There are three important aspects to consider for reliability: Measurement (collecting data related to travel time reliability such as traffic speeds from the link or network of interest), Modeling (methodology for simulating scenarios for assessing reliability changes), and Valuation (monetary equivalents to reliability changes; covered in detail in the main article).
Recent efforts has focused on developing measures of reliability based on current deployed data collection systems. Loop detectors are the obvious candidate as they are almost ubiquitous and should already provide a significant amount of collected data. Loop detectors collect traffic flow rates, and detector occupancy (used to estimate traffic densities); also traffic speeds in the case of dual detectors. For single loop detectors, traffic speeds can be estimated. This information can be used to estimate travel times for the instrumented network. Typically, the instrumented network is composed of limited access links (i.e. freeways/highways). Other links' travel times may be estimated using other methods such as license plate matching. However, these methods do not generate a continuous data stream unlike loop detectors (see Zhang and Kwon, 1997).
The estimated travel times can be used to generate daily, weekly... distributions for the links of interest. These distributions can be characterized by statistical moments (i.e. average, variance...). Measures of reliability (or variability) can be applied on the travel time distributions. Common measures include: standard deviation, percentiles difference (also referred as time buffers), and others. In principle, other statistical moments (i.e. kurtosis, skewness) may also be significant for characterizing travel time distributions depending on how travel times are distributed (see Fosgerau 2009).
Two important aspects of links' travel time distributions are: theoretical distribution fitting (or shape), and routes' travel time distributions for given origin-destination pairs. Generally, normal distributions have been used to represent link travel times, but this is due more to tractability. The sum of normally distributed variates is also normally distributed, and thus routes travel time distributions will be normally distributed. Other distributions also include log-normal distributions as observed travel times are more likely asymmetric (i.e. skewed) than symmetric. Furthermore, recent research indicates that the Burr distribution might provide a good fit to the observed travel times (see Susilawati et al, 2010). Burr distributions has been used before in economics because of their closed form expressions, and are appropriate to random variables with only positive values. In econometrics, Burrit models have been used where the link function in the limited dependent model is defined by a Burr Cumulative Distribution function (see Maddala, 1983). In addition, a route travel time may be affected by nonzero elements in the covariance matrix (i.e. correlation among links) of the vector of random variates representing each of the links-travel times. This correlation means that the standard deviation for a route travel time distribution (if assumed to be obtained by the sum of identically and independently distributed links' travel times) may be overestimated or underestimated with large inaccuracy depending on the sign and magnitude of the covariances among the links' travel time variates. At the moment, most researchers assume links travel times to be identically and independently distributed. Taylor (2009) provides an example where the mentioned assumption may be inadequate. Taylor (2009) finds significant correlations among links using data from Tokyo. Another example is Zhu (2010), where possible route candidates are studied among commuters instrumented with GPS (Global Positioning System) devices in the Twin Cities. Zhu (2010) aggregates observations of travel times from GPS data (95 drivers deployed on the Twin Cities network) to estimate the travel time distribution of the links. Zhu empirically tests for normal distribution, and it provides a reasonable fit. Furthermore, Zhu explores two cases to estimate routes' travel time distributions where the links travel time distributions are perfectly correlated or independently distributed. In both cases, Zhu finds that travelers may be more likely to prefer diversity (as the number of commuters with dominant routes [defined as always superior to others in terms of mean travel time and variance of travel time] are few) in their route selection to deal with variability.
