The value of travel time variance

This paper considers the value of travel time variability under scheduling preferences that are defined in terms of linearly time varying utility rates associated with being at the origin and at the destination. The main result is a simple expression for the value of travel time variability that does not depend on the shape of the travel time distribution. The related measure of travel time variability is the variance of travel time. These conclusions apply equally to travellers who can freely choose departure time and to travellers who use a scheduled service with fixed headway. Depending on parameters, travellers may be risk averse or risk seeking and the value of travel time may increase or decrease in the mean travel time.     

The congestion multiplier: Variations in motorists’ valuations of travel time with traffic conditions

The value of travel time savings in part depends upon the disutility of the travel time that is saved and partly on the use to which the time saved is put. It has long been recognised that the disutility of the time spent travelling also depends upon a wide range of factors such as the journey length or the effort, comfort and safety associated with travelling.Hence we might expect the value of motorists’ travel time to vary with the traffic conditions as represented by the degree of congestion, in part to reflect the more difficult driving environment when there are more vehicles, but also a higher sense of frustration, similar to that associated with waiting time and contributing to its premium valuation.In this context, and despite the predominance of car travel in developed countries, the empirical evidence specifically relating to car values of travel time tends to fail to distinguish between different types of time according to the degree of congestion. Thus we are often left unclear as to precisely what type of time has been valued. Moreover, when a distinction is made, it tends to be into a simple dichotomy of congested and uncongested traffic.This paper provides new evidence on the variation in the valuation of motorists’ travel time savings across a finer gradation of types of time than has been hitherto attempted. This is obtained from the same Stated Choice exercise conducted in the United Kingdom and the United States. The paper also provides an extensive account of previous research into how congestion impacts on motorists’ values of time.     

On the value of highway travel time information systems

After the widespread deployment of Advanced Traveler Information Systems, there exists an increasing concern about their profitability. The costs of such systems are clear, but the quantification of the benefits still generates debate. This paper analyzes the value of highway travel time information systems. This is achieved by modeling the departure time selection and route choice with and without the guidance of an information system. The behavioral model supporting these choices is grounded on the expected utility theory, where drivers try to maximize the expected value of their perceived utility. The value of information is derived from the reduction of the unreliability costs as a consequence of the wiser decisions made with information. This includes the reduction of travel times, scheduling costs and stress. This modeling approach allows assessing the effects of the precision of the information system in the value of the information.Different scenarios are simulated in a generic but realistic context, using empirical data measured on a highway corridor accessing the city of Barcelona, Spain. Results show that travel time information only has a significant value in three situations: (1) when there is an important scheduled activity at the destination (e.g. morning commute trips), (2) in case of total uncertainty about the conditions of the trip (e.g. sporadic trips), and (3) when more than one route is possible. Information systems with very high precision do not produce better results. However, an acceptable level of precision is completely required, as information systems with very poor precision may even be detrimental. The paper also highlights the difference between the user value and the social value of the information. The value of the information may not benefit only the user. For instance, massive dissemination of travel time information contributes to the reduction of day-to-day travel time variance. This favors all drivers, even those without information. In these situations travel time information has the property that its social benefits exceed private benefits (i.e. information has positive externalities). Of course, drivers are only willing to cover costs equal or smaller than their private benefits, which in turn may justify subsidies for information provision.     

On the income elasticity of the value of travel time

Transport infrastructure is long-term and in appraisal it is necessary to value travel time savings for future years. This requires knowing how the value of time (VTT) will develop over time as incomes grow. This paper investigates if the cross-sectional income elasticity of the VTT is equal to inter-temporal income elasticity. The study is based on two identical stated choice experiments conducted with a 13 year interval. Results indicate that the relationship between income and the VTT in the cross-section has remained unchanged over time. As a consequence, the inter-temporal income elasticity of the VTT can be predicted based on cross-sectional income elasticity. However, the income elasticity of the VTT is not a constant but increases with income. For this reason, the average income elasticity of the VTT in the cross-sections has increased between the two survey years and can be expected to increase further over time.     

