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14 C h a p t e r 2 Definitions for reliability Reliability is defined in engineering applications as âthe proba- bility that a component part, equipment, or system will satisfac- torily perform its intended function under given circumstances.â In statistics, reliability is defined as âthe amount of credence placed in a result. The precision of a measurement, as measured by the variance of repeated measurements of the same objectâ (Parker 2003). The Future Strategic Highway Research Program (F-SHRP) defined travel time reliability as the variation in travel times over time (e.g., hour-to-hour, day-to-day) (Cambridge Systematics, Inc. et al. 2003). SHRP 2 Project L03, Analytical Procedures for Determining the Impacts of Reliability Mitigation Strategies, defined the term as âthe level of consistency in travel conditions over time, [which] is measured by describing the distribution of travel times that occur over a substantial period of timeâ (Cam- bridge Systematics Inc. et al. 2013). Other SHRP 2 projects also used the concept of variability to define reliability. Given the wide range of viewpoints on what travel time reli- ability should encompass, the HCM2010 should have a broad definition of reliability. The following definition of travel time reliability is proposed: Travel time reliability aims to quantify the variation of travel time. It is defined using the entire range of travel times for a given trip, for a selected time period (e.g., the p.m. peak hour during weekdays) over a selected horizon (e.g., a year). For the purpose of measuring reliability, a trip can be defined as occur- ring on a specific segment, facility (combination of multiple consecutive segments), or any subset of the transportation net- work; or the definition can be broadened to include a travelerâs initial origin and final destination. Measuring travel time reli- ability requires that a sufficient history of travel times be present to track travel time performance. This history is described by the travel time distribution for a given trip. Once the travel time distribution is established, several per- formance measures can be established to capture reliability. The two general types of reliability performance measures are the following: 1. Those that capture the variability in travel times that occurs for a trip over the course of time; and 2. Those that reflect the number of trips that either âfailâ or âsucceedâ according to a predetermined performance stan- dard or schedule. In both cases, reliability (more appropriately, unreliability) is caused by the interaction of the factors that influence travel times: fluctuations in demand (which may result from daily or seasonal variation, or special events), traffic control devices, traffic incidents, inclement weather, work zones, and physical capacity (based on prevailing geometrics and traffic patterns). These factors produce travel times that vary from day to day for the same trip. Both types of reliability measures are quantified from the distribution of travel times, for a given facility or trip and the time period (e.g., weekday peak period), which occurs over a significant span of time. One year is generally long enough to capture nearly all of the variability caused by disruptions. A variety of metrics can be computed once the travel time dis- tribution has been established, including standard statistical measures (e.g., standard deviation, kurtosis), percentile-based measures (e.g., 95th percentile travel time, buffer index), on-time measures (e.g., percentage of trips completed within a travel time threshold), and failure measures (e.g., percent- age of trips that exceed a travel time threshold). The reliabil- ity of a facility or trip can be reported for different slices of time, such as weekday peak hour, weekday peak period, or weekend. Whether performance is being measured or predicted, uncertainty will intrude into the estimation of performance. In statistics, uncertainty is defined as âthe estimated amount . . . by which an observed or calculated value may differ from the true value.â Defining and Measuring Reliability
15 For the L08 project, no attempt was made to isolate the effects of measurement error or prediction error from the reliability measurements or estimates. The separate effects of measure- ment uncertainty on the reliability data sets were not accounted for. Similarly, when dealing with predictions of performance, no attempt was made to add a separate component for predic- tion uncertainty. Therefore, this projectâs measurements of reli- ability include measurement uncertainty and its predictions of reliability exclude prediction uncertainty. To the extent possible, analysts should compare model results with the performance of several facilities in their area by using locally developed inputs to gain an idea of the prediction uncertainty. terminology The following terminology from the HCM2010 is used in this report: â¢ Analysis period is the smallest time unit for which the HCM analysis procedure is applied. In the case of freeway and urban street facility analysis, the HCM analysis period is 15 min, although it can be of greater of duration, at the discretion of the analyst. Alternative tools may define dif- ferent analysis period lengths. â¢ Study period is the sum of the sequential analysis periods for which the HCM facility analysis procedure is applied (e.g., a 4-hour peak period). The study period is defined by the analyst for each specific application, on the basis of the guidance provided in the HCM. For the purposes of the L08 research, the following additional term is used: â¢ Reliability reporting period is the period over which reliability is to be estimated (e.g., the 250 nonholiday weekdays in a year). In essence, the reliability reporting period specifies the number of days for which the reliability analysis is to be performed. The three terms are illustrated in Figure 2.1. reliability Metrics A variety of measurement and modeling methods have been used to calculate travel time, which is the basis for reliability. In their purest form, travel times are directly measured as the time it takes vehicles to traverse