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Travel Time Reliability


Travel time is understood as the time elapsed when a traveler displaces between two places in a network. Its duration is related to several factors including but not limited to: characteristics of the driver, and the vehicle; interaction of drivers in the network (e.g. heterogeneity in other drivers and their vehicles); traffic regulations, and traffic management systems; traffic incidents (e.g. traffic signal failure, vehicular crashes); and weather patterns. Thus, travel time is likely to be dissimilar for similar trips (i.e. same spatial trajectories). This underlines the need to think of travel time in terms of frequency, and not just of magnitude. In other words, travel time is defined as a statistical distribution, where the statistics of the (unpredictable or uncertain) variations are thought to exhibit statistical regularity. In this way, travel time reliability can be defined as a measure of the dispersion (or spread) of the travel time distribution. It should be noted that in the transportation research literature Value of Travel Time (un)Reliability is used interchangeably with Value of Travel Time Variability. The basic idea is that low  (high) dispersion means high (low) reliability.

The economic benefits from improved travel time reliability are appearing more commonly in benefit-cost analyses. There are a number of different potential causes of travel time reliability that trace their source at both the demand side (e.g. travelers' heterogeneous behavior), and supply side (e.g. traffic signal failure) of a transportation system.
To incorporate travel time reliability in benefit-cost analysis, the following are needed:
  • A measure for travel time reliability
  • A value for reliability
  • A method for predicting future reliability
  • A method for estimating changes in reliability due to a project.

Valuation of Reliability: Theoretical Frameworks

In the transportation research literature, several approaches have been formulated for estimating the value of travel time reliability. The three main theoretical frameworks are: Mean-Variance, Scheduling Delays, and Mean-Lateness. Furthermore, these approaches are defined from the viewpoint of the consumer (i.e. traveler in this case) similarly as it is done to estimate the value of travel time savings.


It is similar to the risk-return models in finance, and it was originally introduced into travel demand modeling by Jackson and Jucker (1982). It is assumed that a decision-maker's objective is to minimize the sum of two terms (both assumed to be sources of disutility): expected travel time, and the travel time variability. The expected travel time is represented by a measure of centrality (e.g. mean) of the travel time distribution, and the travel time variability as a measure of dispersion of the travel time distribution. The statistical measure of centrality is typically the mean, and the measure of variability is the standard deviation. Hence, the name of the framework. Other measures have been used in the literature for dispersion such as interquartile range, differences of percentiles (e.g. 90th percentile and median). The median have been used for centrality as well.

This approach allows the estimation of the Value of Travel Time Reliability (also referred as the Value of Travel Time Variability). This value represents the travelers' monetary weight for reducing variability (i.e. improving reliability). In addition, the Reliability Ratio is defined as the ratio of the value of travel time reliability, and the value of travel time savings. This ratio permits estimation of the Value of Reliability, especially when only the Value of Travel Time Savings is known.

Several drawbacks exist with this approach. For example, it is assumed that decision-makers desire to avoid similarly all forms of variability; only an estimate is computed for the dispersion measure in the model. In addition, researchers have yet to agree on the appropriate measure of travel time variability. The most common dispersion measure is standard deviation.

Recent research in this framework has focused on the inclusion of risk attitudes, and accounting for heterogeneity in the value of reliability (i.e. the value of reliability is different across the population).

Furthermore, most researchers and practioners agree that the standard deviation (or coefficient of variation) of travel time is the measure of reliability most applicable to benefit-cost analysis. However, there are compounding issues, such as the need for travelers to include a buffer time that may have a lower value of reliability.
Scheduling Delays (with uncertainty)

Vickrey (1969), and Gaver (1968) introduced the earlier versions of the framework based on the trip scheduling behavior of travelers. However, it was Small (1982) that formally presented the framework. It is assumed that travelers posses a preferred arrival time, and thus will prefer to choose a departure time that allows them to arrive at exactly their preferred arrival time. Therefore, travelers incur disutilities for late, and early arrivals besides simply disutility due to travel time.

This approach allows for the estimation of the Value of Scheduling Delay Early, and the Value of Scheduling Delay Late. These values represent the traveler's monetary weight for reducing early and late arrivals, respectively. 

It should be noted that the original framework in Small (1982) did not consider explicitly reliability (as in measures based on the travel time distribution). It was until Noland and Small (1995) and Bates et al. (2001), where the early and late penalties are defined in terms of expected values with respect to the travel time distribution. This allows for dissimilarities (or asymmetric) measures of unreliability in the model.

A serious drawback with this approach is the requirement of establishing a preferred arrival time. Unfortunately, for the most part this value is unknown to the analyst.

Recent research has shown equivalence (under certain conditions) between mean-variance and the scheduling delays model (see Fosgerau and Karlstrom (2010)), and also the focus has shifted to heterogeneity, and risk attitudes. Other important contributions are in terms of time-varying early/late penalties (see Tseng and Verhoef (2008), and Fosgerau and Engelson (2011)). Also, time-varying early/late penalties for chained trips is developed in Jenelius et al (2010).  