Estimation of value of travel time reliability

In mode choice decision, travelers consider not only travel time but also reliability of its modes. In this paper, reliability was expressed in terms of standard deviation and maximum delay that were measured based on triangular distribution. In order to estimate value of time and value of reliability, the Multinomial and Nested Logit models were used. The analysis results revealed that reliability is an important factor affecting mode choice decisions. Elasticity is used to estimate the impacts of the different policies and system improvements for water transportation mode. Among these policies, decision maker can assess and select the best alternative by doing the benefit and cost analysis based on a new market share, the value of time, and the value of reliability. Finally, a set of promising policies and system improvement of the water transportation were proposed.     

Meta-analysis of UK values of travel time: An update

Numerous travel demand studies have been carried out over the past five decades, many of which produce estimates of the value of travel time. This includes a rich body of largely unpublished evidence, which can provide valuable insights into the impact of variables such as GDP, travel distance, purpose and mode on this critical parameter for transport modelling and appraisal. The work reported in this paper updates and extends our previous meta-analyses of UK values of time ( [Wardman, 1998], [Wardman, 2001a] and [Wardman, 2004]) by adding recent studies and widening the range of explanatory variables included. Our current research covers 226 studies carried out between 1960 and 2008, yielding a total of 1749 valuations (a 50% increase relative to our previous work) and making this the largest data set of its kind to the best of our knowledge. This is also the most comprehensive study to date of parameters other than in-vehicle time and includes valuations of walk, wait, headway, congested, free flow, late, departure time shift and search time. Exploratory analysis of the data set provides interesting insights into methodological trends in travel demand modelling.For each valuation, over thirty quantitative and categorical variables were recorded and then included in a multivariate regression model to explain variations in the value of time. A large number of statistically significant effects were obtained from this meta-analysis, some of which are in marked contrast with, or not present in, our previous work. One finding that stands out is that the estimated elasticity of the value of time with respect to GDP per capita is 0.9 and highly significant, a much closer correspondence to the widely used convention of a unit income elasticity over time than we have previously obtained. The ratio between walk and wait time and in-vehicle time was found to be substantially lower than the commonly used value of two. We also found large and significant differences between the results from studies based on different types of Stated Preference survey presentation. Other important effects include variations by mode used, mode valued, travel purpose, attribute type and distance. It is envisaged that the results are of direct relevance in the British context, as inputs to appraisal or for benchmarking, whilst the methodological implications are of broader interest and the results, in terms of time equivalents and variations in values of time, can be transferred to other contexts.     

On the cost of misperceived travel time variability

Because individuals may misperceive travel time distributions, using the implied reduced form of the scheduling model might fall short of capturing all costs of travel time variability. We reformulate a general scheduling model employing rank-dependent utility theory and derive two special cases as econometric specifications to study these uncaptured costs. It is found that reduced-form expected cost functions still have a mean–variance form when misperception is considered, but the value of travel time variability is higher. We estimate these two models with stated-preference data and calculate the empirical cost of misperception. We find that: (i) travelers are mostly pessimistic and thus tend to choose departure times too early to achieve a minimum cost, (ii) scheduling preferences elicited using a stated-choice method can be relatively biased if probability weighting is not considered, and (iii) the extra cost of misperceiving the travel time distribution might be nontrivial when time is valued differently over the time of day and is substantial for some people.     

The influence of travel time variability on the value of time

Current benefits from travel time savings have only been related to the benefits from reducing mean travel time. Some previous attempts of including variability in the generalised cost function have mainly assumed commuters with fixed arrival time. This paper presents a comprehensive framework for valuing travel time variability that allows for any journey purpose and arrival time constraint. The proposed model is based on the expected utility approach and the mean-standard deviation approach. Stated Preference methods are considered the best technique for providing the data for calibrating the models. The values of time derived from the models are highly influenced by the value of travel time variability and it strongly depends on the probability distribution function travellers are faced with.     