a highway section with known or fixed endpoints. Excepting manual methods, this may be done with roadway or vehicle-based detection methods. In the roadway method, equipment placed at the endpoints detects the times that an individual vehicle passes the points. Several technologies can be used to detect vehicles passing a point, including toll tag readers, electronic license plate readers, vehicle signature recognition, and interception of signals from on-board electronic devices (e.g., Bluetooth). Vehicle-based methods require that equipment on the vehicle be capable of detecting and transmitting the vehicleâs time and location; this is usually done using global positioning system (GPS) technologies. Calculation of Travel Time Roadway and vehicle-based methods are the most accurate for measuring travel time because they are direct measurements. An indirect method of measuring travel times that is in wide- spread use is to use spot measurements of speeds from roadway detectors on uninterrupted-flow facilities; volumes and loop occupancies are usually measured as well. In this method, which relies on a series of relatively closely spaced (Â½ mile or less) roadway detectors, the spot speed measurement (generally HCM Study Period HCM Facility 66 66 69 70 63 66 66 66 66 68 68 65 69 63 63 63 68 66 60 67 63 39 64 64 64 70 70 65 38 39 67 67 62 64 68 40 18 37 69 69 64 70 37 14 14 40 65 65 69 39 25 21 16 37 69 69 66 65 38 13 11 37 70 70 68 63 62 40 18 38 67 67 63 63 62 68 40 37 68 68 64 61 65 62 61 39 61 61 63 63 60 65 67 63 63 63 65 70 64 63 67 64 64 6415:00 18:00 Reliability Reporting Period Da ily Re pe titi on s HCM Analysis Period HCM Analysis Segment Figure 2.1. Study facility and period, and analysis segment and period.
16 considered to be a time mean speed) from a detector is assumed to be constant over a fixed distance (e.g., half the distance to the next upstream and downstream detectors). If that distance is known, a travel time can be computed from the assumed speed and length. As already stated, the distribution of travel times is the starting point for measuring reliability. In a statistical sense, the distribution is continuous only if it is based on measuring travel times from individual vehicles. At the time of writ- ing, the data used to monitor travel timesâas well as model- ing methodsâare rarely managed in this way. For example, consider roadway detectors of spot speeds, which measure every vehicle that crosses their detection zone. These systems are designed to aggregate field measurements into 20- or 30-s summaries before transmission. Therefore, in its lowest form, the speed âmeasurementâ is really an average. The data are sometimes further aggregated to 1-, 5-, or 15-min summaries for archiving. At each aggregation, variability in the measure- ments is reduced. (When aggregating travel times over analy- sis periods, it is important to weight the travel time averages by volume or vehicle miles traveled, VMT, rather than taking just the arithmetic mean.) On the other hand, roadway- and vehicle-based systems have a sampling rate well below 100%. This discussion is relevant to this research. The macroscopic analysis engines used hereâFREEVAL (FREeway EVALuation) and STREETVAL (STREET eVALuation)âare not intended to produce travel times for individual vehicles. Instead, they produce an estimate of the mean travel time for each time slice studied, set at 15-min intervals by the HCM. Therefore, some variability is not accounted for in the analysis. The basic unit of measurement used to construct the travel time distribution, from which reliability metrics emerge, is then a 15-min aver- age. Likewise, if archived roadway spot speed detectors are used, the unit of measurement is also an average travel time for whatever aggregation level is used. Does this loss of variability information matter? The answer depends on the viewpoint and use of the method. If travel times from individual vehicles are used, then the result- ing reliability metrics will capture not only the effect of exter- nal sources (such as incidents and inclement weather) but the differences in driver behavior as well. Capturing the total amount of variation may be important for some applications. For practitioners, at least with current technologies, control- ling driver behavior is not an optionâdriver âaggressionâ is not affected by the control strategies that can currently be implemented. For capturing the effect of the major sources of congestion and reliability, the effect on driver behavior may be ignored. If this is done, then the resulting documentation must state that the reliability statistics developed do not account for differences in driver behavior. This is the case for the methods developed by this research. The research team emphasizes that, in interpreting the reliability metrics produced by HCM2010 methods, the estimate corresponds to the dis- tribution of aggregated travel times (into 15-min bins), as opposed to the individual driver experience. In other words, the mean of the HCM-based travel time distribution really is a mean of 15-min averages, as opposed to a (true) mean of individual travel time observations. Recommended Reliability Metrics As a starting point, the reliability metrics developed in SHRP 2 Project L03 (Cambridge Systematics, Inc. et al. 2013) were reviewed for relevancy to the HCM. A discussion of those measures follows. Metrics that describe the right half of the travel time distribution are the most appropriate for reliabil- ity, because that is the region in which the causes of unreli- able travel (disruptions and high demand) exert the most influence. The reliability rating is the percentage of trips experiencing a travel time index (TTI) less than 1.33 for freeways and 2.50 for urban streets. (The TTI is the travel time divided by the free-flow travel time.) The selected thresholds approximate the points at which most travelers would consider a facility congested; thus, the measure reflects the percentage of trips on a facility that experience conditions better than level of ser- vice F (LOS F). The difference in threshold TTI values results from differences in how the HCM defines free-flow speed for freeways versus