National Academies Press: OpenBook

Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability (2008)

Chapter: Chapter 3 - Data Collection and Processing

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Suggested Citation:"Chapter 3 - Data Collection and Processing." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
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Suggested Citation:"Chapter 3 - Data Collection and Processing." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
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Suggested Citation:"Chapter 3 - Data Collection and Processing." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
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Suggested Citation:"Chapter 3 - Data Collection and Processing." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
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Suggested Citation:"Chapter 3 - Data Collection and Processing." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
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Suggested Citation:"Chapter 3 - Data Collection and Processing." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
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Suggested Citation:"Chapter 3 - Data Collection and Processing." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
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Suggested Citation:"Chapter 3 - Data Collection and Processing." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
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Suggested Citation:"Chapter 3 - Data Collection and Processing." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
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25 3.1 Introduction This chapter provides guidance on the collection of travel time, delay, and variability data from TMC, as well as other sources. The purpose of this chapter is to advise the analyst on the development of a data collection plan to support measures of travel time, delay, and reliability data for use in typical planning applications. This chapter is designed to address two very different data collection situations that the analyst is likely to confront. Most agencies will either be data-rich or data-poor. A data-rich agency will have continuous surveillance capabilities on some of the facilities being studied, usually from a TMC. A data- poor agency may have typical traffic volume data, but must put in place temporary data collection equipment or vehicles to gather travel-time data. Both data-rich and data-poor agencies can estimate mean travel time and mean delay using the strategies described in this chapter. This guidebook provides methods for estimat- ing mean travel time and mean delay for either data-rich or data-poor situations. Recommended minimum sample sizes are provided in this chapter. In contrast, data-poor agencies generally cannot measure travel-time reliability very well in the field without significant expense to gather the required data. An agency must have con- tinuous surveillance capabilities, or nearly so, in order to de- velop useful, cost-effective measures of reliability. As such, this guidebook does not provide a method for estimating travel- time reliability for data-poor situations, and no minimum sample sizes are provided for estimating travel-time reliabil- ity. The analyst generally must have continuous monitoring capabilities in order to adequately estimate reliability. 3.2 Data Collection Methods Analysts have the option of conducting their own travel-time data collection effort or obtaining the needed data from another agency or source. Before initiating an independent data collec- tion effort the analyst should first see if the data they need is already being collected by other agencies. If so, analysts should assess the extent to which this data meets their needs. Using data being collected for other purposes saves on data collection costs, which are not insignificant. Using data already being used for other purposes also is likely to ensure that the data is of acceptable quality. However, the data may not be in exactly the format or contain all of the variables required by the analyst. Additional time and effort may be needed to fill gaps and reformat the data to satisfy the needs of the analyst. A custom data collection effort has the advantage that the analyst gets exactly the data they need for the study. However, the set-up time and cost of custom data collection efforts are high. Exhibit 3.1 lists some of the typical advantages and disadvantages of using data collected for other purposes to generate travel time performance measures. The term typical is used to alert the reader that conditions, cost, and quality vary; each situation should be examined to reveal its unique characteristics. Exhibit 3.2 highlights typical agency or third-party travel time and delay data collection programs. The FHWA publication, Travel-Time Data Collection Handbook is an excellent source of information on the strengths, weaknesses, and costs of various travel-time data collection methods. Exhibits 3.3 and 3.4 highlight the strengths and weaknesses of various travel-time data collec- tion methods. 3.3 Data Collection Sampling Plan It is necessary to develop a sampling plan to collect data for selected time periods and at selected locations within the re- gion. Data collection that supports the desired analysis and measures will be more cost-effective and less problematic if a rigorous sampling plan is first developed. C H A P T E R 3 Data Collection and Processing

