Probe vehicle data sampled by time or space: Consistent travel time allocation and estimation

A characteristic of low frequency probe vehicle data is that vehicles traverse multiple network components (e.g., links) between consecutive position samplings, creating challenges for (i) the allocation of the measured travel time to the traversed components, and (ii) the consistent estimation of component travel time distribution parameters. This paper shows that the solution to these problems depends on whether sampling is based on time (e.g., one report every minute) or space (e.g., one every 500 m). For the special case of segments with uniform space-mean speeds, explicit formulae are derived under both sampling principles for the likelihood of the measurements and the allocation of travel time. It is shown that time-based sampling is biased towards measurements where a disproportionally long time is spent on the last segment. Numerical experiments show that an incorrect likelihood formulation can lead to significantly biased parameter estimates depending on the shapes of the travel time distributions. The analysis reveals that the sampling protocol needs to be considered in travel time estimation using probe vehicle data.     

On some traffic equilibrium theory paradoxes

We consider the asymmetric equilibrium problem with fixed demands in a transportation network where the travel cost on each link may depend on the flow on this as well as other links of the network and we study how the travellers' cost is affected by changes in the travel demand or addition of new routes. Assuming that the travel cost functions are strongly monotone, we derive formulas which express, under certain conditions, how a change in travel demand associated with a particular origin-destination (O / D) pair will affect the travelers' cost for any O / D pair. We then use these formulas to show that an increase in the travel demand associated with a particular O / D pair (all other remaining fixed) always results in an increase in the travelers' cost on that O / D pair, however, the travelers' cost on other O / D pairs may decrease. We then derive formulas yielding, under certain conditions, the change in travelers' cost on every O / D pair induced by the addition of a new path. These can be used to determine, whether Braess' paradox occurs in the network. We then show that when a new path is added, the travelers' cost associated with the particular O / D pair joined by this path will decrease (hence Braess' paradox does not occur) if a test matrix is positive semidefinite.     

A structured flexible transit system for low demand areas

Public transit structure is traditionally designed to contain fixed bus routes and predetermined bus stations. This paper presents an alternative flexible-route transit system, in which each bus is allowed to travel across a predetermined area to serve passengers, while these bus service areas collectively form a hybrid “grand” structure that resembles hub-and-spoke and grid networks. We analyze the agency and user cost components of this proposed system in idealized square cities and seek the optimum network layout, service area of each bus, and bus headway, to minimize the total system cost. We compare the performance of the proposed transit system with those of comparable systems (e.g., fixed-route transit network and taxi service), and show how each system is advantageous under certain passenger demand levels. It is found out that under low-to-moderate demand levels, the proposed flexible-route system tends to have the lowest system cost.     

TTB or not TTB, that is the question: a review and analysis of the empirical literature on travel time (and money) budgets

This paper summarizes and analyses findings from more than two dozen aggregate and disaggregate studies of travel time (and sometimes money) expenditures, exploring the question of the existence of a constant travel time budget. We conclude (with prior researchers) that travel time expenditures are not constant except, perhaps, at the most aggregate level. Nevertheless, individuals’ travel time expenditures do show patterns that can be partly explained by measurable characteristics. Travel time expenditure is strongly related to individual and household characteristics (e.g., income level, gender, employment status, and car ownership), attributes of activities at the destination (e.g., activity group and activity duration), and characteristics of residential areas (e.g., density, spatial structure, and level of service). To the extent that travel time expenditures are constant at the aggregate level, the underlying mechanisms explaining that regularity are not well understood. Consequently, further research into explaining travel time and money expenditure patterns is justified.     

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.     

A revised branch‐and‐price algorithm for dial‐a‐ride problems with the consideration of time‐dependent travel cost

Developing demand responsive transit systems are important with regard to meeting the travel needs for elderly people. Although Dial‐a‐ride Problems (DARP) have been discussed for several decades, most researchers have worked to develop algorithms with low computational cost under the minimal total travel costs, and fewer studies have considered how changes in travel time might affect the vehicle routes and service sequences. Ignoring such variations in travel time when design vehicle routes and schedules might lead to the production of inefficient vehicle routes, as well as incorrect actual vehicle arrival times at the related nodes. The purpose of this paper is to construct a DARP formulation with consideration of time‐dependent travel times and utilizes the traffic simulation software, DynaTAIWAN, to simulate the real traffic conditions in order to obtain the time‐dependent travel time matrices. The branch‐and‐price approach is introduced for the time‐dependent DARP and tested by examining the sub‐network of Kaohsiung City, Taiwan. The numerical results reveal that the length of the time window can significantly affect the vehicle routes and quantitative measurements. As the length of the time window increases, the objective value and the number of vehicles will reduce significantly. However, the CPU time, the average pickup delay time, the average delivery delay time and the average actual ride time (ART)/direct ride time (DRT) will increase significantly as the length of the time window increases. Designing the vehicle routes to reduce operating costs and satisfy the requirements of customers is a difficult task, and a trade‐off must be made between these goals. Copyright © 2014 John Wiley & Sons, Ltd.     

