Prediction of travel time variability for cost-benefit analysis

Unreliable travel times cause substantial costs to travelers. Nevertheless, they are often not taken into account in cost-benefit analyses (CBA), or only in very rough ways. This paper aims at providing simple rules to predict variability, based on travel time data from Dutch highways. Two different concepts of travel time variability are used, which differ in their assumptions on information availability to drivers. The first measure is based on the assumption that, for a given road link and given time of day, the expected travel time is constant across all working days (rough information: RI). In the second case, expected travel times are assumed to reflect day-specific factors such as weather conditions or weekdays (fine information: FI). For both definitions of variability, we find that the mean travel time is a good predictor. On average, longer delays are associated with higher variability. However, the derivative of variability with respect to delays is decreasing in delays. It can be shown that this result relates to differences in the relative shares of observed traffic ‘regimes’ (free-flow, congested, hyper-congested) in the mean delay. For most CBAs, no information on the relative shares of the traffic regimes is available. A non-linear model based on mean travel times can then be used as an approximation.     

Additive measures of travel time variability

This paper derives a measure of travel time variability for travellers equipped with scheduling preferences defined in terms of time-varying utility rates, and who choose departure time optimally. The corresponding value of travel time variability is a constant that depends only on preference parameters. The measure is unique in being additive with respect to independent parts of a trip. It has the variance of travel time as a special case. Extension is provided to the case of travellers who use a scheduled service with fixed headway.     

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.     

Assessing the effects of stochastic perception error under travel time variability

Perceived mean-excess travel time is a new risk-averse route choice criterion recently proposed to simultaneously consider both stochastic perception error and travel time variability when making route choice decisions under uncertainty. The stochastic perception error is conditionally dependent on the actual travel time distribution, which is different from the deterministic perception error used in the traditional logit model. In this paper, we investigate the effects of stochastic perception error at three levels: (1) individual perceived travel time distribution and its connection to the classification by types of travelers and trip purposes, (2) route choice decisions (in terms of equilibrium flows and perceived mean-excess travel times), and (3) network performance measure (in terms of the total travel time distribution and its statistics). In all three levels, a curve fitting method is adopted to estimate the whole distribution of interest. Numerical examples are also provided to illustrate and visualize the above analyses. The graphical illustrations allow for intuitive interpretation of the effects of stochastic perception error at different levels. The analysis results could enhance the understanding of route choice behaviors under both (subjective) stochastic perception error and (objective) travel time uncertainty. Some suggestions are also provided for behavior data collection and behavioral modeling.     

Behavioural implications of preferences, risk attitudes and beliefs in modelling risky travel choice with travel time variability

The appropriate interpretation of a behavioural outcome requires allowing for risk attitude and belief of an individual, in addition to identification of preferences. This paper develops an Attribute-Specific Extended Rank-Dependent Utility Theory model to better understand choice behaviour in the presence of travel time variability, in which these three important components of choice are empirically addressed. This framework is more behaviourally appealing for travel time and travel time variability research than the traditional approach in which risk attitude and belief are overlooked. This model also reveals significant unobserved between-individual heterogeneity in preferences, risk attitudes and beliefs.     

Quantifying the benefit of responsive pricing and travel information in the stochastic congestion pricing problem

This paper is concerned with roadway pricing amidst the uncertainty which characterizes long-term transportation planning. Uncertainty is considered both on the supply-side (e.g., the effect of incidents on habitual route choice behavior) and on the demand-side (e.g., due to prediction errors in demand forecasting). The framework developed in this paper also allows the benefits of real-time travel information to be compared directly against the benefits of responsive pricing, allowing planning agencies to identify the value of these policy options or contract terms in publicly-operated toll roads. Specifically, six scenarios reflect different combinations of policy options, and correspond to different solution methods for optimal tolls. Demonstrations are provided on both the Sioux falls and Anaheim networks. Results indicate that providing information to drivers implemented alongside responsive tolling may reduce expected total system travel time by over 9%, though more than 8% of the improvement is due to providing information, with the remaining 1% improvement gained from responsive tolling.     

Identifying optimal data aggregation interval sizes for link and corridor travel time estimation and forecasting

With the recent increase in the deployment of ITS technologies in urban areas throughout the world, traffic management centers have the ability to obtain and archive large amounts of data on the traffic system. These data can be used to estimate current conditions and predict future conditions on the roadway network. A general solution methodology for identifying the optimal aggregation interval sizes for four scenarios is proposed in this article: (1) link travel time estimation, (2) corridor/route travel time estimation, (3) link travel time forecasting, and (4) corridor/route travel time forecasting. The methodology explicitly considers traffic dynamics and frequency of observations. A formulation based on mean square error (MSE) is developed for each of the scenarios and interpreted from a traffic flow perspective. The methodology for estimating the optimal aggregation size is based on (1) the tradeoff between the estimated mean square error of prediction and the variance of the predictor, (2) the differences between estimation and forecasting, and (3) the direct consideration of the correlation between link travel time for corridor/route estimation and forecasting. The proposed methods are demonstrated using travel time data from Houston, Texas, that were collected as part of the automatic vehicle identification (AVI) system of the Houston Transtar system. It was found that the optimal aggregation size is a function of the application and traffic condition.