The previous discussion is tied directly to the development of Volume-Delay-Reliability (VDR) functions (or link performance functions with reliability) for travel demand models. VDR functions represent standard deviation of travel time as a function of variables including travel time, volume-capacity ratio, and others. The importance in the development of VDR functions is because travel demand modeling can be enhanced to model reliability changes (variability reduction improvements) due to changes to the network. At the moment, this is a topic of active research with several promising results. Vovsha (2009) presents several attempts of describing standard deviation through regression models with others variables such as: average travel time per mile; volume-capacity ratio; mean of median minutes per mile; and others. Vovsha concludes that an important difficulty (already mentioned in the previous discussion) lies in the correlation of links' standard deviations that compromise the standard deviation of routes for origin-destination pairs. A similar attempt to Vovsha is currently being researched in New Zealand (see Taylor, 2009) with similar variables (e.g. volume-capacity ration), but with other functional forms. Another attempt is by Franklin (2009), where the dependent variable is expected lateness (lateness - freeflow travel time ratio) instead of standard deviation. Franklin (2009) was able to fit a log-log polynomial regressions. The regressions included link attributes, such as length, free-flow speed, and a location indicator. However, the empirical approach taken by Franklin is simplistic. Franklin (2009) suggests that future research should attempt to model the supply and demand causes of travel time variation rather than simply model the variation. One approach would be to use a queuing model.
The research and practices of selected countries with respect to travel time reliability and its inclusion to Benefit-Cost Analyses are summarized here.
Readers should also refer to: http://www.internationaltransportforum.org/Proceedings/reliability/index.html
Australia and New Zealand.
Australia and New Zealand share transportation resources and research through Austroads (the Association of Australian and New Zealand Road Transport and Traffic Authorities), so the guidelines in the two countries are connected. Both countries use the standard deviation of travel time as a reliability performance indicator and explicitly include reliability in benefit-cost analysis.
Like the United States, Australia has a federal structure. The federal government can suggest guidelines, but states are free to adopt their own policies and evaluation techniques. The National Guidelines for Transport System Management in Australia focuses on providing benefit-cost guidelines for urban public transit. The states have their own well-developed benefit-cost guidelines for highway projects. In New Zealand, decisions are centralized, so benefit-cost guidelines apply across the country (Taylor 2009).
The National Guidelines for Transport System Management in Australia provides general guidance for incorporating travel time reliability in benefit-cost analysis. The guidelines note that unreliability “can be measured in standard deviations of trip times. Under plausible assumptions, the value of unreliability in trip times will be proportional to the number of standard deviations multiplied by the value of time” (Australian Transport Council 2009, p. 65). The background material in Volume 5 of the guidelines presents a suggested method for estimating the standard deviation of travel time for roadway initiatives and valuing the reliability benefits. This guidance is based on the NZ Transport Agency’s Economic Evaluation Manual. Specific dollar values are not specified for monetizing the value of reliability. However, Volume 5 of the Australian guidelines cites Bates et al (2001) and concludes that a value for the reliability ratio of 1.3 is plausible for car travel (Australian Transport Council 2009).
For public transportation, the guidelines estimate reliability benefits in terms of services running behind travel. Benefits are monetized using a value for “unexpected waiting time.” This is set at three times the value of time (Taylor 2009).
The NZ Transport Agency provides benefit-cost guidelines for New Zealand in its Economic Evaluation Manual. The manual assumes that standard deviations will be available in network skim matrices from travel demand models for major projects. For single roadway sections, the manual provides a formula for estimating the standard deviation of travel time.
The formula estimates the standard deviation from the v/c ratio. It takes the form of a log-shaped curve that approaches the base uncongested level of standard deviation at low v/c ratios and the maximum standard deviation at high v/c levels. The midpoint of the curve is calibrated to the average value at a v/c ratio of 1.0 (Australian Transport Council 2009). For the valuation, the Economic Evaluation Manual provides the following reliability ratio values: 0.8 for cars, 1.2 for commercial vehicles, and 0.9 for typical mixed urban traffic (NZ Transport Agency 2010).
Current French practices emphasize mobility and address reliability implicitly (see Delache, 2009). The most recent benefit-cost guidelines (Provisional Instruction for Road Project Appraisal) were published in 2007. The guidelines cover several benefits, such as travel time, safety, vehicle operating costs, greenhouse gases, biodiversity, noise, pollution, and comfort, but they do not mention reliability.
