A multi‐class mean‐excess traffic equilibrium model with elastic demand

Recent empirical studies have revealed that travel time variability plays an important role in travelers' route choice decisions. To simultaneously account for both reliability and unreliability aspects of travel time variability, the concept of mean‐excess travel time (METT) was recently proposed as a new risk‐averse route choice criterion. In this paper, we extend the mean‐excess traffic equilibrium model to include heterogeneous risk‐aversion attitudes and elastic demand. Specifically, this model explicitly considers (1) multiple user classes with different risk‐aversions toward travel time variability when making route choice decisions under uncertainty and (2) the elasticity of travel demand as a function of METT when making travel choice decisions under uncertainty. This model is thus capable of modeling travelers' heterogeneous risk‐averse behaviors with both travel choice and route choice considerations. The proposed model is formulated as a variational inequality problem and solved via a route‐based algorithm using the modified alternating direction method. Numerical analyses are also provided to illustrate the features of the proposed model and the applicability of the solution algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiclass fuzzy user equilibrium with endogenous membership functions and risk‐taking behaviors

Over the last decades, several approaches have been proposed in the literature to incorporate users' perceptions of travel costs, their bounded rationality, and risk‐taking behaviors into network equilibrium modeling for traffic assignment problem. While theoretically advanced, these models often suffer from high complexity and computational cost and often involve parameters that are difficult to estimate. This study proposes an alternative approach where users' imprecise perceptions of travel times are endogenously constructed as fuzzy sets based on the probability distributions of random link travel times. Two decision rules are proposed accordingly to account for users' heterogeneous risk‐taking behaviors, that is, optimistic and pessimistic rules. The proposed approach, namely, the multiclass fuzzy user equilibrium, can be formulated as a link‐based variational inequality model. The model can be solved efficiently, and parameters involved can be either easily estimated or treated as factors for calibration against observed traffic flow data. Numerical examples show that the proposed model can be solved efficiently even for a large‐scale network of Mashhad, Iran, with 2538 links and 7157 origin–destination pairs. The example also illustrates the calibration capability of the proposed model, highlighting that the model is able to produce much more accurate flow estimates compared with the Wardropian user equilibrium model. Copyright © 2016 John Wiley & Sons, Ltd.     

A solution algorithm for a dynamic deterministic user equilibrium assignment model with departure time choice

Abstract

A route-based combined model of dynamic deterministic route and departure time choice and a solution method for many origin and destination pairs is proposed. The divided linear travel time model is used to calculate the link travel time and to describe the propagation of flow over time. For the calculation of route travel times, the predictive ideal route travel time concept is adopted. Solving the combined model of dynamic deterministic route and departure time choice is shown to be equivalent to solving simultaneously a system of non-linear equations. A Newton-type iterative scheme is proposed to solve this problem. The performance of the proposed solution method is demonstrated using a version of the Sioux Falls network. This shows that the proposed solution method produces good equilibrium solutions with reasonable computational cost.     

Performance measure for reliable travel time of emergency vehicles

Travel time is very critical for emergency response and emergency vehicle (EV) operations. Compared to ordinary vehicles (OVs), EVs are permitted to break conventional road rules to reach the destination within shorter time. However, very few previous studies address the travel time performance of EVs. This study obtained nearly 4-year EV travel time data in Northern Virginia (NOVA) region using 76,000 preemption records at signalized intersections. First, the special characteristics of EV travel time are explored in mean, median, standard deviation and also the distribution, which display largely different characteristics from that of OVs in previous studies. Second, a utility-based model is proposed to quantify the travel time performance of EVs. Third, this paper further investigates two important components of the utility model: benchmark travel time and standardized travel time. The mode of the distribution is chosen as benchmark travel time, and its nonlinear decreasing relationship with the link length is revealed. At the same time, the distribution of standardized travel time is fitted with different candidate distributions and Inv. Gaussian distribution is proved to be the most suitable one. Finally, to validate the proposed model, we implement the model in case studies to estimate link and route travel time performance. The results of route comparisons also show that the proposed model can support EV route choice and eventually improve EV service and operations.     