First-best marginal cost toll for a traffic network with stochastic demand

First-best marginal cost pricing (MCP) in traffic networks has been extensively studied with the assumption of deterministic travel demand. However, this assumption may not be realistic as a transportation network is exposed to various uncertainties. This paper investigates MCP in a traffic network under stochastic travel demand. Cases of both fixed and elastic demand are considered. In the fixed demand case, travel demand is represented as a random variable, whereas in the elastic demand case, a pre-specified random variable is introduced into the demand function. The paper also considers a set of assumptions of traveler behavior. In the first case, it is assumed that the traveler considers only the mean travel time in the route choice decision (risk-neutral behavior), and in the second, both the mean and the variance of travel time are introduced into the route choice model (risk-averse behavior). A closed-form formulation of the true marginal cost toll for the stochastic network (SN-MCP) is derived from the variational inequality conditions of the system optimum and user equilibrium assignments. The key finding is that the calculation of the SN-MCP model cannot be made by simply substituting related terms in the original MCP model by their expected values. The paper provides a general function of SN-MCP and derives the closed-form SN-MCP formulation for specific cases with lognormal and normal stochastic travel demand. Four numerical examples are explored to compare network performance under the SN-MCP and other toll regimes.     

A bayesian dynamic linear model approach for real-time short-term freeway travel time prediction

This paper presents a Bayesian inference-based dynamic linear model (DLM) to predict online short-term travel time on a freeway stretch. The proposed method considers the predicted freeway travel time as the sum of the median of historical travel times, time-varying random variations in travel time, and a model evolution error, where the median is employed to recognize the primary travel time pattern while the variation captures unexpected supply (i.e. capacity) reduction and demand fluctuations. Bayesian forecasting is a learning process that revises sequentially the state of a priori knowledge of travel time based on newly available information. The prediction result is a posterior travel time distribution that can be employed to generate a single-value (typically but not necessarily the mean) travel time as well as a confidence interval representing the uncertainty of travel time prediction. To better track travel time fluctuations during non-recurrent congestion due to unforeseen events (e.g., incidents, accidents, or bad weather), the DLM is integrated into an adaptive control framework that can automatically learn and adjust the system evolution noise level. The experiment results based on the real loop detector data of an I-66 segment in Northern Virginia suggest that the proposed method is able to provide accurate and reliable travel time prediction under both recurrent and non-recurrent traffic conditions.     

An aggregate demand model for intercity passenger travel in Sri Lanka

Inspite of the inherent weaknesses in aggregate demand models, they continue to be used in everyday applications, especially in developing countries. The largely data intensive disaggregate model preclude its application in many cases. This paper attempts the formulation and calibration of an aggregate total demand model for estimating inter-district passenger travel by public transport in Sri Lanka. In its process, an investigation is made of the common problems in the aggregate approach while examining possible remedial measures to improve the accuracy and (hence) the usability of the aggregate model. It is argued that commonly used variables and functional forms are inappropriate for making accurate estimates in developing countries. Consequently, the model calibration is shown to incorporate variables representing urbanisation, under-development, transfers, a mode-abstract cost function and intrinsic features. The necessity for functional form for each variable to be based on behavioral assumptions that are tested using the Box-Cox transformation for ensuring the best fit of the data is also observed. Although, the model form was calibrated for Sri Lanka, the model is generalised in order for its applications to other countries as well as, both, inter-district and intercity travel demand estimation.     

