13. The CAFs for segments with incidents on I-40 are selected based on the number of lanes in the subject direction for the segment where the incident is located (Table I.14). The free- flow SAF for incidents is set at 1.00. It is important to note that the factors in Table I.14 do not include the effect of the number of closed lanes. In other words, both the number of lanes closed and the resulting capacity per open lane on the segment must be specified by the user. For scenarios with both incidents and severe weather, the CAFs are multiplied to estimate their combined effect. CAFs and SAFs are also applied to the merge, diverge, and weaving segments along the facility, as described in HCM2010, Chapter 37, Travel Time Reliability: Supplemental. Step 8. Performing Quality Control and Error Checking and Determining Inclusion Thresholds Quality control and error checking start with the base scenario (seed file) and proceed to the nonincident, nonsevere weather scenarios. Error Checks of the Seed File It is difficult to quality control 2,058 scenarios, so it is rec- ommended that the analyst focus on error checking and quality control on the single initial HCM seed file that is used to generate the 2,058 scenarios. The file should be error checked to the analyst’s satisfaction to ensure that it accu- rately represents real-world congestion on the freeway facil- ity under recurring demand conditions with no incidents and under nonsevere 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 seed file will be crucial, because it will be multiplied 2,058 times by the scenario generator. Error Checks for Nonincident and Nonsevere Weather Scenarios Once the seed file has been error checked, the next step is to look at the denied entry statistic for each of the scenarios that do not involve severe weather or incidents. The number of vehicles denied entry to the facility (and not stored on one of its entry links or ramps) should be as near zero as possible for nonsevere weather, nonincident conditions. If feasible, the entry links and ramps should be extended in length to ensure Table I.13. CAFs and Free-Flow SAFs for Weather on I-40 Medium Rain Heavy Rain Light Snow Light– Medium Snow Low Visibility Nonsevere Weather CAF 0.91 0.84 0.95 0.90 0.90 1.00 SAF 0.93 0.92 0.87 0.86 0.94 1.00 Table I.14. CAFs per Open Lane for Incidents on I-40 Initial Lanes No Incident Shoulder Closure One Lane Closed Two Lanes Closed Three Lanes Closed 2 1.00 0.81 0.70 N/A N/A 3 1.00 0.83 0.74 0.51 N/A 4 1.00 0.85 0.77 0.50 0.52 N/A = not applicable, scenario not feasible.

245 that all vehicle delays for these demand-only scenarios are accounted for within the facility or its entry links and ramps. The number of vehicles queued on the facility (and its entry links and ramps) during the first analysis period should be nearly the same as the number of vehicles queued in the last analysis period. If necessary, the study period should be extended with one or more artificial analysis periods to ensure that there is not a great change in the number of vehicles queued within the facility between the beginning and the end of the study period. Ideally, the number of vehicles queued in the first and last analysis periods should be zero. Inclusion Thresholds As mentioned earlier, the procedure can generate several thousand scenarios, many of which may have exceptionally low or exactly zero probability. In addition, some scenarios may be infeasible. The infeasible scenarios are automatically filtered out by the freeway scenario generation procedure. The scenarios with extremely low probability are not expected to be observed in the field in a single year; however, they are included in the predicted TTI distribution (with an inclusion threshold of zero). Their inclusion makes the comparison of the predicted and observed distributions hard to interpret. In addition, these scenarios tend to have exceptionally large TTI values that significantly shift the tail of the cumulative distri- bution to the right (i.e., toward higher TTI values). The procedure allows the user to specify an inclusion threshold to only include scenarios with a probability larger than the threshold specified in the analysis. For instance, an inclusion threshold of 1.0% means that only the scenarios with probability larger than 0.01 are considered in the analy- sis. Figure I.4 presents the TTI cumulative distributions for four inclusion threshold values for the subject facility, as well as the observed TTI distribution obtained from the INRIX. com data warehouse. For the subject facility, including all the scenarios with a nonzero probability in the analysis (i.e., an inclusion threshold equal to zero) resulted in a general over- estimation in the TTI cumulative distribution. Increasing the threshold to 1.0% brought the TTI distribution much closer to the observed distribution. An inclusion threshold of 1.2% resulted in matching PTI values for the predicted and observed TTI distributions. Inclusion thresholds larger than 1.2% yielded a general underestimation in the TTI distribution. Increasing the value of the inclusion threshold reduces the number of scenarios and consequently the runtime; however, at the same time it reduces the percentage of the coverage of feasible scenarios. In other words, the larger the value of the inclusion threshold, the higher the number of scenarios excluded from the analysis; thus, fewer numbers of feasible scenarios are covered (see Table I.15). As Table I.15 shows, the number of scenarios significantly drops as the value of the inclusion threshold increases. By going from an inclusion threshold of 0.00% to 0.01% half of the scenarios were eliminated, the runtime from more than 17 hours to around 6.5 hours was reduced, and the coverage of the distribution was decreased by only 0.29%. This means that more than a thousand of the scenarios contributed to only 0.29% of the TTI distribution. Step 9. Calculating Performance Measures The core and supplemental reliability performance measures computed for the example problem are shown in Table I.16. It should be noted that each observation from the I-40 data represents a 15-min mean TTI. For example, the PTI value of 5.34 is interpreted as the TTI associated with the highest fifth percentile analysis period out of all analysis periods covered in the reliability reporting period (in this case, 2,058 × 24 = 49,392 periods). It is critical that when certain TTI parame- ters are compared with each other that they are computed for identical time periods. The reliability rating was computed by summing the VMT in all analysis periods with TTI values below 1.33 and divid- ing the summed results by the sum of VMT in all analysis periods, as shown by Equation I.5: ∑ ∑= ∈RR VMT VMT (I.5)1.33 ss S s s where RR = reliability rating; S1.33 = a set including all analysis periods with TTI values less than 1.33; and VMTs = VMT in analysis period s. Figure I.4. Travel time distribution results for different inclusion thresholds.