Estimating the willingness to pay and value of risk reduction for car occupants in the road environment

In recent years there has been a re-focus on the valuation of a statistical life from the ex post or human capital method to an ex ante willingness to pay (WTP) approach. This is in part a recognition that we may have been undervaluing the cost of fatalities and injuries to society associated with crashes, but also a strong belief in the need to focus on establishing the amount, ex ante, that individuals are willing to pay to reduce the risk of exposure to circumstances that might lead to death or degree of injury on the road network. This study has developed a framework in which to identify the degree of preference heterogeneity in willingness to pay by individuals who are drivers or passengers in cars to avoid being killed or injured. A stated choice experiment approach is developed. The empirical setting is a choice of route for a particular trip that a sample of individuals periodically undertakes in Australia. The particular trip is described in enough detail to provide the respondent with a familiar market environment, providing all the relevant background information required for making a decision. Mixed logit models are estimated to obtain the marginal (dis)utilities associated with each influence on the choice amongst the attribute packages offered in the stated choice scenarios. These estimates are used to obtain the WTP distributions for fatality and injury avoidance, which are then aggregated to obtain estimates of the value of risk reduction (VRR), of which the fatality class is also known as the value of a statistical life (VSL).     

The valuation of commuter travel time savings for car drivers: evaluating alternative model specifications

The empirical valuation of travel time savings is a derivative of the ratio of parameter estimates in a discrete choice model. The most common formulation (multinomial logit) imposes strong restrictions on the profile of the unobserved influences on choice as represented by the random component of a preference function. As we progress our ability to relax these restrictions we open up opportunities to benchmark the values derived from simple (albeit relatively restrictive) models. In this paper we contrast the values of travel time savings derived from multinomial logit and alternative specifications of mixed (or random parameter) logit models. The empirical setting is urban car commuting in six locations in New Zealand. The evidence suggests that less restrictive choice model specifications tend to produce higher estimates of values of time savings compared to the multinomial logit model; however the degree of under-estimation of multinomial logit remains quite variable, depending on the context.     

Investigating travel utility elements in association with travel time and mode choice: the case of Seoul,South Korea

In this paper, travel utility is conceptualized into the elements of disutility, or derived utility, and positive utility, which includes synergistic and intrinsic utility, and then analyzed in terms of the effects of these elements on weekly travel time according to three travel modes – the automobile, public transit, and nonmotorized modes – and on the choice of the annually most used mode. Linear regressions on mode-specific travel time and a multinomial logistic regression on mode choice show that, compared to life situation and land-use characteristics, utility elements are among the strongest travel determinants. Specifically, while some utility elements contribute exclusively to shifting the mode of travel and others to increasing nonmotorized travel, modal shift is most strongly affected by a disutility element, trip timeliness, and the increase in nonmotorized travel by a positive utility element, amenities.     

Values of travel time in Europe: Review and meta-analysis

This paper reports the most extensive meta-analysis of values of time yet conducted, covering 3109 monetary valuations assembled from 389 European studies conducted between 1963 and 2011. It aims to explain how valuations vary across studies, including over time and between countries. In addition to the customary coverage of in-vehicle time in review studies, this paper covers valuations of walk time, wait time, service headway, parking space search time, departure time switching, time in congested traffic, schedule delay early and late, mean lateness and the standard deviation of travel time. Valuations are found to vary with type of time, GDP, distance, journey purpose, mode, the monetary numeraire and a number of factors related to estimation. Model output values of time compare favourably with earnings data, replicate well official recommended values obtained from major national studies, and are transferable across countries. These implied monetary values serve as very useful benchmarks against which new evidence can be assessed and the meta-model provides parameters and values for countries and contexts where there is no other such evidence.     