Cost and time damping: evidence from aggregate rail direct demand models

There is a significant body of evidence from both disaggregate choice modelling literature and practical travel demand forecasting that the responsiveness to cost and possibly to time diminishes with journey length. This has, in Britain at least, been termed ‘Cost Damping’, and is recognised in guidance issued by the UK Department for Transport. However, the consistency of the effect across modes and data types has not been established. Cost damping, if it exists, affects both the forecasting of demand and our understanding of behaviour. This paper aims to investigate the evidence for cost and time damping in rail demand using aggregate rail ticket sales data. The rail ticket sales data in Britain has, for many years, formed the basis of analysis of a wide range of impacts of rail demand. It records the number of tickets sold between station pairs, and it is generally felt to provide a reasonably accurate reflection of travel demand. However, the consistency of these direct demand models with choice modelling and highway demand model structures has not been investigated. Rail direct demand models estimated by ticket sales data indicate only slight variation in the fare elasticity with distance, as is evidenced in the largest meta-analysis of price elasticities conducted to date (Wardman in J Transp Econ Policy 48(3):367–384, 2014). This study of UK elasticities shows strong variation between urban and inter-urban trips, presumably a segmentation at least in part by purpose, but less remaining variation by trip length. A lack of variation by length supports the hypothesis of cost damping, because constant cost sensitivity would imply that fare elasticity would increase strongly with distance, because of the increasing impact of higher fares at longer distances. In this paper we indicate that rail direct demand models have some consistency of behavioural paradigm with utility based choice models used in highway planning. We go on to use rail demand data to estimate time and fare elasticities in the context of various cost damping functions. Our empirical contribution is to estimate time elasticities on a basis directly comparable with cost elasticities and to show that the phenomenon of cost damping is strongly present in ticket sales data. This finding implies that cost damping should be included in models intended for multimodal analysis, which may otherwise give incorrect predictions.     

A bi-objective cyclist route choice model

It is widely acknowledged that cyclists choose their route differently to drivers of private vehicles. The route choice decision of commuter drivers is often modelled with one objective, to reduce their generalised travel cost, which is a monetary value representing the combined travel time and vehicle operating cost. Commuter cyclists, on the other hand, usually have multiple incommensurable objectives when choosing their route: the travel time and the suitability of a route. By suitability we mean non-subjective factors that characterise the suitability of a route for cycling, including safety, traffic volumes, traffic speeds, presence of bicycle lanes, whether the terrain is flat or hilly, etc. While these incommensurable objectives are difficult to be combined into a single objective, it is also important to take into account that each individual cyclist may prioritise differently between travel time and suitability when they choose a route.This paper proposes a novel model to determine the route choice set of commuter cyclists by formulating a bi-objective routing problem. The two objectives considered are travel time and suitability of a route for cycling. Rather than determining a single route for a cyclist, we determine a choice set of optimal alternative routes (efficient routes) from which a cyclist may select one according to their personal preference depending on their perception of travel time versus other route choice criteria considered in the suitability index. This method is then implemented in a case study in Auckland, New Zealand.The study provides a starting point for the trip assignment of cyclists, and with further research, the bi-objective routing model developed can be applied to create a complete travel demand forecast model for cycle trips. We also suggest the application of the developed methodology as an algorithm in an interactive route finder to suggest efficient route choices at different levels of suitability to cyclists and potential cyclists.     

Do travel cost models value transportation properly?

This paper examines whether travel cost models value transportation properly. It uses contingent behavior and contingent pricing analyses to explore the valuation of transport costs within the context of recreation demand. The contingent behavior analysis poses hypothetical increases in travel costs––travel distance and access fees––and examines the demand responses. In contrast, the ‘contingent pricing’ analysis asks respondents to state the increase in travel costs that is consistent with certain reductions in recreation demand, in this case, reductions that eliminate demand. By comparing distance-related responses to fee-related responses, the two analyses estimate factors for testing and improving the valuation of transport costs. To achieve these ends, the two analyses also explore the valuation of time costs.     

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.     

Understanding Travel Time Expenditures Around the World: Exploring the Notion of a Travel Time Frontier

Travel behavior researchers have been intrigued by the amount of time that people allocate to travel in a day, i.e., the daily travel time expenditure, commonly referred to as a “travel time budget”. Explorations into the notion of a travel time budget have once again resurfaced in the context of activity-based and time use research in travel behavior modeling. This paper revisits the issue by developing the notion of a travel time frontier (TTF) that is distinct from the actual travel time expenditure or budget of an individual. The TTF is defined in this paper as an intrinsic maximum amount of time that people are willing to allocate for travel. It is treated as an unobserved frontier that influences the actual travel time expenditure measured in travel surveys. Using travel survey datasets from around the world (i.e., US, Switzerland and India), this paper sheds new light on daily travel time expenditures by modeling the unobserved TTF and comparing these frontiers across international contexts. The stochastic frontier modeling methodology is employed to model the unobserved TTF as a production frontier. Separate models are estimated for commuter and non-commuter samples to recognize the differing constraints between these market segments. Comparisons across the international contexts show considerable differences in average unobserved TTF values.     