There has been a recent shift in philosophy from capacity management to traffic management. The new philosophy emphasizes multimodal approaches and intelligent transportation system (ITS) technologies. While reliability is not the main policy objective, its importance should increase under the new philosophy.
In 2004, the General Board of Roads and Bridges recommended that benefit-cost analysis be applied to traffic management strategies. French researchers are now making sure that evaluation tools appropriately capture reliability for traffic management strategies. Delache (2009) suggests one area for investigation is the value of travel time for unexpected delays, which is defined as delays beyond a set buffer time. Using this definition, Delache (2008) recently found that the value of unreliable travel varies from 2 to 20 times the value of time. For public transportation in Paris, the Syndicat des Transports d'Ile-de-France (STIF 2000) uses a value of six times the value of time for delays.
The Ministry of Land, Transport, and Infrastructure (MLIT) started a pilot study to determine how travel time reliability could be included in benefit-cost analysis for highway projects. MLIT is taking a “safety margin” approach. The idea is that some drivers operate under schedule constraints and allow additional time to ensure on-time arrival. MLIT assumes that travel times are normally distributed and estimate the safety margin using the coefficient of variation (standard deviation of travel time divided by the mean of travel time). Survey data suggests that the 95th percentile is a reasonable margin, so the safety margin would be calculated as:
Safety Margin = Travel Time × Coefficient of Variation × Z95th (Fukuda 2009)
The coefficient of variation is estimated from a curve that relates the coefficient to the average vehicle speed. MLIT is developing this relationship using probe and global positioning system (GPS) data for sample highway sections.
Although this pilot approach has not been adopted, Fukuda (2009) offers some issues with the approach. First, the reliability benefits should be estimated for travelers with schedule constraints. It is not clear whether this should include all travelers or a subset with specific constraints. Second, a value of reliability must be applied to the estimated safety margin. It is not clear whether this should equal the value of travel time or vary by type of traveler. The appropriate probability for the safety margin might also vary by traveler. Third, the current methodology assumes normally distribution travel times. Actual travel times are not normally distributed (as described by other researchers) and may be correlated across highway sections.
Fukuda at al (2009) have tried a new approach for valuing reliability based on the Fogerau-Karlström (2009) model. Using data from the Tomei Intercity Expressway near Tokyo, Fukuda et al (2009) estimated the reliability ratio (value of travel time reliability divided by the value of time). The estimate used 2.5 months of weekday travel data for travel between 6 am and 10 pm. Based on these data, Fukuda estimated that the value of travel time reliability is 0.966 times the value of time. Fukuda (2009) suggested that future studies in Japan need to explore the definition and measurement of travel time variability as well as estimate values of time and travel time reliability using stated preference methods (which are not common in Japan).
The Dutch define reliability as “the ability of the transport system to provide the expected level of service quality, on which users have organized their activities.” (Van der Waard 2009) Van der Waard noted that reliability can be improved by changing travel times or the expectation of travel time. Improvements can be made on the supply or the demand side to change reliability. Furthermore, reliability is compared to the expected travel time, which suggests that reliability can be measured by a scheduling equation or by measuring the standard deviation of the travel time distribution.
The 2020 Dutch Strategic Mobility Policy Document (“Nota Mobiliteit” or NoMo) sets a number of reliability goals. Examples include travelers reaching their destinations on time in 95 percent of cases and peak travel times not exceeding one and a half times the off-peak travel time. Key issues are identifying the causes of unreliability on a given link or network and implementing cost-effective strategies that improve reliability. Currently, benefit-cost analysis in the Netherlands does not incorporate reliability benefits. Incorporating these benefits may change investment priorities.
From the Dutch perspective, incorporating travel time reliability into the planning process requires three steps. In the first step, reliability needs to be measured. This assessment of the current problem can be accomplished through on-going monitoring. The second step is to model reliability, which allows the future conditions to be forecasted and the potential impacts of solutions to be predicted. The third step is to value reliability in benefit-cost assessments.