Reliability models for the most part focused on car drivers, and thus may not translate adequately to other modes of travel such as public transit. In the United Kingdom, the mean-lateness approach was proposed for passenger rail by the Association of Train Operating Companies. It consists of two components: schedule time (the travel time between actual departure time and scheduled arrival time of the train), and the mean-lateness at the destination (the mean of the travel time between scheduled arrival and actual arrival). Readers should refer to Batley and Ibanez (2009) for more details.

Valuation of Reliability: Empirical Evidence

The initial research on reliability is of qualitative nature. Mostly questionnaires ascertaining travelers' preferences with respect to the quality (including predictability) of their commute. Examples of these studies include Vaziri and Lam (1983), Prashker (1979), and Chang and Stopher (1981). These results have been also evaluated recently by surveys and Global Positioning System (GPS) data in Carrion and Levinson (2011).

Most of the initial quantitative estimates of the valuation of reliability has been based on stated preference (SP) techniques. The main reason as Bates et al (2001) elaborates was the lack of real life examples to adequately isolate reliability estimates using revealed preference (RP) data. However, the introduction of High Occupancy Toll Lanes (HOTL) provides a suitable testing ground. This is because the traffic speeds are kept close to free flow on the HOTL based dynamic pricing (i.e. typically prices are set according to traffic density; high density means higher price). Thus, it is plausible that there are benefits pertaining to reliability (low variability) besides the obvious travel time savings. Recent studies exploiting HOTL data include Small et al (2005) (using RP data from questionnaires, and in field measures of travel time), and Carrion and Levinson (2010) (using GPS data). Unfortunately, these studies are not so common, and thus most of the estimates of Value of Reliability (and other affine measures) are based on stated preference data. 

Empirical evidence shows that the value for reliability is likely to vary by individual, trip purpose (which may not be same classification as used in travel demand models), and monetary advantage from better scheduling in the case of freight.

In terms of estimates' magnitude, the value of reliability and the reliability ratio exhibit a significant variation across studies. This is due to several reasons including: data source (SP vs. RP); dispersion measures (standard deviation, interquartile range...); experimental designs (e.g. presentation of SP questions to subjects); and others.

The reliability ratio has been shown to be between 0.8 and 1.3 (see Small and Verhoef, 2007). This means that the Value of Reliability (measured using standard deviation) may be smaller, equal or greater to the value of travel time savings. In terms of the value of reliability, the magnitude has been shown to vary significantly from values as low as USD$8/hr (Tilahun and Levinson, 2010) to as high as USD$25/hr (Small et al, 2005).   

Recent Research

SHRP2 Reliability

Congress established the Second Strategic Highway Research Program (SHRP 2) in 2006 to investigate the underlying causes of highway crashes and congestion in a short-term program of focused research. SHRP 2 targets goals in four interrelated focus areas, one of which is travel time reliability. Reliability research in SHRP 2 focuses on reducing congestion through incident reduction, management, response, and mitigation. Achieving this goal will significantly improve travel time reliability for both people and freight. More information can be found at the SHRP2 website.

International Conference on Travel Time Reliability

SHRP 2 held a joint conference with the Joint Transport Research Centre (JTRC), the Organization for Economic Co-Operation and Development (OECD), and the International Transport Forum (ITF) on "Value of Travel Time Reliability and Cost-Benefit Analysis" in Vancouver, Canada October 15 - 16, 2009. The meeting brought together researchers and decision makers to examine recent research results and country experiences on reliability measurement, valuation, and to explore successful practices in integrating reliability into benefit-cost analysis. It aimed at identifying methodologies for incorporating reliability into project evaluation, and explored the pitfalls that need to be avoided.  The ITF has developed a 2009 report entitled "Improving Reliability on Surface Transportation Networks."
A number of countries are moving towards incorporating travel time reliability into their benefit-cost analysis methods. The Netherlands, Sweden, and Norway appear to be the furthest along, but the United Kingdom is studying reliability as well. Both Australia and the New Zealand already include travel time reliability in benefit-cost analysis. Japan is just starting to look at methods.
Copies of presentations from the meeting are available.

International Symposium on Transportation Network Reliability

"The aim of the International Symposium on Transportation Network Reliability (INSTR) is to bring together researchers and professionals interested in transportation network reliability, to discuss both recent research and future directions in this increasingly important field of research. The scope of the symposium includes all aspects of analysis and design to improve network reliability, including: user perception of unreliability; public policy and reliability of travel times; the valuation of reliability; the economics of reliability; network reliability modelling and estimation; transport network robustness; reliability of public transportation; travel behaviour under uncertainty; vehicle routing and scheduling under uncertainty; risk evaluation and management for transportation networks; and ITS to improve network reliability" (Source INSTR description). Presentations are available


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