Some features of non-linear travel time models for dynamic traffic assignment

Abstract

This paper investigates some features of non-linear travel time models for dynamic traffic assignment (DTA) that adopt traffic on the link as the sole determinant for the calculation of travel time and have explicit relationships between travel time and traffic on the link. Analytical proofs and numerical examples are provided to show first-in-first-out (FIFO) violation and the behaviour of decreasing outflow with increasing traffic in non-linear travel time models. It is analytically shown that any non-linear travel time model could violate FIFO in some circumstances, especially when inflow drops sharply, and some convex non-linear travel time models could show behaviour with outflow decreasing as traffic increases. It is also shown that the linear travel time model does not show these behaviours. A non-linear travel time model in general form was used for analytical proofs and several existing non-linear travel time models were adopted for numerical examples. Considering the features addressed in this study, non-linear travel time models seem to have limitations for use in DTA in practical terms and care should be taken when they are used for modelling time-varying transportation networks.     

Reducing average comprehensive travel cost by rationally allocating trips to different travel modes

To study the effect of different transport policies on reducing the average comprehensive travel cost (CTC) of all travel modes, by increasing public transport modal share and decreasing car trips, an optimization model is developed based on travel cost utility. A nested logit model is applied to analyze trip modal split. A Genetic Algorithm is then used to determine the implementation of optimal solutions in which various transport policies are applied in order to reduce average CTC. The central urban region of Beijing is selected as the study area in this research. Different policies are analyzed for comparison, focusing on their optimal impacts on minimizing the average CTC utility of all travel modes by rationally allocating trips to different travel modes in the study area. It is found that the proposed optimization model provides a reasonable indication of the effect of policies applied.     

A demand model for recreational travel

A model is developed to describe and to predict the patterns of regional recreational travel. The model is designed in such a manner to allow its calibration and use without the need to conduct extensive travel surveys in a large region. To allow its use for prediction, the model is based on a causal structure and attempts to derive recreational travel demand from behavioural variables. The main hypothesis of the model is that the amount of recreational travel a recreation area attracts is affected by the accessibility of this area to points of demand potential and by its attractiveness relative to the recreation areas.

The calibration is founded on actual data on recreational travel to national forests in California, U.S.A. It is found in the calibration that accessibility to demand potential is the single most important determinant of recreational travel attraction. A simple relationship is derived to relate travel to each national forest to the relative accessibility of the forest. The model is calibrated and statistically validated.

It is suggested that when constructing travel demand models simplicity be sought, even at the risk of the loss of some explanatory power. In the calibration of such models statistical significant is more important than the ability to reproduce observed patterns.     

Out-of-home activities,daily travel,and subjective well-being

It is argued that utility theory that underpins current cost-benefit analyses of daily travel needs to be complemented. An alternative theoretical framework is to this end proposed which applies subjective well-being (SWB) to travel behaviour analysis. It is posited in this theoretical framework that participation in goal-directed activities, facilitated or hindered by travel, contributes to SWB, that the degree of travel-related stress in participating in these activities reduces SWB, and that positive affect associated with travel in itself has an impact on SWB.     

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.     

What do commuters think travel time reliability is worth? Calculating economic value of reducing the frequency and extent of unexpected delays

The measurement of transportation system reliability has become one of the central topics of travel demand studies. A growing literature concerns the measurement of value of travel time reliability which provides a monetary cost of avoiding unpredictable travel time. The goal of this study is to measure commuters’ sensitivities to travel time reliability and their willingness to pay (WTP) to avoid unreliable routes. The preferences are elicited through a pivoted stated preference survey technique. To circumvent the issue of presenting numerical distributions and statistical terms to day-to-day commuters, we use the frequency of delay days as a means of measuring traveler’s sensitivities to travel time reliability. The advantage of using simplified measures to elicit traveler preferences for travel time reliability is that these methods simply compare days with high delay to days with usual travel time. It was found that travelers are not only averse to the amount of unexpected delay but also to the frequency of days with unexpected delays. The paper presents WTP findings for three measures: travel time, frequency embedded travel time, and travel time reliability. The ‘reliability’ increase in WTP for travel time is found to be nearly proportional to the frequency of experiencing unexpected delays. For example, the WTP for mean travel time is calculated at $6.98/h; however, reliability adds $3.27 (about 50 % of $6.98) to avoid unexpected delays ‘5 out of 10 days’. The results of the study would provide valuable inputs to cost-benefit analyses and traffic and revenue studies required for road tolling investment projects.     

Travel mode choice and travel satisfaction: bridging the gap between decision utility and experienced utility

Over the past decades research on travel mode choice has evolved from work that is informed by utility theory, examining the effects of objective determinants, to studies incorporating more subjective variables such as habits and attitudes. Recently, the way people perceive their travel has been analyzed with transportation-oriented scales of subjective well-being, and particularly the satisfaction with travel scale. However, studies analyzing the link between travel mode choice (i.e., decision utility) and travel satisfaction (i.e., experienced utility) are limited. In this paper we will focus on the relation between mode choice and travel satisfaction for leisure trips (with travel-related attitudes and the built environment as explanatory variables) of study participants in urban and suburban neighborhoods in the city of Ghent, Belgium. It is shown that the built environment and travel-related attitudes—both important explanatory variables of travel mode choice—and mode choice itself affect travel satisfaction. Public transit users perceive their travel most negatively, while active travel results in the highest levels of travel satisfaction. Surprisingly, suburban dwellers perceive their travel more positively than urban dwellers, for all travel modes.     

