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 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.     

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.     

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.     

Distributions of travel time variability on urban roads

Reliability is an important factor in route, mode and also departure time choice analysis and is a key performance indicator for transport systems. However, the current metrics used to measure travel time variability may be not sufficient to fully represent reliability. Better understanding of the distributions of travel times is needed for the development of improved metrics for reliability. A comprehensive data analysis involving the assessment of longitudinal travel time data for two urban arterial road corridors in Adelaide, Australia, demonstrates that the observed distributions are more complex than previously assumed. The data sets demonstrate strong positive skew, very long upper tails, and sometimes bimodality. This paper proposes the use of alternative statistical distributions for travel time variability, with the Burr Type XII distribution emerging as an appropriate model for both links and routes. This statistical distribution has some attractive properties that make it suitable for explicit definition of many travel time reliability metrics. Copyright © 2011 John Wiley & Sons, Ltd.     

Investigating empirical implications of hysteresis in day-to-day travel time variability

Day-to-day travel time variability plays a significant role in travel time reliability. Nowadays, travelers not only seek to minimize their travel time on average, but also value its variation. The variation in the mean and the variance of travel time (across days, for the same departure time) has not been thoroughly investigated. A temporary decrease in capacity (e.g. congestion caused by an active bottleneck) leads to a quite significant difference in the variance of travel time for congestion onset and offset periods. This phenomenon results in hysteresis loops where the departure time periods in congestion offset exhibit a higher travel time variance than the ones in congestion onset with the same mean travel time. The aim of this paper is to identify empirical implications that yield to the hysteresis phenomenon in day-to-day travel times. First, empirical hysteresis loop observations are provided from two different freeway sites. Second, we investigate the potential link with the hysteresis observed in traffic networks on macroscopic fundamental diagram (MFD). Third, we build a piecewise linear function that models the evolution of travel time within the day. This allows us to decompose the problem into its components, e.g. start time of congestion, peak travel time, etc. These components, along with their probability distribution functions, are employed in a Monte Carlo simulation model to investigate their partial effects on the existence of hysteresis. Correlation among critical variables is the most influential factor in this phenomenon, which should be further investigated regarding traffic flow and traffic equilibrium principles.     

Intrapersonal variability in daily urban travel behavior: Some additional evidence

Researchers have used multiday travel data sets recently to examine day-to-day variability in travel behavior. This work has shown that there is considerable day-to-day variation in individuals' urban travel behavior in terms of such indicators of behavior as trip frequency, trip chaining, departure time from home, and route choice. These previous studies have also shown that there are a number of important implications of the observed day-to-day variability in travel behavior. For example, it has been shown that it may be possible to improve model parameter estimation precision, without increasing the cost of data collection, by drawing a multiday sample (rather than a single day sample) of traveler behavior, if there is considerable day-to-day variability in the phenomenon being modeled. This paper examines day-to-day variability in urban travel using a three-day travel data set collected recently in Seattle, WA. This research replicates and extends previous work dealing with day-to-day variability in trip-making behavior that was conducted with data collected in Reading, England, in the early 1970s. The present research extends the earlier work by examining day-to-day variations in trip chaining and daily travel time in addition to the variation in trip generation rates. Further, the present paper examines day-to-day variations in travel across the members of two-person households. This paper finds considerable day-to-day variability in the trip frequency, trip chaining and daily travel time of the sample persons and concludes that, in terms of trip frequency, the level of day-to-day variability is very comparable to that observed previously with a data set collected almost 20 years earlier in Reading, England. The paper also finds that day-to-day variability in daily travel time is similar in magnitude to that in daily trip rates. The analysis shows that the level of day-to-day variability is about the same for home-based and non-homebased trips, thus indicating that day-to-day variability in total trip-making is attributable to variation in both home-based and non-home-based trips. Day-to-day variability in the travel behaviors of members of two-person households was also found to be substantial.     

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.     

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.     