Comparison of inter‐city bi‐modal split models

Using data collected from rail and air passengers on two inter‐city routes in the U.K., seven different model formulations were set up and tested in order to ascertain the most appropriate model format. As a result of the work carried out, it is concluded that a simple Entropy‐type model based on the theoretical work of A. G. Wilson and utilising a linear generalised cost function is the most suitable. Other useful parameters emerging from the work are perceived values of travel time, and a weighting factor for night travel.     

The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation

In this paper, a dynamic user equilibrium traffic assignment model with simultaneous departure time/route choices and elastic demands is formulated as an arc-based nonlinear complementarity problem on congested traffic networks. The four objectives of this paper are (1) to develop an arc-based formulation which obviates the use of path-specific variables, (2) to establish existence of a dynamic user equilibrium solution to the model using Brouwer's fixed-point theorem, (3) to show that the vectors of total arc inflows and associated minimum unit travel costs are unique by imposing strict monotonicity conditions on the arc travel cost and demand functions along with a smoothness condition on the equilibria, and (4) to develop a heuristic algorithm that requires neither a path enumeration nor a storage of path-specific flow and cost information. Computational results are presented for a simple test network with 4 arcs, 3 nodes, and 2 origin–destination pairs over the time interval of 120 periods.     

Understanding suburban travel demand: Flexible modelling with revealed and stated choice data

We analyse the choice of mode in suburban corridors using nested logit specifications with revealed and stated preference data. The latter were obtained from a choice experiment between car and bus, which allowed for interactions among the main policy variables: travel cost, travel time and frequency. The experiment also included parking cost and comfort attributes. The attribute levels in the experiment were adapted to travellers’ experience using their revealed preference information. Different model specifications were tested accounting for the presence of income effect, systematic taste variation, and incorporating the effect of latent variables. We also derived willingness-to-pay measures, such as the subjective value of time, that vary among individuals as well as elasticity values. Finally, we analysed the demand response to various policy scenarios that favour public transport use by considering improvements in level-of-service, fare reductions and/or increases in parking costs. In general, demand was shown to be more sensitive to policies that penalise the private car than those improving public transport.     

Measuring inaccuracy in travel demand forecasting: methodological considerations regarding ramp up and sampling

Project promoters, forecasters, and managers sometimes object to two things in measuring inaccuracy in travel demand forecasting: (1) using the forecast made at the time of making the decision to build as the basis for measuring inaccuracy and (2) using traffic during the first year of operations as the basis for measurement. This paper presents the case against both objections. First, if one is interested in learning whether decisions about building transport infrastructure are based on reliable information, then it is exactly the traffic forecasted at the time of making the decision to build that is of interest. Second, although ideally studies should take into account so-called demand “ramp up” over a period of years, the empirical evidence and practical considerations do not support this ideal requirement, at least not for large-N studies. Finally, the paper argues that large samples of inaccuracy in travel demand forecasts are likely to be conservatively biased, i.e., accuracy in travel demand forecasts estimated from such samples would likely be higher than accuracy in travel demand forecasts in the project population. This bias must be taken into account when interpreting the results from statistical analyses of inaccuracy in travel demand forecasting.     

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.     

Consistency and fungibility of monetary valuations in transport: An empirical analysis of framing and mental accounting effects

Governments around the world use monetised values of transport externalities to undertake project appraisal and cost–benefit analysis. However, because different types of benefits are monetised (e.g., travel time savings, preventing statistical fatalities, reliability, etc.) the question naturally arises as to whether they are consistent. That is, whether a “dollar is a dollar” as welfare economics requires, or whether spending money in one area carries a different disutility from spending money in another area. This would equate to a violation of fungibility, which is the property of a good or a commodity whose individual units are capable of mutual substitution. The view that money is not fungible is explained in behavioural economics through theories of framing and mental accounting. This paper describes the results of a stated choice experiment designed to test the fungibility and consistency of monetary valuations in transport. From a nationally representative sample, we elicit direct values for the three pairwise trade-offs between travel time, travel cost, and safety. We then show that in the context of our analysis, any trade-offs inferred on the basis of other trade-offs, as is common practice (e.g. inferring a safety vs time trade-off on the basis of monetary valuations for time and safety), produces biased results, suggesting that the assumption of fungibility does not hold. Specifically, we find that time is valued more highly when valued directly by cost than when traded with safety, and the reverse is true for safety.