Preferences for travel time under risk and ambiguity: Implications in path selection and network equilibrium

In this paper, we study the preferences for uncertain travel times in which probability distributions may not be fully characterized. In evaluating an uncertain travel time, we explicitly distinguish between risk, where the probability distribution is precisely known, and ambiguity, where it is not. In particular, we propose a new criterion called ambiguity-aware CARA travel time (ACT) for evaluating uncertain travel times under various attitudes of risk and ambiguity, which is a preference based on blending the Hurwicz criterion and Constant Absolute Risk Aversion (CARA). More importantly, we show that when the uncertain link travel times are independently distributed, finding the path that minimizes travel time under the ACT criterion is essentially a shortest path problem. We also study the implications on Network Equilibrium (NE) model where travelers on the traffic network are characterized by their knowledge of the network uncertainty as well as their risk and ambiguity attitudes under the ACT. We derive and analyze the existence and uniqueness of solutions under NE. Finally, we obtain the Price of Anarchy that characterizes the inefficiency of this new equilibrium. The computational study suggests that as uncertainty increases, the influence of selfishness on inefficiency diminishes.     

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.     

Perception bias in route choice

Travel time is probably one of the most studied attributes in route choice. Recently, perception of travel time received more attention as several studies have shown its importance in explaining route choice behavior. In particular, travel time estimates by travelers appear to be biased against non-chosen options even if these are faster. In this paper, we study travel time perception and route choice of routes with different degrees of road hierarchy and directness. In the Dutch city of Enschede, respondents were asked to choose a route and provide their estimated travel times for both the preferred and alternative routes. These travel times were then compared with actual travel times. Results from previous studies were confirmed and expanded. The shortest time route was chosen in 41 % of the cases while the perceived shortest time route was chosen by almost 80 % of the respondents. Respondents overestimated travel time in general but overestimated the travel time of non-chosen routes more than the travel time of chosen routes. Perception of travel time depends on road hierarchy and route directness, as more direct routes and routes higher up in the hierarchy were perceived as being relatively fast. In addition, there is evidence that these attributes also influence route choice independently of perceived travel time. Finally, travel time perceptions appear to be most strongly biased against non-chosen options when respondents were familiar with the route or indicated a clear preference for the chosen routes. This result indicates that behavior will be more difficult to change for the regular travelers.     

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.     

Application of Lagrangian relaxation approach to α-reliable path finding in stochastic networks with correlated link travel times

This study investigates the important problem of determining a reliable path in a stochastic network with correlated link travel times. First, the distribution of path travel time is quantified by using trip records from GPS probe vehicles. Second, the spatial correlation of link travel time is explicitly considered by using a correlation coefficient matrix, which is incorporated into the α-reliable path problem by Cholesky decomposition. Third, the Lagrangian relaxation based framework is used to handle the α-reliable path problem, by which the intractable problem with a non-linear and non-additive structure can be decomposed into several easy-to-solve problems. Finally, the path-finding performance of this approach is tested on a real-world network. The results show that 15 iterations of calculation can yield a small relative gap between upper and lower bounds of the optimal solution and the average running time is about 5 s for most OD settings. The applicability of α-reliable path finding is validated by a case study.     

A stochastic optimization model for transit network timetable design to mitigate the randomness of traveling time by adding slack time

Transit network timetabling aims at determining the departure time of each trip of all lines in order to facilitate passengers transferring either to or from a bus. In this paper, we consider a bus timetabling problem with stochastic travel times (BTP-STT). Slack time is added into timetable to mitigate the randomness in bus travel times. We then develop a stochastic integer programming model for the BTP-STT to minimize the total waiting time cost for three types of passengers (i.e., transferring passengers, boarding passengers and through passengers). The mathematical properties of the model are characterized. Due to its computational complexity, a genetic algorithm with local search (GALS) is designed to solve our proposed model (OPM). The numerical results based on a small bus network show that the timetable obtained from OPM reduces the total waiting time cost by an average of 9.5%, when it is tested in different scenarios. OPM is relatively effective if the ratio of the number of through passengers to the number of transferring passengers is not larger than a threshold (e.g., 10 in our case). In addition, we test different scale instances randomly generated in a practical setting to further verify the effectiveness of OPM and GALS. We also find that adding slack time into timetable greatly benefits transferring passengers by reducing the rate of transferring failure.     