26 Option Typical Advantages Typical Disadvantages Custom Data Collection Tailor to specific analysis needs Greater quality control Expensive Time-consuming to collect Obtaining Data from Others Less expensive Readily available May not be exactly what is needed Quality less well known Exhibit 3.1. Advantages/disadvantages of using data collected for other purposes. 3.3.1 Sampling Strategies for O-D Trip Time Monitoring The collection of origin to destination trip times can be very expensive because of the numerous possible origins and destinations within any region. A region divided into 1,000 traffic analysis zones will have 1,000,000 possible O-D combinations. In addition, there are numerous paths between each O-D pair to further complicate the process of trip-time measurement. The analyst must therefore adopt a stratified sampling approach to reduce the measurement problem to a tractable size. A wide range of sampling strategies may be pursued, depending on the objectives of the analysis. Two strategies are described here to illustrate the general approach. The first sampling strategy described here seeks to gather travel-time data representative of the region as a whole. Possible O-D pairs are grouped into 10 categories (The num- ber of categories is determined by the analyst based upon the resources available to perform the data collection.) according to the minimum path trip length between each O-D pair. For example the O-D pairs might be grouped into those with trip lengths under 5 miles, those with trip lengths between 5 and 10 miles, etc. The analyst then randomly selects three O-D pairs from each category and measures the travel time several times for each O-D pair. The results can be summed to obtain regional totals by weighting the average travel time results for each category by the number of trips contained within each category. Another strategy would be to group the zones into super- districts. Three zones would then be randomly selected from each super-district and the travel times measured for the selected zone pairs. The results can be aggregated weighting the average travel times according to the number of trips represented by each super-district. 3.3.2 Sampling Strategies for System Monitoring If it is desired to develop travel-time information for the re- gional freeway system (or surface street system), collection of travel time for 100 percent of the road system will probably be beyond the means of most urban areas (unless the system is 100 percent instrumented with permanent vehicle detectors or travel time data collection devices). Even if the system is 100 percent instrumented, the number of locations and the volume of data may be much greater than the analyst can han- dle. In either case it becomes desirable to reduce the resources required by focusing on a select sample for freeway or road system segments within the region. A wide variety of sampling strategies are possible. The following two are described to illustrate the approach. If the objective of the study is to obtain travel-time meas- urements that could be used to characterize overall system performance then one sampling strategy would be to collect data every 5 miles (or every 10th detector) on the system. The length and mean speed for each sample location would be measured. The travel-time results for the individual sample segments would be expanded to system totals and averages using the ratio of total system miles to sample miles, or the ratio of total system vehicle-miles traveled to the vehicle-miles traveled on the sample sections. If the objective of the study is to identify system deficien- cies, then the analyst might adopt a different sampling strategy that focuses on system bottlenecks. Travel-time information would be collected only for the congested peri- ods or days and only on the higher volume segments of the regional freeway system. 3.3.3 Sample Size Requirements for Estimating Mean Delay or Travel Time Travel time varies randomly from hour to hour, day to day, and week to week throughout the year. It is never adequate to measure travel time only once. The analyst must measure the travel time between two points several times and compute the average travel time from the data. This section describes how to estimate the minimum num- ber of travel-time observations that would be required. The minimum number of observations is determined by preci- sion desired by the analyst. If the analyst needs to know the mean travel time very precisely, a large number of observa- tions will be required.