246 Table I.15. Number of Scenarios, Runtime, and Coverage of Feasible Scenarios Inclusion Threshold No. of Scenarios Total Runtime (h:min) Average Runtime per Scenarios Coverage of the Distribution (%) 0.00% 2,058 17:18 30.3 100.00 0.01% 1,004 6:31 23.4 99.71 0.10% 496 3:03 22.1 97.46 1.00% 264 1:30 20.5 89.63 1.20% 210 1:05 18.6 85.07 1.30% 174 0:57 19.7 82.55 2.00% 84 0:26 18.6 75.91 3.00% 81 0:24 17.8 67.04 4.00% 4 0:01 15.0 37.32 Table I.16. Reliability Performance Measure Results for I-40 Measure Value Reliability rating 54.0% (core measure) Mean TTI 1.97 PTI 5.34 80th percentile TTI 2.03 Semistandard deviation 2.41 Failure/on-time (40 mph) 0.26 Standard deviation 2.21 Misery index 9.39 The PTI was computed by finding the 95th percentile high- est analysis period average facility TTI for the subject direction of travel. The 80th percentile TTI was simply the 80th percen- tile highest TTI (each of which is the average TTI for the analy- sis period for that scenario). The semistandard deviation was computed by subtracting one (in essence, the TTI at free-flow speed) from each of the facility average TTIs for each of the analysis periods, squaring each result, weighting each result by its probability, and sum- ming the results. The square root of the summed results was then taken to obtain the semistandard deviation, as shown by Equation I.6: ∑ ( )= −SSD TTI 1 (I.6)2ps s s where SSD = semistandard deviation (unitless); ps = probability for analysis period s; and TTIs = facility average TTI for analysis period s. The failure/on-time index was computed by summing the probability of all analysis periods that have an average speed less than 40 mph, as shown by Equation I.7: FOTI (I.7) 40 ∑= ∈ ps s S where FOTI is the failure/on-time ratio, and S40 is a set including all analysis periods with average speeds less than 40 mph. The standard deviation was computed by subtracting the average analysis period TTI (over the reliability reporting period) from each of the facility average TTIs for each of the analysis periods, squaring each of the results, weighting each result by its probability, and summing the results. The square root of the summed results was then taken to obtain the stan- dard deviation, as shown by Equation I.8: SD TTI TTI (I.8) 2∑ ( )= −ps s s where SD is standard deviation, and TTI is the average analy- sis period TTI over the reliability reporting period. The misery index was computed by averaging the highest 5% of travel times divided by the free-flow travel time, or in other words, by averaging the highest 5% TTIs, as shown by Equation I.9: MI TTI (I.9)5 5 p P s ss T ss T ∑ ∑= ∈ ∈ where MI is misery index, and T5 is a set including the highest 5% TTIs.

247 Table I.17. Evaluation of TTI and PTI Results for I-40 Statistic I-40 Reliability Agency Threshold of Acceptability Conclusion Mean TTI 1.97 <1.93 Marginally unsatisfactory PTI 5.34 <3.55 Unsatisfactory Table I.18. Evaluation of Policy TTI and PTI Results for I-40 Statistic I-40 Reliability at Agency Threshold of Acceptability Conclusion70 mph 40 mph 25 mph Policy index 1.97 1.13 0.68 >1.00 Unsatisfactory Step 10. Interpreting Results This step compares the reliability results with the agency’s established thresholds of acceptability and the diagnoses of the major contributors to unreliable travel times on I-40. During the scoping process for this example, the agency selected the mean TTI and the PTI as its reliability per- formance measures for this study. The calculated TTI and the PTI were compared with the thresholds of acceptable performance established at the start of this example prob- lem. Both statistics fell above the 90th percentile among freeways in the weekday a.m. peak period in the SHRP 2 Project L08 data set, and consequently did not meet the agency’s threshold of acceptability for reliable performance (see Table I.17). The agency’s congestion management goal is to operate its freeways at better than 40 mph during 50% of the peak peri- ods of the year and better than 25 mph during 95% of the peak periods during the year. The TTI shown in Table I.17 was recomputed for 40 mph and found to be 1.13 (Table I.18). This value is larger than 1.00, which means that the agency has not achieved this congestion management goal for the I-40 freeway. Similarly, the PTI shown in Table I.17 was recomputed for 25 mph and found to be less than or equal to 1.00, meaning that this goal was achieved. Reference Transportation Research Board. Highway Capacity Manual 2010. TRB of the National Academies, Washington, D.C., 2010.