“I can do perfectly well without a car!”

This article presents the results of a study exploring travellers’ preferences for middle-distance travel using Q-methodology. Respondents rank-ordered 42 opinion statements regarding travel choice and motivations for travel in general and for car and public transport as alternative travel modes. By-person factor analysis revealed four distinct preference segments for middle-distance travel: (1) choice travellers with a preference for public transport, (2) deliberate-choice travellers, (3) choice travellers with car as dominant alternative, and (4) car-dependent travellers. These preference segments differ in terms of the levels of involvement and cognitive effort in travel decision making, the travel consideration-set and underlying motivations. The study showed that for most people there is more to travel than getting from point A to point B, and that there is considerable heterogeneity in middle-distance travel preferences. Policy implications for reducing the need for travel and promoting a modal shift from car to other travel modes are discussed.     

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.     

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.     

Modeling the structural relationships among short-distance travel amounts,perceptions, affections,and desires

Using structural equation modeling, the relationships among travel amounts, perceptions, affections, and desires across five short-distance (one-way trips of less than 100 miles) travel categories (overall, commute, work/school-related, entertainment/social/recreation, and personal vehicle) are examined. The models are estimated using data collected in 1998 from more than 1300 working commuters in the San Francisco Bay Area. A cross-model analysis reveals three robust relationships, namely: (1) myriad measures of travel amounts work together to affect perceptions; (2) perceptions are consistently important in shaping desires; and (3) affections have a positive relationship with desires. The second finding suggests that two individuals who travel the same objective amount may not have the same desire to reduce their travel: how much individuals perceive their travel to be is important. The third point argues that the degree to which travel is enjoyed is a key determinant of shaping desires to reduce travel: the more travel is enjoyed, the less the desire to reduce it.     

The life cycle concept as a tool for travel research

For understanding individual and household travel behavior, the concept of the life cycle holds promise. The history of this concept is presented, and the theoretical and methodological issues surrounding its use are examined.In travel research, the life-cycle concept tends to be adopted uncritically. Utilizing the 1977 Nationwide Personal Transportation Study, an analysis of travel behavior is presented in an attempt to address some of these inadequacies. A set of five houshold types and their life-cycle stages are identified: the typical (nuclear) family, the single parent family, the childless married couple, the single person household, and households of unrelated individuals, The average daily trip frequencies of households at each life cycle stage are reported.Comparison of trip-making by life-cycle stage for the five household types points to the presence of a life-cycle effect in travel, but the effect appears to consist of two separate components: household structure (the relationships among household members) and the age of household members. Also discussed, but not examined in this study, are other factors potentially contributing to the observed life-cycle patterns.It is concluded that further efforts to deal with the complexities of the life-cycle concept in travel research will be worthwhile. These efforts will provide a framework for viewing travel behavior over the human life span and this will be especially useful in assessing the impact of demographic change for transportation system planning.     

Adaptive traffic signal control with equilibrium constraints under stochastic demand

This study develops a methodology to model transportation network design with signal settings in the presence of demand uncertainty. It is assumed that the total travel demand consists of commuters and infrequent travellers. The commuter travel demand is deterministic, whereas the demand of infrequent travellers is stochastic. Variations in demand contribute to travel time uncertainty and affect commuters’ route choice behaviour. In this paper, we first introduce an equilibrium flow model that takes account of uncertain demand. A two-stage stochastic program is then proposed to formulate the network signal design under demand uncertainty. The optimal control policy derived under the two-stage stochastic program is able to (1) optimize the steady-state network performance in the long run, and (2) respond to short-term demand variations. In the first stage, a base signal control plan with a buffer against variability is introduced to control the equilibrium flow pattern and the resulting steady-state performance. In the second stage, after realizations of the random demand, recourse decisions of adaptive signal settings are determined to address the occasional demand overflows, so as to avoid transient congestion. The overall objective is to minimize the expected total travel time. To solve the two-stage stochastic program, a concept of service reliability associated with the control buffer is introduced. A reliability-based gradient projection algorithm is then developed. Numerical examples are performed to illustrate the properties of the proposed control method as well as its capability of optimizing steady-state performance while adaptively responding to changing traffic flows. Comparison results show that the proposed method exhibits advantages over the traditional mean-value approach in improving network expected total travel times.     

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.     