27 Agency Comments State DOTs On freeways within major urban areas the state DOT may have continuous count stations with counts and point speeds available every half mile of freeway and most ramps. In some states (e.g., Washington and California) the data may be available on a real-time basis over the Internet. 1 Floating car measurements of mean segment speed may be gathered on an annual basis for certain freeways in major urban areas as part of a congestion monitoring program. For freeways outside of major urban areas (and conventional state highways everywhere in the State), the state DOT may have a couple of weeks of hourly count data collected quarterly at scattered count stations. Speed, travel time, and delay data are not typically gathered at count stations outside of major urban areas. Counts, speed, and other data are often collected on an “as-needed” basis for upcoming highway improvement projects. Traffic Management Centers TMCs gather real-time speed and volume data for freeway segments at intervals that typically range from one-third to one mile. Data in some cases stored for longer than 24 hours. Detector reliability can be low depending on maintenance budget. A few TMCs (Los Angeles ATSAC for example) gather real-time volume data for city streets. TMC speed data for urban streets are generally considered less reliable. MPOs MPOs conduct travel behavior surveys every 5 to 10 years in which they ask travel-time information. MPOs involved in congestion management may commission annual surveys of peak-period speeds and travel times on specific road segments. Local Agencies Counties and cities gather traffic count data generally as part of specific studies for improvement projects. Speed data on road segments may be measured every few years in support of enforcement efforts (radar spot speed surveys). Private Company Several private companies collect travel time or speed data to disseminate as real- time traffic information. Other companies offer vehicle fleet monitoring services for real-time fleet management and dispatching, and may save “anonymized” vehicle position data that could be used to calculate travel time-based measures. A key consideration for this type of data is the negotiation of data rights such that the privately owned data can be used as needed by public agencies. American Community Survey The ACS is the annual replacement for the decennial census travel data. Some commuting measures are available if a region has invested in additional surveys to ensure statistical reliability at the local level. National Household Travel Survey As states have taken a more active role in measuring and forecasting travel demand, the NHTS is becoming more important as a source of state-level indicators for transportation planning and performance measurement. Products, such as the state profiles, freight data and statistics, seasonality statistics, etc., provide agencies with improved ability to apply national travel behavior data to local, regional, and state performance measurement and forecasting. 1The California Department of Transportation (Caltrans) has teamed with Partnership for Advanced Technology on Highways (PATH) at the University of California, Berkeley, to store traffic data and make it available on-line. Access to this data, known as the Freeway Performance Measurement System (PeMS), can be requested at http://pems.eecs.berkeley.edu/public/index.phtml. The Minnesota Department of Transportation (Mn/DOT) has a data collection and storage center at its Twin Cities office that integrates traffic, weather, and traffic incident data. Mn/DOT’s Regional Transportation Management Center (RTMC) can be reached at www.dit.state.mn.us/tmc/index.html. Interested parties may visit their office and download desired data onto a storage device. The State of Washington’s DOT, the first to archive real-time traffic data in the United States, will download requested information onto a suitable storage device such as a CD (see http://www.wsdot.wa.gov/traffic/seattle/traveltimes). Exhibit 3.2. Potential sources of travel time, delay, and reliability data.

Method Accuracy for General Purpose Vehicle Travel Time Variability Geographic Time of Day Modes Comments Floating Cars GPS DMI Excellent. Limited ability to collect variability data. Best for single facilities. Very costly to acquire data for extensive geographic area. Best for limited peak periods. Too costly for obtaining 24-hour data. Not practical for gathering bike data. Floating cars are cost inefficient for gathering travel time and delay, but the technology is commonly available and easy to apply. Too costly to collect data over broad arterial network or in nonpeak periods. Not practical for OD travel times. Feasible, but very costly to collect data for transit and freight modes. Transit Schedules Fair. Does not provide data on variance. Full coverage of region is inexpensive. No data outside service hours. Transit only. Average transit travel times can be approximated with transit schedules if transit agency has good schedule compliance. Not uniformly reliable for individual routes; may supplement with on-time performance statistics. Not reliable for systems that do not routinely monitor on-time performance. Retrospective survey Home Telephone Employer Piggyback on Other Efforts Limited because of respondents’ memories and tendency to round travel times. Limited ability to collect variability data due to rounding of reported times. Full geographic area coverage possible; costs vary. Unlikely to obtain good travel-time data for light travel periods of day (overnight). No Freight. Retrospective surveys which rely on travelers’ memories are generally less precise than prospective surveys. Good for obtaining OD trip times, although times not likely to be more accurate than to nearest 5 to 10 minutes. Costs decrease as tolerance for bias increases (sampling can be less rigorous (e.g., using employee surveys or web surveys)). Other variations on sampling possible. Many MPOs currently conduct commuter surveys; may be possible to piggyback on those current surveys. Prospective Home Survey (Manual Trip Diary) Fair to Good. Fair. Full coverage costly. Unlikely to obtain good travel-time data for light travel periods of day (overnight). No Freight. Prospective survey where the traveler is contacted in advance and asked to record all trip making the next day are generally more precise than retrospective surveys. Good for obtaining OD trip times. Most expensive and most accurate traveler survey method. GPS diaries have excellent accuracy but increase costs and require a long-term implementation timeframe. Exhibit 3.3. Travel-time data collection methods requiring little or no technology investment.