An adaptive information fusion model to predict the short-term link travel time distribution in dynamic traffic networks

As intelligent transportation systems (ITS) approach the realm of widespread deployment, there is an increasing need to robustly capture the variability of link travel time in real-time to generate reliable predictions of real-time traffic conditions. This study proposes an adaptive information fusion model to predict the short-term link travel time distribution by iteratively combining past information on link travel time on the current day with the real-time link travel time information available at discrete time points. The past link travel time information is represented as a discrete distribution. The real-time link travel time is represented as a range, and is characterized using information quality in terms of information accuracy and time delay. A nonlinear programming formulation is used to specify the adaptive information fusion model to update the short-term link travel time distribution by focusing on information quality. The model adapts good information by weighing it higher while shielding the effects of bad information by reducing its weight. Numerical experiments suggest that the proposed model adequately represents the short-term link travel time distribution in terms of accuracy and robustness, while ensuring consistency with ambient traffic flow conditions. Further, they illustrate that the mean of a representative short-term travel time distribution is not necessarily a good tracking indicator of the actual (ground truth) time-dependent travel time on that link. Parametric sensitivity analysis illustrates that information accuracy significantly influences the model, and dominates the effects of time delay and the consistency constraint parameter. The proposed information fusion model bridges key methodological gaps in the ITS deployment context related to information fusion and the need for short-term travel time distributions.     

A stated preference examination of time of travel choice for a recreational trip

A stated preference experiment was performed in Calgary in Canada to examine how people are influenced in the selection of a departure time for a hypothetical trip to see a movie. A total of 635 complete observations were obtained. In each observation the respondent was presented with a set of possible departure time scenarios and asked to indicate the order of preference for these scenarios. Each scenario was described by specifying the automobile travel time, the expected arrival time relative to the movie start time, the parking cost, the probability of being at least ten minutes late for the movie and the length of time the movie had been running. This forced the respondent to trade off between conditions regarding these attributes. Age, gender and frequency of movie attendance were also recorded. The observations thus obtained were used to estimate the parameter values for a range of alternative utility functions in logit models representing this choice behaviour. The results indicate that all of the attributes included have significant effects on departure time choice in the situation being considered. They also indicate that travellers are prepared to arrive roughly two minutes early for each minute of travel time saved; that the money value of driving time for trips to recreational activities is about half that for trips to work; that one additional percent in the probability of arriving late is equivalent to roughly 0.20 Canadian dollars or 1.93 minutes drive time; and that there is a preference for a non-zero expected early arrival time regardless of the associated probability of arriving late. Some of these results are novel and others are consistent with findings for work trips in work done by others, which is seen to add credence to the approach being used here.     

Estimation of the perceived value of transit time for containerized cargoes

This paper proposes a novel method for estimating the perceived value of transit time of containers by shipping lines. The key idea is that a shipping line’s published schedule is the optimal decision that minimizes the sum of fuel cost and time-associated costs of the containers adopted by the shipping line. Using the proposed method, we find that the adopted values of transit time for nine trans-Pacific services operated by Orient Overseas Container Line and five trans-Pacific services operated by Maersk Line are between US$5/TEU/day and US$30/TEU/day. We further demonstrate how the adopted value can be used for designing the optimal transit times between ports, analyzing the viability of slow-steaming, checking whether ships should speed up to catch up to connecting ships on other services, and helping to predict the market share of less polluting fuels in view of rules on air emission.     

A travel time reliability model of urban expressways with varying levels of service

Urban expressways usually experience several levels of service (LOS) because of the stop-and-go traffic flow caused by congestion. Moreover, multiple shock waves generate at different LOS interfaces. The dynamic of shock waves strongly influences the travel time reliability (TTR) of urban expressways. This study proposes a path TTR model that considers the dynamic of shock waves by using probability-based method to characterize the TTR of urban expressways with shock waves. Two model parameters are estimated, namely distribution of travel time (TT) per unit distance and travel distances in different LOS segments. Generalized extreme value distribution and generalized Pareto distribution are derived as distributions of TT per unit distance for six different LOS. Distribution parameters are estimated by using historical floating car data. Travel distances in different LOS segments are calculated based on shock wave theory. The range of TT along the path, which can help drivers arrange their trips, can be obtained from the TTR model. Finally, comparison is made among the proposed TTR model, generalized Pareto contrast model, which does not consider different LOS or existence of shock waves, and normal contrast model, which assumes TT per unit distance as normal distribution without considering shock wave. Results show that the proposed model achieves higher prediction accuracy and reduces the prediction range of TT. The conclusions can be further extended to TT prediction and assessment of measures to improve reliability of TT in a network.     