The cost of travel time variability: Three measures with properties

This paper explores the relationships between three types of measures of the cost of travel time variability: measures based on scheduling preferences and implicit departure time choice, Bernoulli type measures based on a univariate function of travel time, and mean-dispersion measures. We characterise measures that are both scheduling measures and mean-dispersion measures and measures that are both Bernoulli and mean-dispersion. There are no measures that are both scheduling and Bernoulli. We consider the impact of requiring that measures are additive or homogeneous, proving also a new strong result on the utility rates in an additive scheduling measure. These insights are useful for selecting cost measures to use in applications.     

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.     

An examination of the determinants of day-to-day variability in individuals' urban travel behavior

Day-to-day variability in individuals' travel behavior (intrapersonal variability) has been recognized in conceptual discussions, yet the analysis and modeling of urban travel are typically based on a single day record of each individual's travel. This paper develops and examines hypotheses regarding the determinants of intrapersonal variability in urban travel behavior.Two general hypotheses are formulated to describe the effects of motivations for travel and related behavior and of travel and related constraints on intrapersonal variability in weekday urban travel behavior. Specific hypotheses concerning the effect of various sociodernographic characteristics on intrapersonal variability are derived from these general hypotheses. These specific hypotheses are tested empirically in the context of daily trip frequency using a five-day record of travel in Reading, England.The empirical results support the two general hypotheses. First, individuals who have fewer economic and role-related constraints have higher levels of intrapersonal variability in their daily trip frequency. Second, individuals who fulfil personal and household needs that do not require daily participation in out-of-home activities have higher levels of intrapersonal variability in their daily trip frequency.     

An examination of the determinants of day-to-day variability in individuals' urban travel behavior

Day-to-day variability in individuals' travel behavior (intrapersonal variability) has been recognized in conceptual discussions, yet the analysis and modeling of urban travel are typically based on a single day record of each individual's travel. This paper develops and examines hypotheses regarding the determinants of intrapersonal variability in urban travel behavior.Two general hypotheses are formulated to describe the effects of motivations for travel and related behavior and of travel and related constraints on intrapersonal variability in weekday urban travel behavior. Specific hypotheses concerning the effect of various sociodemographic characteristics on intrapersonal variability are derived from these general hypotheses. These specific hypotheses are tested empirically in the context of daily trip frequency using a five-day record of travel in Reading, England.The empirical result support the two general hypotheses. First, individuals who have fewer economic and role-related constraints have higher levels of intrapersonal variability in their daily trip frequency. Second, individuals who fulfil personal and household needs that do not require daily participation in out-of-home activities have higher levels of intrapersonal variability in their daily trip frequency.     

Accounting for travel time variability in the optimal pricing of cars and buses

A number of studies have shown that in addition to travel time and cost as the common influences on mode, route and departure time choices, travel time variability plays an increasingly important role, especially in the presence of traffic congestion on roads and crowding on public transport. The dominant focus of modelling and implementation of optimal pricing that incorporates trip time variability has been in the context of road pricing for cars. The main objective of this paper is to introduce a non-trivial extension to the existing literature on optimal pricing in a multimodal setting, building in the role of travel time variability as a source of disutility for car and bus users. We estimate the effect of variability in travel time and bus headway on optimal prices (i.e., tolls for cars and fares for buses) and optimal bus capacity (i.e., frequencies and size) accounting for crowding on buses, under a social welfare maximisation framework. Travel time variability is included by adopting the well-known mean–variance model, using an empirical relationship between the mean and standard deviation of travel times. We illustrate our model with an application to a highly congested corridor with cars, buses and walking as travel alternatives in Sydney, Australia. There are three main findings that have immediate policy implications: (i) including travel time variability results in higher optimal car tolls and substantial increases in toll revenue, while optimal bus fares remain almost unchanged; (ii) when bus headways are variable, the inclusion of travel time variability as a source of disutility for users yields higher optimal bus frequencies; and (iii) including both travel time variability and crowding discomfort leads to higher optimal bus sizes.     