Method Accuracy Variability Geographic Time of Day Modes Observations Freight Tracking Logs GPS Excellent. Yes, but limited by sample size. Coverage dependent on participants. All Only Freight. Reliance on carriers to provide data likely impractical due to imposition on carrier. Loaner GPS units costly but provide incentive for carrier participation and increase accuracy. TMC Roadside Sensors Loops/RTMS (spot speeds) Excellent (for spot speeds, assuming adequate maintenance). Excellent Full coverage costly. All Best for freeways. Loop infrastructure unreliable without significant maintenance commitment. Possible to extrapolate travel time from speed data, depending on accuracy need. Vehicle signature matching, under development; may generate travel-time data in the long term. ETC Passive Probes Excellent. Excellent. Full coverage costly. All All, bike possible. ETC tags cheap, but roadside readers costly; therefore costly to get broad coverage, especially on arterials and therefore on transit. Deployed successfully for other purposes. Vehicle type identification nontrivial to implement. Areawide Passive Probes (GPS) Excellent. Good. Full coverage inexpensive. All No bike. GPS units currently expensive and complicated to install (by operators); costs may decrease, but this is a risk factor. Collecting data from GPS units is costly, and likely inconvenient. The only nonsurvey method that can collect door-to- door travel time. Transit Monitoring Systems Good. Yes, but limited by sample size. Depends on routes and roads covered. All Transit; may be used to estimate general purpose travel as well. Transit agencies are using a variety of tracking systems to provide on-time data to their patrons. This data can be synthesized for use in general-purpose traffic monitoring. License Plate Matching with OCR Excellent. Excellent. Full coverage costly. All No bike. Manual matching possible in short-term, but cost prohibitive without (long term) advances in OCR. Video equipment also expensive, especially to cover broad arterial network; therefore limited transit coverage. Exhibit 3.4. Travel-time data collection methods requiring major technology investment.

30 The minimum number of observations required to estab- lish a target confidence interval for the mean travel time or the mean delay is given by the following equation: (Eq. 3.1) where N = Minimum required number of observations; CI(1−alpha)% = The confidence interval for the true mean with probability of (1-alpha)%, where “alpha” equals the probability of the true mean not lying within the confidence interval; t(1−alpha/2), N−1 = The Student’s t statistic for the probability of two-sided error summing to alpha with N − 1 degrees of freedom; and s = The standard deviation in the measured travel times and the square root of the variance. Exhibit 3.5 illustrates the minimum number of observations required for various target levels of precision, expressed here in units of the standard deviation of the measured travel times or delay times. The desired precision is defined as the desired con- fidence interval (CI) in seconds divided by standard deviation (S) in seconds. For example, if the standard deviation in the delay is 1.5 seconds and the desired confidence interval is 3.0 seconds, the desired precision is 2.0 (i.e., 3.0 divided by 1.5 equals 2.0 standard deviations). It will take a minimum of eight observations to estimate the mean delay to within plus or minus 1.5 seconds (a total range or CI of 3.0 seconds) at a 95 percent confidence level. It is rare for an analyst to actually know what the standard deviation will be before conducting the delay or travel-time measurements. So the usual strategy is to take 10 measure- ments of the delay (or travel time), and then compute the sample standard deviation from those 10 measurements. The confidence interval for the mean is then computed, and if the computed confidence interval is satisfactory (e.g., less than the desired precision for the mean), no more measurements are required. If the computed confidence interval is unsatis- factory (e.g., too large), additional measurements of delay (or travel time) are made. Equation 3.1 is used to compute the total number of measurements required. The required num- ber of additional measurements is the difference between the total computed per Equation 3.1 and the number of measure- ments already completed (in this example, 10 measurements already would have been completed). 3.4 Collecting Data from TMCs Collecting data from TMC requires some special consider- ations. Most TMCs were created to monitor existing traffic conditions for the purpose of relaying information to the N t s CI N= ⎡ ⎣⎢ ⎤ ⎦⎥− − − 4 1 2 1 1 2 * *( / ), % α α public and to decrease response time to incidents for safety and congestion relief reasons. Most TMCs gather real-time traffic data using stationary devices such as in-pavement in- duction loop detectors, closed circuit television cameras, and other mounted systems. The future of data collection may in- clude gathering moving vehicle information from mobile phones and in-vehicle Global Positioning Systems (GPS) components. On freeways, in-pavement induction loop detectors are most common and collect traffic flow (vehicles per hour per lane), instantaneous speeds at the detector, and detector occupancy (fraction per time interval that vehicles occupy the detector). If the detectors in a roadway segment or facility are mostly functional and are located close together (no more than one mile apart), reasonable travel-time esti- mates can be made from the instantaneous speed data. A few agencies store this data and make it available to per- sons outside of the agency. Some TMCs, however, do not store their real-time data for more than 24 hours and do not make the stored data accessible to persons outside of the agency. Storage and dissemination of traffic data are technically feasi- ble. What is often the barrier is the lack of appointed responsi- bilities within the agency for data archiving, lack of a use for the data beyond the operation of the roadway, and developing policies for public access to the data. TMCs that collect real- time traffic data are primarily concerned with real-time oper- ations and are not funded or given directives for archiving data for nonagency use. Nonetheless, as transportation analysis incrementally includes more quantitative performance meas- ures related to travel time and delay, the necessity to collect and archive data, develop funding mechanisms, and implement policies on data access will become more pressing and agencies can be expected to respond positively. Planners conducting travel-time-related analysis on in- strumented highways should first explore what the TMC has to offer in terms of data before instituting a primary data col- lection effort. If a planning agency anticipates regular need for this type of data, it would be cost-effective to work with the TMC to develop general policies and protocols for obtaining TMC data. Once the planner has established a data collection plan, the following steps will provide useful guidance in collecting travel-time data on roadways covered by the TMC. Step 1. Identify TMC(s) and Traffic Manager(s) The first step is to identify the relevant TMC and agency operator collecting data for the desired geographic area and facility types. Some major urban areas have more than one TMC. If you are unsure where to begin, the state depart- ment of transportation is a good default starting point. State-operated TMC may focus exclusively on freeways,