A copula-based approach for estimating the travel time reliability of urban arterial

Estimating the travel time reliability (TTR) of urban arterial is critical for real-time and reliable route guidance and provides theoretical bases and technical support for sophisticated traffic management and control. The state-of-art procedures for arterial TTR estimation usually assume that path travel time follows a certain distribution, with less consideration about segment correlations. However, the conventional approach is usually unrealistic because an important feature of urban arterial is the dependent structure of travel times on continuous segments. In this study, a copula-based approach that incorporates the stochastic characteristics of segments travel time is proposed to model arterial travel time distribution (TTD), which serves as a basis for TTR quantification. First, segments correlation is empirically analyzed and different types of copula models are examined. Then, fitting marginal distributions for segment TTD is conducted by parametric and non-parametric regression analysis, respectively. Based on the estimated parameters of the models, the best-fitting copula is determined in terms of the goodness-of-fit tests. Last, the model is examined at two study sites with AVI data and NGSIM trajectory data, respectively. The results of path TTD estimation demonstrate the advantage of the proposed copula-based approach, compared with the convolution model without capturing segments correlation and the empirical distribution fitting methods. Furthermore, when considering the segments correlation effect, it was found that the estimated path TTR is more accurate than that by the convolution model.     

Accommodating risk in the valuation of expected travel time savings

Valuation of travel time savings is a critical measure in transport infrastructure appraisal, traffic modelling and network performance. It has been recognised for some time that the travel times associated with repeated trips are subject to variation, and hence there is risk embedded in the treatment of expected travel time. In the context of the expected utility framework, we use a nonlinear probability weighting function to accommodate choice made under risk. Although the empirical findings suggest small differences between the value of expected travel time savings (VETTS) in the presence and absence of risk, the mean estimate does make a noticeable difference to time benefits when applied to real projects. By incorporating nonlinear probability weighting, our model reveals that the probabilities associated with specific travel times that are shown to respondents in the choice experiment are transformed, resulting in overweighting of outcomes with low probabilities and underweighting of outcomes with high probabilities. Copyright © 2011 John Wiley & Sons, Ltd.     

Embedding risk attitude and decision weights in non-linear logit to accommodate time variability in the value of expected travel time savings

In recent years we have seen important extensions of logit models in behavioural research such as incorporation of preference and scale heterogeneity, attribute processing heuristics, and estimation of willingness to pay (WTP) in WTP space. With rare exception, however, a non-linear treatment of the parameter set to allow for behavioural reality, such as embedded risk attitude and perceptual conditioning of occurrence probabilities attached to specific attributes, is absent. This is especially relevant to the recent focus in travel behaviour research on identifying the willingness to pay for reduced travel time variability, which is the source of estimates of the value of trip reliability that has been shown to take on an increasingly important role in project appraisal. This paper incorporates, in a generalised non-linear (in parameters) logit model, alternative functional forms for perceptual conditioning (known as probability weighting) and risk attitude in the utility function to account for travel time variability, and then derives an empirical estimate of the willingness to pay for trip time variability-embedded travel time savings as an alternative to separate estimates of time savings and trip time reliability. We illustrate the richness of the approach using a stated choice data set for commuter choice between unlabelled attribute packages. Statistically significant risk attitude parameters and parameters underlying decision weights are estimated for multinomial logit and mixed multinomial logit models, along with values of expected travel time savings.