Estimation of the value of travel time and of travel time reliability for heterogeneous drivers in a road network

Transportation - Travel time reliability has been recognized as an important factor in cost–benefit analysis in a transportation network. To estimate the benefit and cost of travel time...     

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.     

Systematic variability in repetitious travel

The focus of this paper is the degree to which day-to-day variability in the individual's travel pattern has a systematic, or nonrandom, component. We first review the different sources of variability in travel, emphasizing the difference between between-individual and within-individual variation and the implications of this difference for travel analysis. After discussing the impact of measurement (i.e. the way in which travel behavior is measured) on the study of repetition and variability, we use the Uppsala data to examine the level of systematic variability in an individual's longitudinal travel record. The analysis focuses on two questions:

- How well does observation over one week capture longer-term (five-week) travel behavior; in other words, is behavior highly repetitive from week to week?

- How systematic is within-individual variability; in other words, are certain stops distributed over the five-week record in a nonrandom, that is either regular or clustered, fashion?

Using measures of travel that include more than one stop attribute (e.g. activity, mode, time of day, and location), we found that:

- A seven-day record of travel does not capture most of the separate behaviors exhibited by the individual over a five-week period, but it does capture, for most people, a good sampling of the person's different typical daily travel patterns.

- Whereas a considerable portion of intraindividual variability is systematic (nonrandom), clustering is a more important source of nonrandom variation than is regularity.

The results suggest that behavior does not follow a weekly cycle closely enough for a one-week travel record to measure the longer-term frequency with which the individual makes certain stops or to assess the level of day-to-day variation present in the individual's record. Because these results are likely to reflect the particular measures of behavior we used, one conclusion of this study is the need for other studies that replicate the aims of this one but use a variety of other travel measures. Only through such additional work can we truly assess the sensitivity of our findings to measurement techniques.     

Inter-temporal variation in the travel time and travel cost parameters of transport models

The parameters for travel time and travel cost are central in travel demand forecasting models. Since valuation of infrastructure investments requires prediction of travel demand for future evaluation years, inter-temporal variation of the travel time and travel cost parameters is a key issue in forecasting. Using two identical stated choice experiments conducted among Swedish drivers with an interval of 13 years, 1994 and 2007, this paper estimates the inter-temporal variation in travel time and cost parameters (under the assumption that the variance of the error components of the indirect utility function is equal across the two datasets). It is found that the travel time parameter has remained constant over time but that the travel cost parameter has declined in real terms. The trend decline in the cost parameter can be entirely explained by higher average income level in the 2007 sample compared to the 1994 sample. The results support the recommendation to keep the travel time parameter constant over time in forecast models, but to deflate the travel cost parameter with the forecasted income increase among travellers and the relevant income elasticity of the cost parameter. Evidence from this study further suggests that the inter-temporal and the cross-sectional income elasticities of the cost parameter are equal. The average elasticity is found to be ?0.8 to ?0.9 in the present sample of drivers, and the elasticity is found to increase with the real income level, both in the cross-section and over time.     

The significance and measurement of variability in travel behaviour

It is argued that an understanding of variability is central to the modelling of travel behaviour and the assessment of policy impacts, and is not the peripheral issue that it has often been considered. Drawing on recent studies in the UK and Australia, in conjunction with a review of the literature, the paper first examines the policy and analytical rationale for using multi-day data, then illustrates different ways of measuring variability, and finally discusses issues relating to the collection of suitable data for such analyses. In a policy context, there is a growing need for multi-day data to examine issues that affect general rather than one-day behaviour (e.g. to assess the distribution of user charges for road pricing, or patterns of public transport usage); while analytically, multi-day data is needed to improve our ability to identify the mechanisms behind travel behaviour and to derive better empirical relationships. Three measures of variability are presented: a graphical form showing daily differences in behaviour at the individual level; an aggregate, similarity index; and a hybrid graphical/numerical measure, which provides new insights into variability in daily patterns of behaviour. The paper raises a number of issues for debate, probably the most crucial of which is: variability in what? The way in which behaviour is measured crucially affects our conception of stability and variability.     

Modeling the interaction between buses,passengers and cars on a bus route using a multi-agent system

This paper models part of a public transport network (PTN), specifically, a bus route, as a small-size multi-agent system (MAS). The proposed approach is applied to a case study considering a ‘real world’ bus line within the PTN in Auckland, New Zealand. The MAS-based analysis uses modeling and simulation to examine the characteristics of the observed system – autonomous agents interacting with one another – under different scenarios, considering bus capacity and frequency of service for existing and projected public transport (PT) demand. A simulation model of a bus route is developed, calibrated and validated. Several results are attained, such as when the PT passenger load is not close to bus capacity, this load has no effect on average passenger waiting time at bus stops. The model proposed can be useful to practitioners as a tool to model the interaction between buses and other agents.     