31 Desired Precision (CI/S) Desired Confidence Minimum Observations 0.5 99% 130 0.5 95% 83 0.5 90% 64 1.0 99% 36 1.0 95% 23 1.0 90% 18 1.5 99% 18 1.5 95% 12 1.5 90% 9 2.0 99% 12 2.0 95% 8 2.0 90% 6 CI = desired confidence interval in seconds; and S = standard deviation in seconds. Exhibit 3.5. Minimum observations to obtain desired confidence interval. while locally operated TMCs often focus exclusively on city and county streets. Once all relevant TMCs have been iden- tified, contact the traffic manager for each, who is usually located in the Operations Department. Step 2. Communicate Data Collection Needs Determining the suitable data for your planning applica- tion will require direct contact with the TMC Traffic Manager or operations staff. Calculating performance measures will require real-time traffic surveillance data for the roadway seg- ments and time periods that are the focus of your analysis. This data must be archived (i.e., one or more days of data stored in readily retrievable format) to be useful. Ideally, the TMC will collect and archive speed and traffic flow data. If so, proceed to the next step regarding data access policies. If not, ask whether other agencies or private companies collect speed and traffic flow data for the study area roadway segments. If not, the planner will probably need to institute a primary data collection effort to generate measures of reliability. Step 3. Ascertain Data Access Policies Determine whether TMC policy allows access to real-time and/or archived data for downloading, and whether the agency will provide a copy of the unprocessed data for the roadway segments and times you specify. Asking for verbatim copies of unprocessed data bypasses most institutional prob- lems for agencies lacking policies and protocols for sharing data. Access to archived data will allow the planner to collect needed data in one pass. Access only to real-time data will require an extended collection effort, the length of which is determined by your sampling plan. If access is granted, pro- ceed to Step 4. If traffic managers are unable or unwilling to allow data access, ask if they share their data with Value Added Resellers (VAR) and, if so, whom. You may be able to obtain data from VARs for a fee. If not, the planner will probably need to institute a primary data collection effort. Step 4. Acquire Data The analyst can be quickly buried under the enormous amounts of detailed data available from TMCs, and should therefore establish in advance what locations, what times of day, what days of the week, and which weeks the data will be collected. The analyst should consult with the TMC staff regarding the reliability of the traffic detectors and whether certain locations tend to be more reliable than others. There are some readily available algorithms and techniques that can be used to manage these large datasets; the analyst should not sample the real-time data. If the traffic manager or VAR is able and willing to allow access to the database or make a copy of unprocessed data, you will need to ascertain what computer software is required for copying and/or reading the data. For answers to this question, the analyst may need to speak with IT personnel at the TMC. Depending on the TMC and the data requirements of the analyst, data acquisition may be feasible over the Internet or require the installation of specialized equipment at the