Travel time reliability can be measured in the Netherlands using loop detector data. Two indicators applicable to measuring reliability are: 1) percent of users on roadway with expect travel time objectives met, and 2) the standard deviation of travel time. The first measure is similar to the TTI Buffer Index and is close to the NoMO goal, while the second measure is more useful for research and benefit-cost applications (Van der Waard 2009).
The Dutch have taken two approaches to modeling reliability. The first approach examines the vulnerability of the network from a system perspective. The “robustness scanner application” allows planners to determine the number of alternative routes and the remaining capacity on the alternative routes. This approach is probably more applicable to system planning than to benefit-cost analysis. The second approach models travel time variation from the user perspective using the Simulation Model for Analyzing the Reliability of Accessibility (SMARA). The model uses output from a network travel demand model. The variations of travel times are estimated by applying Monte Carlo simulation of input variables, such as travel demand and link capacity. The output is presented as percent of trips on time. A post processing tool can calculate the reliability indicators using relationships with output variables (Van der Waard 2009).
The Dutch have begun to value travel time reliability for benefit-cost analysis. A uniform approach to benefit-cost analysis was adopted in 1998. A 2004 literature search on reliability valuation identified travel time reliability as an important benefit that should be incorporated into benefit-cost analysis. An international expert meeting was convened in 2005. The expert panel concluded that the standard deviation of travel time is an appropriate indicator for including in benefit-cost analysis.
Eliasson (2009) presented the current state of the practice for incorporating reliability in benefit-cost analysis in Sweden. Eliasson indicated that travel time reliability should be included in benefit-cost analysis, because uncertain travel times add travel costs through experienced delays and the need for margins (or buffers) when choosing departure times. ITS technology and pricing are important operational tools that point to the need to include reliability in benefit-cost analysis. For example, the implementation of congestion charges in Stockholm in 2006 resulted in 30 to 50 percent less time in queues and less variability. Reliability must be measured to capture this benefit.
Several studies have placed values on travel time reliability. Assuming free choice of departure time, short headways, and a given travel time distribution, the disutility of travel time uncertainty can be shown to be proportional to the standard deviation of travel time. Eliasson also noted that stated preference surveys indicate that value of time estimates are independent of the standard deviation (i.e., value of time estimates do not have some portion of reliability “built in”).
For evaluating projects, a method is needed to forecast travel time variation. Eliasson (2006) has estimated relationships between congestion and the standard deviation of travel time. The estimated standard deviations are not used during traffic assignment, but as an evaluation measure for the benefit-cost analysis once the travel is forecasted in the model. To make the skimming of the standard deviations easier, link travel times are assumed to be uncorrelated. Although this assumption is not true, the error does not seem to be large for Stockholm freeways. Also, Emme/2 tends to underestimate high congestion, so the standard deviation is underestimated (Eliasson 2009). For long-distance trains, the Swedes use a slightly different method for valuing travel time reliability. Delays are defined as the difference between actual and scheduled arrival time (assuming the actual arrival occurs after later). In practice, the delay is valued at two times the value of time. However, recent research (Börjesson and Eliasson 2009) has shown that the value of delay rises slower than the risk. The two times factor should be higher (five to ten times), but in practice the two times factor is changed to three or four. Freight travel is treated the same as person travel (two times the value of time).
The UK introduced the New Approach to Appraisal (NATA) in 2008 as an analytical framework for appraising major transportation projects seeking funding or approval from the Department for Transport. Value for Money (VfM) analysis is an important factor in decision making and helps in project prioritization. VfM includes both qualitative and quantitative assessments of benefits as well as factors that can be monetized in a benefit-cost analysis.
The UK includes only factors with adequate evidence for valuation in the benefit-cost analysis. These factors (e.g. time savings, noise, operations cost...) have dedicated units in the online WebTAG (Transport Analysis Guidance), which describes the appropriate procedure for monetizing the benefits. The AST also includes factors with some evidence for monetization, but not enough evidence for inclusion in the benefit-cost analysis. Travel time reliability improvements fall under some valuation evidence category, but no monetized values are assigned to them.