Investigating the effect of travel time variability on drivers' route choice decisions in Shanghai,China

Abstract

This paper investigates the effect of travel time variability on drivers' route choice behavior in the context of Shanghai, China. A stated preference survey is conducted to collect drivers' hypothetical choice between two alternative routes with designated unequal travel time and travel time variability. A binary choice model is developed to quantify trade-offs between travel time and travel time variability across various types of drivers. In the model, travel time and travel time variability are, respectively, measured by expectation and standard deviation of random travel time. The model shows that travel time and travel time variability on a route exert similarly negative effects on drivers' route choice behavior. In particular, it is found that middle-age drivers are more sensitive to travel time variability and less likely to choose a route with travel time uncertainty than younger and elder drivers. In addition, it is shown that taxi drivers are more sensitive to travel time and more inclined to choose a route with less travel time. Drivers with rich driving experience are less likely to choose a route with travel time uncertainty.     

A finite mixture model of vehicle-to-vehicle and day-to-day variability of traffic network travel times

This study proposes an approach to modeling the effects of daily roadway conditions on travel time variability using a finite mixture model based on the Gamma–Gamma (GG) distribution. The GG distribution is a compound distribution derived from the product of two Gamma random variates, which represent vehicle-to-vehicle and day-to-day variability, respectively. It provides a systematic way of investigating different variability dimensions reflected in travel time data. To identify the underlying distribution of each type of variability, this study first decomposes a mixture of Gamma–Gamma models into two separate Gamma mixture modeling problems and estimates the respective parameters using the Expectation–Maximization (EM) algorithm. The proposed methodology is demonstrated using simulated vehicle trajectories produced under daily scenarios constructed from historical weather and accident data. The parameter estimation results suggest that day-to-day variability exhibits clear heterogeneity under different weather conditions: clear versus rainy or snowy days, whereas the same weather conditions have little impact on vehicle-to-vehicle variability. Next, a two-component Gamma–Gamma mixture model is specified. The results of the distribution fitting show that the mixture model provides better fits to travel delay observations than the standard (one-component) Gamma–Gamma model. The proposed method, the application of the compound Gamma distribution combined with a mixture modeling approach, provides a powerful and flexible tool to capture not only different types of variability—vehicle-to-vehicle and day-to-day variability—but also the unobserved heterogeneity within these variability types, thereby allowing the modeling of the underlying distributions of individual travel delays across different days with varying roadway disruption levels in a more effective and systematic way.     

Hysteresis in travel demand

This paper presents evidence that there is a hysteresis effect in the demand for transport usage with respect to price. Consequently the neoclassical concept of a smooth continuous demand curve is questioned. The author presents a hysteresis model whereby changes in demand and of demand are embraced in a single theory related to generalized cost.     

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.     

A utility-theory travel demand model incorporating travel budgets

A model of traveler behavior is proposed which is consistent with the possibility that travelers expend average daily amounts of time and money on travel with stable regularities both among urban areas and over time in the same area. The model is founded on economic utility theory. It is designed to forecast: (1) the amount of total travel generated by types of households, (2) the division of travel among available modes, and (3) the relationship between the amounts of time and money allocated to travel expenditures. The qualitative properties of the model are shown to be consistent with economic principles. Specific theoretical results reveal that, in the simultaneous presence of constraints on both time and money, travel budgets are not strictly constant proportions of income and time available as they are in the cases of single constraints relevant to classes of travelers to whom time is scarce compared to money, or conversely. Constant expenditure proportions are shown to be linear approximations which are subject to empirical validation. The relevant economic principle is that expenditures can be considered fixed in the short run but become flexible in the long run when utility maximization is applied to the expenditures themselves and not just to their allocation. Empirical tests of the model using data from three urban areas are positive, but additional tests are called for. The most important output of the research is deemed to be the establishment of theoretical hypotheses which can be used in continuing tests of travel budgets.