A real time forecasting tool for dynamic travel time from clustered time series

This paper addresses the problem of dynamic travel time (DTT) forecasting within highway traffic networks using speed measurements. Definitions, computational details and properties in the construction of DTT are provided. DTT is dynamically clustered using a K-means algorithm and then information on the level and the trend of the centroid of the clusters is used to devise a predictor computationally simple to be implemented. To take into account the lack of information in the cluster assignment for the new predicted values, a weighted average fusion based on a similarity measurement is proposed to combine the predictions of each model. The algorithm is deployed in a real time application and the performance is evaluated using real traffic data from the South Ring of the Grenoble city in France.     

Selfishness and altruism in the distribution of travel time and income

Most economic models assume that individuals act out their preferences based on self-interest alone. However, there have also been other paradigms in economics that aim to capture aspects of behavior that include fairness, reciprocity, and altruism. In this study we empirically examine preferences of travel time and income distributions with and without the respondent knowing their own position in each distribution. The data comes from a Stated Preference experiment where subjects were presented paired alternative distributions of travel time and income. The alternatives require a tradeoff between distributional concerns and the respondent’s own position. Choices also do not penalize or reward any particular choice. Overall, choices show individuals are willing forgo alternatives where they would be individually well off in the interest of distributional concerns in both the travel time and income cases. Exclusively self-interested choices are seen more in the income questions, where nearly 25 % of respondents express such preferences, than in the travel time case, where only 5 % of respondents make such choices. The results also suggest that respondents prioritize their own position differently relative to regional distributions of travel time and income. Estimated choice models show that when it comes to travel time, individuals are more concerned with societal average travel time followed by the standard deviation in the region and finally their own travel time, while in the case of income they are more concerned with their own income, followed by a desire for more variability, and finally increasing the minimum income in their region. When individuals do not know their fate after a policy change that affects regional travel time, their choices appear to be mainly motivated by risk averse behavior and aim to reduce variability in outcomes. On the other hand, in the income context, the expected value appears to drive choices. In all cases, population-wide tastes are also estimated and reported.     

Expenditure of time and money on travel

The report examines the suggestion that the total amount of time, money or generalised cost spent on personal travel may be constant over time, in cross-section or under changes of travel costs or policies. Invariant expenditure of either time or money on travel is inconsistent with rational economic behaviour and with conventional transport modelling. A theoretical analysis concludes that generalised expenditure on travel might be invariant. Data from the National Travel Survey indicate that generalised expenditure is much the same in urban as in rural areas, despite the wide variation in modes available and distances to destinations. In comparisons of households at different income levels, generalised expenditure per person is almost directly proportional to gross income per person; in other words, consumption of “generalised time” is constant. Time series data from 1953 to 1976 are also examined and, though the data are poor, they indicate that generalised travel expenditure per person has increased over the years appreciably faster than has real income per person. Caution is therefore needed in using constant budget concepts in forecasting models.     

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.     

Subjective value of time in bus transit travel

A psychological scaling technique, magnitude estimation, is used to rate time spent on various elements of bus transit trips. Relative values of time are found for in-vehicle portions of trips, walking, waiting and transferring. Because magnitude estimation produces a ratio scale, results can be directly incorporated into modal choice analyses, route planning and evaluation procedures where monetary values of time are not necessarily required.     

The tax treatment of company cars, commuting and optimal congestion taxes

In Europe, the preferential tax treatment of company cars implies that many employees receive a company car as part of their compensation package. In this paper, we consider a model in which wages and the decision whether or not to provide a company car are the result of direct negotiation between employer and employee. Using this framework, we theoretically and numerically study first- and second-best optimal tax policies on labour and transport markets, focusing on the role of the tax treatment of company cars. We obtain the following results. First, higher labour taxes and a more favourable tax treatment of company cars raise the fraction employees that receives a company car; congestion and congestion tolls reduce it. Second, in countries that provide large implicit subsidies to company cars, eliminating the preferential tax treatment of company cars may be an imperfect but quite effective substitute for currently unavailable congestion tolls. The numerical illustration, calibrated using Belgian data, suggests that it yields about half the welfare gain attainable through optimal congestion taxes. Third, the favourable tax treatment of company cars justifies large public transport subsidies; the numerical results are consistent with zero public transport fares. Finally, we find that earlier models that ignored the preferential tax treatment of company cars may have substantially underestimated optimal congestion tolls in Europe. The numerical illustration suggests that about one third of the optimal congestion toll we obtain can be attributed to the current tax treatment of company cars.