The UK Department for Transport has worked on developing guidance for incorporating travel time reliability in project evaluations. WebTAG Unit 3.5.7 is in draft form and provides the current appraisal guidance. The WebTAG suggests using the standard deviation of travel time (SD TT) as the measure of reliability for highways and the “average lateness about the scheduled arrival time” as the measure for transit (i.e., rail and buses). For highways, the WebTAG suggests valuing one minute of SD TT equal to 0.8 times the value of time (VOT) for one minute. For transit, the WebTAG suggests valuing one minute of average lateness equal to three times the VOT for one minute (UK Department for Transport 2009).
The general approach to appraising reliability varies by mode. For rail projects, more data are collected and the UK Department for Transport has better confidence in the reliability of assessments. Since the supply issues are understood in models, rail reliability is included in the benefit-cost analysis. In contrast, reliability is not included in the benefit-cost analysis for the highway projects. The data requirements are more complex and users impact roadway reliability. As a result, the Department for Transport has less confidence in the reliability assessment for highway projects, so it goes into the AST. The Department for Transport sees having different approaches for the two modes as a limitation that should be improved through future research.
The UK has been developing techniques for evaluating the reliability impacts of highway projects. The UK Department for Transport developed an Incident Cost-Benefit Assessment (INCA) spreadsheet that provides an estimate of travel time reliability using an incident history database and estimating delays due to queuing. This model is described more in a later section of this memorandum. INCA has not been included in UK benefit-cost analysis because of unresolved theoretical issues. The UK Department for Transport views incorporating reliability into the AST as a first step while capabilities for estimating reliability are improved (Chiang 2009).
According to Chiang (2009), the UK will consider moving reliability into the benefit-cost evaluation after techniques are fine-tuned and the Department gains confidence in the results. However, the UK Department for Transport would like to develop a better understanding of the relationship among reliability, demand and network characteristics, and the valuation of reliability. The Department for Transport also wants to make sure that the resulting guidance is supported by appraisal tools and does not significantly increase the burden for producing appraisals.
The Federal government has an extensive research program focusing on reliability. The United States Congress authorized Second Strategic Highway Research Program (SHRP 2) to investigate the causes of high fatality rates and intensified congestion and to find methods for renewing aging infrastructure without contributing to fatality rates or congestion. SHRP 2 is intended to be a short-term research program that operates from 2006 to 2013 only and targets four focus areas (Safety, Capacity, Renewal, and Reliability) to achieve major advances. The research program is managed by the Transportation Research Board (TRB) and is funded through a collaborative agreement with the Federal Highway administration (FHWA).
Key research projects of SHRP 2 related to BCA are:
• Project L03: Analytical Procedures for Determining the Impacts of Reliability Mitigation Strategies
• Project L04: Incorporating Reliability Performance Measures into Planning and Operations Modeling Tools
• Project L11: Evaluating Alternative Operational Strategies to Improve Travel Time Reliability
• Project L14: Effectiveness of Different Approaches to Disseminating Traveler Information on Travel Time Reliability.
The work on Project L03 was recently completed and the final report is in publication. The final products of the project are expected to include guidance, analytic procedures, and examples to determine the impacts on travel time reliability of strategies to mitigate nonrecurring congestion (SHRP 2 website).
Margiotta (2009) described some of the statistical modeling from Project L03 and added thoughts on improving reliability estimation and valuation in travel models. Margiotta defined reliability as predictability or consistency in travel for the user. For the operator, reliability describes how the system performs over time against a standard or how susceptible the system is to breakdown. Margiotta noted that comparing recurrent and incident delay is too simplistic. Even in the absence of incidents, travel times vary due to weather, volume fluctuations (usual changes in demand, special events, and emergencies), and driver behavior.