The electric vehicle touring problem

The increasing concern over global warming has led to the rapid development of the electric vehicle industry. Electric vehicles (EVs) have the potential to reduce the greenhouse effect and facilitate more efficient use of energy resources. In this paper, we study several EV route planning problems that take into consideration possible battery charging or swapping operations. Given a road network, the objective is to determine the shortest (travel time) route that a vehicle with a given battery capacity can take to travel between a pair of vertices or to visit a set of vertices with several stops, if necessary, at battery switch stations. We present polynomial time algorithms for the EV shortest travel time path problem and the fixed tour EV touring problem, where the fixed tour problem requires visiting a set of vertices in a given order. Based on the result, we also propose constant factor approximation algorithms for the EV touring problem, which is a generalization of the traveling salesman problem.     

Network impacts of a road capacity reduction: Empirical analysis and model predictions

In spite of their widespread use in policy design and evaluation, relatively little evidence has been reported on how well traffic equilibrium models predict real network impacts. Here we present what we believe to be the first paper that together analyses the explicit impacts on observed route choice of an actual network intervention and compares this with the before-and-after predictions of a network equilibrium model. The analysis is based on the findings of an empirical study of the travel time and route choice impacts of a road capacity reduction. Time-stamped, partial licence plates were recorded across a series of locations, over a period of days both with and without the capacity reduction, and the data were ‘matched’ between locations using special-purpose statistical methods. Hypothesis tests were used to identify statistically significant changes in travel times and route choice, between the periods of days with and without the capacity reduction. A traffic network equilibrium model was then independently applied to the same scenarios, and its predictions compared with the empirical findings. From a comparison of route choice patterns, a particularly influential spatial effect was revealed of the parameter specifying the relative values of distance and travel time assumed in the generalised cost equations. When this parameter was ‘fitted’ to the data without the capacity reduction, the network model broadly predicted the route choice impacts of the capacity reduction, but with other values it was seen to perform poorly. The paper concludes by discussing the wider practical and research implications of the study’s findings.     

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.

The implications on willingness to pay of respondents ignoring specific attributes

Individuals processing the information in a stated choice experiment are typically assumed to evaluate each and every attribute offered within and between alternatives, and to choose their most preferred alternative. However, it has always been thought that some attributes are ignored in this process for many reasons, including a coping strategy to handle ones perception of the complexity of the choice task. Nonetheless, analysts typically proceed to estimate discrete choice models as if all attributes have influenced the outcome to some degree. The cognitive processes used to evaluate trade-offs are complex with boundaries often placed on the task to assist the respondent. These boundaries can include prioritising attributes and ignoring specific attributes. In this paper we investigate the implications of bounding the information processing task by attribute elimination through ignoring one or more attributes. Using a sample of car commuters in Sydney we estimate mixed logit models that assume all attributes are candidate contributors, and models that assume certain attributes are ignored, the latter based on supplementary information provided by respondents. We compare the value of travel time savings under the alternative attribute processing regimes. Assuming that all attributes are not ignored and duly processed, leads to estimates of parameters which produce significantly different willingness to pay (WTP) to that obtained when the exclusion rule is invoked.     

Modeling stochastic perception error in the mean-excess traffic equilibrium model

In this paper, we extend the α-reliable mean-excess traffic equilibrium (METE) model of Chen and Zhou (Transportation Research Part B 44(4), 2010, 493-513) by explicitly modeling the stochastic perception errors within the travelers’ route choice decision processes. In the METE model, each traveler not only considers a travel time budget for ensuring on-time arrival at a confidence level α, but also accounts for the impact of encountering worse travel times in the (1 − α) quantile of the distribution tail. Furthermore, due to the imperfect knowledge of the travel time variability particularly in congested networks without advanced traveler information systems, the travelers’ route choice decisions are based on the perceived travel time distribution rather than the actual travel time distribution. In order to compute the perceived mean-excess travel time, an approximation method based on moment analysis is developed. It involves using the conditional moment generation function to derive the perceived link travel time, the Cornish-Fisher Asymptotic Expansion to estimate the perceived travel time budget, and the Acerbi and Tasche Approximation to estimate the perceived mean-excess travel time. The proposed stochastic mean-excess traffic equilibrium (SMETE) model is formulated as a variational inequality (VI) problem, and solved by a route-based solution algorithm with the use of the modified alternating direction method. Numerical examples are also provided to illustrate the application of the proposed SMETE model and solution method.     