urban streets, as TTI is measured relative to free-flow speed. The planning time index (PTI) and buffer index are starting to be used in practice, primarily for performance monitoring applications. The PTI is the 95th percentile travel time divided by the free-flow travel time, while the buffer index is the 95th percentile travel time divided by the mean or median travel time. SHRP 2 Project L03 found that the buffer index can be an unstable indicator of changes in reliability because it can move in a direction opposite to the mean and percentile-based mea- sures. This occurs because it uses both the 95th percentile and the median or mean travel time, and the percentage change in those values can vary from year to year. Although not specifi- cally tested during the L03 project, the skew statistic (the ratio of the difference between the 90th and 50th percentile TTIs and the difference between the 50th and 10th percentile TTIs) may also suffer from this phenomenon. These observations led the research team to the conclusion that L08 reliability metrics should be ones that are measured relative to the free-flow travel time. Metrics that are measured relative to parameters that can change (e.g., the mean or median) are not constant over mul- tiple 15-min time intervals. They are therefore more difficult to quantify across an extended time-space domain. The 80th percentile TTI has not been widely used. How- ever, SHRP 2 Project L03 found this measure to be more sen- sitive to operational changes than the 95th percentile TTI and
17 recommended its use. Furthermore, one of the more reliable past studies of reliability valuation used the difference between the 80th and 50th percentile travel times as the indi- cator of reliability. The misery index, the average of the highest 5% of travel times, approximates the 97.5 percentile TTI. This measure is useful as a descriptor of near-worst-case conditions on rural facilities. Standard deviation was not part of the L03 set of measures, but it should be added because of its use in applications. SHRP 2 Projects C04 and L04 use standard deviation as one of the terms in expanded utility functions that are used to predict traveler behavior. Several studies of reliability valuation have used stan- dard deviation as the measure that is valued. Failure and on-time measures are defined in two ways: (1) in reference to the median travel time (used to indicate âtypicalâ conditions for a trip) and (2) in relation to predetermined per- formance standards based on the space mean speed (SMS) of the trip. Because their construction is binary (a trip either passes or fails the condition), these measures can be insensitive to small changes in underlying performance. Therefore, they have been defined with multiple thresholds so that changes in per- formance can be more easily detected. The median-based mea- sures are constructed as on-time measures, while the SMS measures are constructed as failure measures. SHRP 2 Project L02 investigated two other metricsâthe semi- variance and its companion, the semistandard deviationâ for measuring reliability. These are computed similarly to the typical variance and standard deviation, except they pertain only to observations on one side of a reference value. (The variance and standard deviation measure both sides of a ref- erence value, which is the mean.) Project L02 selected the free-flow travel time as the reference value. The calculation of the semivariance is then the sum of the squared differences between observed travel times and the free-flow travel time, divided by the number of observations. The semistandard deviation is the square root of the semivariance. It is assumed that the free-flow travel time is the minimum travel time for the section. In practice, high-speed vehicles lead to lower travel times than that for free flow, but for consistency in measurement, the free-flow travel time is used. Project L02 found the semivariance to be a stable indicator of variation across multiple types of distributions. The L08 research team recommends adding the semistandard deviation as a reliabil- ity performance metric. In many cases, 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 travelerâs point of view and LOS F conditions as defined in HCM2010 Chapters 10 and 16, the research team recommends reporting the reliability rating as part of any HCM-based reli- ability analysis. On the basis of this discussion, the metrics in Table 2.1 are recommended for Project L08. Both variability- and failure- based metrics are included. Which metric should be highlighted as the primary reliability metric is difficult to say. Much depends on the specific application being used. In the interpretation of Table 2.1, many of the selected performance measures are defined relative to the free-flow travel time, rather than the aver- age travel time. This is deliberate because the average travel time (a) is not known before the analysis is conducted, (b) varies between different facilities, and (c) varies between different sce- narios (e.g., advanced traffic demand management treatments) for the same facility. Performance measures based on the aver- age travel time are therefore deemed to be less appropriate for HCM analysis and stratification of LOS. Table 2.1. Recommended Reliability Performance Measures for SHRP 2 Project L08 Reliability Performance Measure Definition Core Measure Reliability rating Percentage of trips serviced at or below a threshold travel time index (TTI) (1.33 for freeways, 2.50 for urban streets) Planning time index (PTI) 95th percentile TTI (95th percentile travel time divided by the free-flow travel time) 80th percentile TTI 80th percentile TTI (80th percentile travel time divided by the free-flow travel time) Semistandard deviation The standard deviation of travel time pegged to free-flow travel time rather than the mean travel time (variation is measured relative to free-flow travel time) Failure or on-time measures Percentage of trips with space mean speed less than 50, 45, and/or 30 mph Supplemental Measure Standard deviation Usual statistical definition Misery index (modified) The average of the highest 5% of travel times divided by the free-flow travel time