Margiotta (2009) described the concepts of a buffer time and buffer index. These concepts are derived from the Texas Transportation Institute (TTI) congestion monitoring work and are consistent with a scheduling approach to measuring reliability. Margiotta suggested that different travelers and trip types will have different buffers. Routine travelers (e.g., commuters) allow for extra time based on past experience. Travelers making infrequent trips on unfamiliar routes may not allow for large buffers. Margiotta postulated that trips completed within the buffer would be valued at one rate, while trips exceeding the buffer (unplanned lateness) would be valued at a premium.
The statistical modeling in Project L03 shows that reliability can be predicted as a function of the average travel time index. For example, urban freeways can be predicted as a function of the “critical” demand-to-capacity ratio, the number of lane-hours lost due to incidents and work zones, and the number of hours when rainfall exceeds 0.05 inches. It is interesting to note that this function omits several factors that Margiotta described earlier as contributing to unreliability (e.g., fluctuations in demand, special events, and emergencies are not included). Margiotta made an additional point that the relationship may vary based on the length of the trip.
This SHRP 2 project will provide guidance on how planning and traffic simulation models can be modified to incorporate reliability performance measures. It will also include proof-of-concept on adopting reliability performance measures. The project is scheduled for completion in February 2012.
Vovsha (2009) presented insights from Project L04 and a companion SHRP 2 project (C04 Improving Our Understanding How Highway Congestion and Pricing Affect Travel Demand) at the travel time reliability conference in Vancouver. Vovsha described the fundamental challenge facing travel demand modelers. Standard models estimate traveler utility using a Random Utility Model (RUM). This model assumes that travelers have a fixed value of time to estimate mode choice and route assignment. However, travel time variability introduces the idea that travelers may experience random travel times and varying values of time.
Vovsha (2009) categorized measures of travel time variability based on travel time distributions into four groups:
• Mean-variance, which uses the standard deviation as the measure of travel time reliability and assumes that utilities are symmetric. Note that this is the performance indicator for reliability in the Transportation System Performance Measures Initiative.
• Buffer time, which uses the difference between the 80th or 95th percentile compared to the 50th percentile travel time. Note that California CSMPs use the 95th percentile when reporting buffer times.
• Risk measure, which uses the probability of a delay of a certain length occurring.
• Lateness measure, which uses the average travel time delay.
The work on this project was completed March 2010, but the final report has not yet been published. The final products of the project are expected to include: user requirements for travel time reliability, corresponding performance measures and targets, imputations of the value of travel time reliability, and alternative futures and concepts of operation for the year 2035.
As part of Project L11, Pozdena introduced an alternate method of valuing reliability by applying options pricing theory. Pozdena (2009) presented this approach at the travel time reliability conference in Vancouver. SMG also reviewed the draft report submitted to TRB (Kittelson 2009) and provided comments to Caltrans Traffic Operations on the report. Although Pozdena authored the original AASHTO Redbook and its more recent update, the method undertaken in Project L11 appears controversial and inappropriate for incorporation into Cal-B/C. However, Pozdena (2009) has included the method in the Seattle and Portland regional travel demand models.
In Project L11, Pozdena has been applying options theory to value recurring unreliability and the impacts of rare events. A classic application of options theory is the Black Scholes method for pricing stock options. Real options extend options theory to real events in addition to financial matters.
In order to apply options theory to travel time reliability, Pozdena (2009) defines a “certainty-equivalent” value for unreliability. The basic premise is that travelers would accept a reduction in average travel speeds in return for eliminating the risk of slower speeds. Presented this way, the tradeoff is comparable to the value that investors are willing to pay for an option in return for a guaranteed stock price. The “certainty-equivalent” value can be monetized by applying a value of time to the travel time associated with the speed reduction.
This project is scheduled to be completed in August 2011 and no reports have been published. The final products of the project are expected to include:
• Deployment guide for effectively delivering travel time reliability information to travelers
• Recommendations on different approaches to disseminating travel information on travel time reliability.
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