Evaluation of a reactive dynamic route guidance strategy

The aim of the paper is to evaluate the performance of a new strategy which is able to control dynamic route guidance (DRG) systems, mainly in urban road networks. The purpose of this strategy is to achieve dynamic user equilibrium in the network, even in abnormal network conditions, for example when there is an unexpected increase in traffic volume. It is based on feedback concept and it reacts to the traffic conditions observed in real time by adopting a decentralized structure.A series of experiments was performed, by means of a traffic micro-simulator, in a section of an urban road network. In the situations examined, the results seem to be quite positive. The analyses of the link level show that all of the various travel alternatives to reach the destination become more advantageous for users if DRG devices become more widespread among vehicles. In some cases we observe that the strategy succeeds in maintaining the possible alternatives in equilibrium conditions, by distributing users among the feasible turns. At no point in our investigations do we observe an unstable behaviour of the system, even when the number of vehicles fitted with a DRG device increases.     

Modelling contact mode and frequency of interactions with social network members using the multiple discrete–continuous extreme value model

Communication patterns are an integral component of activity patterns and the travel induced by these activities. The present study aims to understand the determinants of the communication patterns (by the modes face-to-face, phone, e-mail and SMS) between people and their social network members. The aim is for this to eventually provide further insights into travel behaviour for social and leisure purposes. A social network perspective brings value to the study and modelling of activity patterns since leisure activities are influenced not only by traditional trip measures such as time and cost but also motivated extensively by the people involved in the activity. By using a multiple discrete-continuous extreme value model (Bhat, 2005), we can investigate the means of communication chosen to interact with a given social network member (multiple discrete choices) and the frequency of interaction by each mode (treated as continuous) at the same time. The model also allows us to investigate satiation effects for different modes of communication. Our findings show that in spite of people having increasingly geographically widespread networks and more diverse communication technologies, a strong underlying preference for face-to-face contact remains. In contrast with some of the existing work, we show that travel-related variables at the ego level are less important than specific social determinants which can be considered while making use of social network data.     

Inferring patterns in the multi-week activity sequences of public transport users

The public transport networks of dense cities such as London serve passengers with widely different travel patterns. In line with the diverse lives of urban dwellers, activities and journeys are combined within days and across days in diverse sequences. From personalized customer information, to improved travel demand models, understanding this type of heterogeneity among transit users is relevant to a number of applications core to public transport agencies’ function. In this study, passenger heterogeneity is investigated based on a longitudinal representation of each user’s multi-week activity sequence derived from smart card data. We propose a methodology leveraging this representation to identify clusters of users with similar activity sequence structure. The methodology is applied to a large sample (n = 33,026) from London’s public transport network, in which each passenger is represented by a continuous 4-week activity sequence. The application reveals 11 clusters, each characterized by a distinct sequence structure. Socio-demographic information available for a small sample of users (n = 1973) is combined to smart card transactions to analyze associations between the identified patterns and demographic attributes including passenger age, occupation, household composition and income, and vehicle ownership. The analysis reveals that significant connections exist between the demographic attributes of users and activity patterns identified exclusively from fare transactions.     

Multi-step prediction of experienced travel times using agent-based modeling

This paper develops an agent-based modeling approach to predict multi-step ahead experienced travel times using real-time and historical spatiotemporal traffic data. At the microscopic level, each agent represents an expert in a decision-making system. Each expert predicts the travel time for each time interval according to experiences from a historical dataset. A set of agent interactions is developed to preserve agents that correspond to traffic patterns similar to the real-time measurements and replace invalid agents or agents associated with negligible weights with new agents. Consequently, the aggregation of each agent’s recommendation (predicted travel time with associated weight) provides a macroscopic level of output, namely the predicted travel time distribution. Probe vehicle data from a 95-mile freeway stretch along I-64 and I-264 are used to test different predictors. The results show that the agent-based modeling approach produces the least prediction error compared to other state-of-the-practice and state-of-the-art methods (instantaneous travel time, historical average and k-nearest neighbor), and maintains less than a 9% prediction error for trip departures up to 60 min into the future for a two-hour trip. Moreover, the confidence boundaries of the predicted travel times demonstrate that the proposed approach also provides high accuracy in predicting travel time confidence intervals. Finally, the proposed approach does not require offline training thus making it easily transferable to other locations and the fast algorithm computation allows the proposed approach to be implemented in real-time applications in Traffic Management Centers.     