A dynamic linear model for the estimation of time‐varying origin–destination matrices from link counts

We propose a dynamic linear model (DLM) for the estimation of day‐to‐day time‐varying origin–destination (OD) matrices from link counts. Mean OD flows are assumed to vary over time as a locally constant model. We take into account variability in OD flows, route flows, and link volumes. Given a time series of observed link volumes, sequential Bayesian inference is applied in order to estimate mean OD flows. The conditions under which mean OD flows may be estimated are established, and computational studies on two benchmark transportation networks from the literature are carried out. In both cases, the DLM converged to the unobserved mean OD flows when given sufficient observations of traffic link volumes despite assuming uninformative prior OD matrices. We discuss limitations and extensions of the proposed DLM. Copyright © 2017 John Wiley & Sons, Ltd.     

A reliability‐based traffic assignment model for multi‐modal transport network under demand uncertainty

In densely populated and congested urban areas, the travel times in congested multi‐modal transport networks are generally varied and stochastic in practice. These stochastic travel times may be raised from day‐to‐day demand fluctuations and would affect travelers' route and mode choice behaviors according to their different expectations of on‐time arrival. In view of these, this paper presents a reliability‐based user equilibrium traffic assignment model for congested multi‐modal transport networks under demand uncertainty. The stochastic bus frequency due to the unstable travel time of bus route is explicitly considered. By the proposed model, travelers' route and mode choice behaviors are intensively explored. In addition, a stochastic state‐augmented multi‐modal transport network is adopted in this paper to effectively model probable transfers and non‐linear fare structures. A numerical example is given to illustrate the merits of the proposed model. Copyright © 2012 John Wiley & Sons, Ltd.     

Accuracy of distance‐based travel time decomposition in probe vehicle systems

Probe vehicle data (PVD) are commonly used for area‐wide measurements of travel time in road networks. In this context, travel times usually refer to fixed edges of an underlying (digital) map. That means measured travel times have to be transformed into so‐called link travel times first. This paper analyzes a common method being applied for solving this task (distance‐based travel time decomposition). It is shown that, in general, its inherent imprecision must not be neglected. Instead, it might cause a serious misinterpretation of data if potential errors in the context of travel time decomposition are ignored. For this purpose, systematic as well as maximum deviations between “decomposed” and “true” link travel times are mathematically analyzed. By that, divergent statements in the literature about the accuracy of PVD are harmonized. Moreover, conditions for the applicability of the so‐called distance‐proportion method are derived depending on the permitted error level. Three examples ranging from pure theory to real world confirm the analytical findings and underline the problems resulting from distance‐based travel time decomposition at local level, for example, at individual intersections. Copyright © 2013 John Wiley & Sons, Ltd.     

Efficient solution algorithm for finding spatially dependent reliable shortest path in road networks

Travel times are generally stochastic and spatially correlated in congested road networks. However, very few existing route guidance systems (RGS) can provide reliable guidance services to aid travellers planning their trips with taking account explicitly travel time reliability constraint. This study aims to develop such a RGS with particular consideration of travellers' concern on travel time reliability in congested road networks with uncertainty. In this study, the spatially dependent reliable shortest path problem (SD‐RSPP) is formulated as a multi‐criteria shortest path‐finding problem in road networks with correlated link travel times. Three effective dominance conditions are established for links with different levels of travel time correlations. An efficient algorithm is proposed to solve SD‐RSPP by adaptively using three established dominance conditions. The complexities of road networks in reality are also explicitly considered. To demonstrate the applicability of proposed algorithm, a comprehensive case study is carried out in Hong Kong. The results of case study show that the proposed solution algorithm is robust to take account of travellers' multiple routing criteria. Computational results demonstrate that the proposed solution algorithm can determine the reliable shortest path on real‐time basis for large‐scale road networks. Copyright © 2016 John Wiley & Sons, Ltd.     