Door-to-door travel times in RP departure time choice models: An approximation method using GPS data

A common way to determine values of travel time and schedule delay is to estimate departure time choice models, using stated preference (SP) or revealed preference (RP) data. The latter are used less frequently, mainly because of the difficulties to collect the data required for the model estimation. One main requirement is knowledge of the (expected) travel times for both chosen and unchosen departure time alternatives. As the availability of such data is limited, most RP-based scheduling models only take into account travel times on trip segments rather than door-to-door travel times, or use very rough measures of door-to-door travel times. We show that ignoring the temporal and spatial variation of travel times, and, in particular, the correlation of travel times across links may lead to biased estimates of the value of time (VOT). To approximate door-to-door travel times for which no complete measurement is possible, we develop a method that relates travel times on links with continuous speed measurements to travel times on links where relatively infrequent GPS-based speed measurements are available. We use geographically weighted regression to estimate the location-specific relation between the speeds on these two types of links, which is then used for travel time prediction at different locations, days, and times of the day. This method is not only useful for the approximation of door-to-door travel times in departure time choice models, but is generally relevant for predicting travel times in situations where continuous speed measurements can be enriched with GPS data.     

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.

Neighborhood services,trip purpose,and tour-based travel

Communities are increasingly looking to land use planning strategies to reduce drive-alone travel. Many planning efforts aim to develop neighborhoods with higher levels of accessibility that will allow residents to shop closer to home and drive fewer miles. To better understand how accessible land use patterns relate to household travel behavior, this paper is divided into three sections. The first section describes the typical range of services available in areas with high neighborhood accessibility. It explains how trip-based travel analysis is limited because it does not consider the linked (chained) nature of most travel. The second section describes a framework that provides a more behavioral understanding of household travel. This framework highlights travel tours, the sequence of trips that begin and end at home, as the basic unit of analysis. The paper offers a typology of travel tours to account for different travel purposes; by doing so, this typology helps understand tours relative to the range of services typically offered in accessible neighborhoods. The final section empirically analyzes relationships between tour type and neighborhood access using detailed travel data from the Central Puget Sound region (Seattle, Washington). Households living in areas with higher levels of neighborhood access are found to complete more tours and make fewer stops per tour. They make more simple tours (out and back) for work and maintenance (personal, appointment, and shopping) trip purposes but there is no difference in the frequency of other types of tours. While they travel shorter distances for maintenance-type errands, a large portion of their maintenance travel is still pursued outside the neighborhood. These findings suggest that while higher levels of neighborhood access influences travel tours, it does not spur households to complete the bulk of their errands close to home.     

An investigation of the reliability of real-time information for route choice decisions in a congested traffic system

This paper investigates the reliability of information on prevailing trip times on the links of a network as a basis for route choice decisions by individual drivers. It considers a type of information strategy in which no attempt is made by some central controller or coordinating entity to predict what the travel times on each link would be by the time it is reached by a driver that is presently at a given location. A specially modified model combining traffic simulation and path assignment capabilities is used to analyze the reliability of the real-time information supplied to the drivers. This is accomplished by comparing the supplied travel times (at the link and path levels) to the actual trip times experienced in the network after the information has been given. In addition, the quality of the decisions made by drivers on the basis of this information (under alternative path switching rules) is evaluated ex-post by comparing the actually experienced travel time (given the decision made) to the time that the driver would have experienced without the real-time information. Results of a series of simulation experiments under recurrent congestion conditions are discussed, illustrating the interactions between information reliability and user response.     

Modeling travel time reliability of freeways using risk assessment techniques

Travel time reliability is considered to be one of the key indicators for the performance of transport systems and is measured in various ways. This paper synthesizes both reliability concepts: traffic breakdown, the indicator of the instability of travel times, is treated as the risk, whereas travel time variability, the indicator of the uncertainty of travel times, is considered as the consequence of this risk. An analytical formula, using risk assessment technique, explicitly expresses the cost of travel time unreliability as the sum of the products of the consequences (i.e. variability) and the corresponding probabilities of breakdown. It provides a novel measure of travel time reliability and is applicable in network performance evaluations. An empirical example based on a large dataset of freeway traffic flow data from loop detectors shows that the developed travel time reliability measure is both intuitively logical and consistent.     

Comparative analysis of three user equilibrium models under stochastic demand

Recent empirical studies on the value of time and reliability reveal that travel time variability plays an important role on travelers' route choice decision process. It can be considered as a risk to travelers making a trip. Therefore, travelers are not only interested in saving their travel time but also in reducing their risk. Typically, risk can be represented by two different aspects: acceptable risk and unacceptable risk. Acceptable risk refers to the reliability aspect of acceptable travel time, which is defined as the average travel time plus the acceptable additional time (or buffer time) needed to ensure more frequent on‐time arrivals, while unacceptable risk refers to the unreliability aspect of unacceptable late arrivals (though infrequent) that have a travel time excessively higher than the acceptable travel time. Most research in the network equilibrium based approach to modeling travel time variability ignores the unreliability aspect of unacceptable late arrivals. This paper examines the effects of both reliability and unreliability aspects in a network equilibrium framework. Specifically, the traditional user equilibrium model, the demand driven travel time reliability‐based user equilibrium model, and the α‐reliable mean‐excess travel time user equilibrium model are considered in the investigation under an uncertain environment due to stochastic travel demand. Numerical results are presented to examine how these models handle risk under travel time variability.