A Trip Reconstruction Tool for GPS-based Personal Travel Surveys

ABSTRACT

This article reports on the development of a trip reconstruction software tool for use in GPS-based personal travel surveys. Specifically, the tool enables the automatic processing of GPS traces of individual survey respondents in order to identify the road links traveled and modes used by each respondent for individual trips. Identifying the links is based on a conventional GIS-based map-matching algorithm and identifying the modes is a rule-based algorithm using attributes of four modes (walk, bicycle, bus and passenger-car). The tool was evaluated using GPS travel data collected for the study and a multi-modal transportation network model of downtown Toronto. The results show that the tool correctly detected about 79% of all links traveled and 92% of all trip modes.     

The estimation of a time-dependent OD trip table with vehicle trajectory samples

Abstract

In this paper we discuss a dynamic origin–destination (OD) estimation problem that has been used for identifying time-dependent travel demand on a road network. Even though a dynamic OD table is an indispensable data input for executing a dynamic traffic assignment, it is difficult to construct using the conventional OD construction method such as the four-step model. For this reason, a direct estimation method based on field traffic data such as link traffic counts has been used. However, the method does not account for a logical relationship between a travel demand pattern and socioeconomic attributes. In addition, the OD estimation method cannot guarantee the reliability of estimated results since the OD estimation problem has a property named the ‘underdetermined problem.’ In order to overcome such a problem, the method developed in this paper makes use of vehicle trajectory samples with link traffic counts. The new method is applied to numerical examples and shows promising capability for identifying a temporal and spatial travel demand pattern.     

Network-wide adaptive tolling for connected and automated vehicles

This article proposes Δ-tolling, a simple adaptive pricing scheme which only requires travel time observations and two tuning parameters. These tolls are applied throughout a road network, and can be updated as frequently as travel time observations are made. Notably, Δ-tolling does not require any details of the traffic flow or travel demand models other than travel time observations, rendering it easy to apply in real-time. The flexibility of this tolling scheme is demonstrated in three specific traffic modeling contexts with varying traffic flow and user behavior assumptions: a day-to-day pricing model using static network equilibrium with link delay functions; a within-day adaptive pricing model using the cell transmission model and dynamic routing of vehicles; and a microsimulation of reservation-based intersection control for connected and autonomous vehicles with myopic routing. In all cases, Δ-tolling produces significant benefits over the no-toll case, measured in terms of average travel time and social welfare, while only requiring two parameters to be tuned. Some optimality results are also given for the special case of the static network equilibrium model with BPR-style delay functions.     

Access control policies without inside queues: Their properties and public policy implications

An access control policy that eliminates all queues beyond the entry points to a network has obvious benefits, which include smooth travel and predictable travel times inside the network. Yet it has never been proven, to the best of our knowledge, whether excluding inside queues yields sub-optimal network performance or, in other words, allowing inside queues can actually further reduce the system travel cost. Moreover, it is not clear whether an optimal control policy derived from efficiency considerations can also be a fair policy to all road users. This paper provide answers to these questions in the context of a monocentric network. By analyzing the structure of the access control problem considering all feasible policies (with/without inside queues), we show that the minimal system cost realizable by access control can be obtained without directly solving a non-convex optimization program, and can indeed always be achieved by a control policy excluding all of the inside queues. These optimal policies are defined by a polyhedral set and a Finite Generation Algorithm can be applied to derive the analytical form of this set. The optimal policies are not unique in general, thus making it possible to achieve both minimal system cost and fairness simultaneously.     

A model and solution algorithm for dynamic deterministic user equilibrium assignment

Abstract

In this paper a route-based dynamic deterministic user equilibrium assignment model is presented. Some features of the linear travel time model are first investigated and then a divided linear travel time model is proposed for the estimation of link travel time: it addresses the limitations of the linear travel time model. For the application of the proposed model to general transportation networks, this paper provides thorough investigations on the computational issues in dynamic traffic assignment with many-to-many OD pairs and presents an efficient solution procedure. The numerical calculations demonstrate that the proposed model and solution algorithm produce satisfactory solutions for a network of substantial size with many-to-many OD pairs. Comparisons of assignment results are also made to show the impacts of incorporation of different link travel time models on the assignment results.