32 TMC. The analyst should monitor (or acquire from the TMC) any incident reports (accidents, work zones, bad weather, police actions, etc.) for the time periods of the data collection effort. 3.5 Processing/Quality Control Before proceeding to the computation of means, variances, and confidence intervals, the analyst should first review the travel time and delay data for errors. 3.5.1 Identification and Treatment of Errors and Outliers in Data An error is an obvious mistake in the measured data. An outlier is an observation that lies so far from the other observations that the investigator suspects that it might be an error. The analyst should first evaluate the measured travel times or delay data to eliminate obvious errors. The analyst should reject any data that violates physical limitations, such as negative travel times or speeds more than twice the design speed of the roadway. Any measured travel times or delays that are greater than the duration of the study are suspect as well. Most data analysis software packages or spreadsheet programs can be used to automatically flag any data record whose value violates a defined minimum or maximum. The analyst also should check records for unusual events occurring during data collection, including accidents, work zones, police actions, and bad weather. In most cases the analyst will not want to eliminate travel time and delay data gathered during unusual events, as this variation is what allows the data to describe variability in travel time or delay. If data are being collected to calibrate the speed-volume relationship in a transportation planning model, however, removing the incidents and events that regularly occur may be appropriate. The search for outliers is more subtle. A scatter plot of the data can be very helpful to the analyst in quickly spotting the few data points that do not seem to belong with the rest. A more mechanical search for outliers can be made by iden- tifying all points greater than 3 standard deviations above the mean, or less than 3 standard deviations below the mean travel time (or delay). Statistically, these outliers are not necessarily invalid observations, however, they are unlikely. The analyst should review the raw data sheets for the outlier observations and verify that no simple arithmetic error was made. If an error is found, it can be corrected. If no obvious error is found, the analyst must make a judgment call whether or not to retain the outliers in the data set. The analyst has four options for dealing with errors and outliers in the data: 1. Correct the error; 2. Repeat the field measurement; 3. Replace the outlier with a maximum or minimum accept- able value; or 4. Drop the data point from the data set. 3.5.2 Computation of Mean and Variance (Travel Time and Delay) The mean travel time is equal to the sum of the measured travel times (T) divided by the number of measurements (N). (Eq. 3.2) The variance is a measure of the spread of the distribution of observed travel times. (Eq. 3.3) where Mean(T) = The mean of the measured travel times; Var(T) = The estimated variance of the measured travel times; Ti = The measured travel time for observation number i; and N = Total number of observations of travel time. The mean delay and its variance are computed similarly, using the above two equations, substituting delay for travel time. Both the mean and variance can be estimated for travel times (or delay) from any desired sampling timeframe (e.g., throughout a 24-hour period) from the peak period or peak hour only, etc. Similarly, they can be computed including or excluding unusual incident-generated data points that lie outside the typical range of observations for periods of recur- ring congestion (i.e., nonincident). 3.5.3 Computation of Confidence Intervals (Travel Time and Delay) The confidence interval is the range of values within which the true mean value may lie. The confidence interval for the mean travel time or the mean delay is given by the following equation: (Eq. 3.4)CI Var 1 1 2 12− − −= ∗α α% ( / ), ( ) t T N N Var ( )T T T N i i i N i N = − ⎡ ⎣⎢ ⎤ ⎦⎥ − ∑∑ 2 2 1 Mean ( )T T N i i N = ∑

33 where CI(1-alpha)% = The confidence interval for the true mean with probability of (1−alpha)%, where “alpha” equals the probability of the true mean not lying within the confidence interval; t(1−alpha/2), N−1 = The Student’s t statistic for the probability of two-sided error summing to “alpha” with N − 1 degrees of freedom, where “N” equals the number of observations; and Var (T) = The variance in the measured travel times. The confidence interval for the true mean of delay also can be estimated with the above equation by substituting delay for travel time. Chapter 6 contains more detailed directions for data sam- pling and calculation of travel time/delay variance and relia- bility measures using estimated data, rather than observed or TMC data.

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TRB's National Cooperative Highway Research Program (NCHRP) Report 618: Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability explores a framework and methods to predict, measure, and report travel time, delay, and reliability from a customer-oriented perspective.

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