The value of travel time variance

This paper considers the value of travel time variability under scheduling preferences that are defined in terms of linearly time varying utility rates associated with being at the origin and at the destination. The main result is a simple expression for the value of travel time variability that does not depend on the shape of the travel time distribution. The related measure of travel time variability is the variance of travel time. These conclusions apply equally to travellers who can freely choose departure time and to travellers who use a scheduled service with fixed headway. Depending on parameters, travellers may be risk averse or risk seeking and the value of travel time may increase or decrease in the mean travel time.     

Estimating time dependent O‐D trip tables during peak periods

Intelligent transportation systems (ITS) have been used to alleviate congestion problems arising due to demand during peak periods. The success of ITS strategies relies heavily on two factors: 1) the ability to accurately estimate the temporal and spatial distribution of travel demand on the transportation network during peak periods, and, 2) providing real‐time route guidance to users. This paper addresses the first factor. A model to estimate time dependent origin‐destination (O‐D) trip tables in urban areas during peak periods is proposed. The daily peak travel period is divided into several time slices to facilitate simulation and modeling. In urban areas, a majority of the trips during peak periods are work trips. For illustration purposes, only peak period work trips are considered in this paper. The proposed methodology is based on the arrival pattern of trips at a traffic analysis zone (TAZ) and the distribution of their travel times. The travel time matrix for the peak period, the O‐D trip table for the peak period, and the number of trips expected to arrive at each TAZ at different work start times are inputs to the model. The model outputs are O‐D trip tables for each time slice in the peak period. 1995 data for the Las Vegas metropolitan area are considered for testing and validating the model, and its application. The model is reasonably robust, but some lack of precision was observed. This is due to two possible reasons: 1) rounding‐off, and, 2) low ratio of total number of trips to total number of O‐D pair combinations. Hence, an attempt is made to study the effect of increasing this ratio on error estimates. The ratio is increased by multiplying each O‐D pair trip element with a scaling factor. Better estimates were obtained. Computational issues involved with the simulation and modeling process are discussed.     

Decomposing travel times measured by probe-based traffic monitoring systems to individual road segments

In probe-based traffic monitoring systems, traffic conditions can be inferred based on the position data of a set of periodically polled probe vehicles. In such systems, the two consecutive polled positions do not necessarily correspond to the end points of individual links. Obtaining estimates of travel time at the individual link level requires the total traversal time (which is equal to the polling interval duration) be decomposed. This paper presents an algorithm for solving the problem of decomposing the traversal time to times taken to traverse individual road segments on the route. The proposed algorithm assumes minimal information about the network, namely network topography (i.e. links and nodes) and the free flow speed of each link. Unlike existing deterministic methods, the proposed solution algorithm defines a likelihood function that is maximized to solve for the most likely travel time for each road segment on the traversed route. The proposed scheme is evaluated using simulated data and compared to a benchmark deterministic method. The evaluation results suggest that the proposed method outperforms the bench mark method and on average improves the accuracy of the estimated link travel times by up to 90%.     

A stochastic multimodal reliable network design problem under adverse weather conditions

This paper formulates a network design problem (NDP) for finding the optimal public transport service frequencies and link capacity expansions in a multimodal network with consideration of impacts from adverse weather conditions. The proposed NDP aims to minimize the sum of expected total travel time, operational cost of transit services, and construction cost of link capacity expansions under an acceptable level of variance of total travel time. Auto, transit, bus, and walking modes are considered in the multimodal network model for finding the equilibrium flows and travel times. In the proposed network model, demands are assumed to follow Poisson distribution, and weather‐dependent link travel time functions are adopted. A probit‐based stochastic user equilibrium, which is based on the perceived expected travel disutility, is used to determine the multimodal route of the travelers. This model also considers the strategic behavior of the public transport travelers in choosing their routes, that is, common‐line network. Based on the stochastic multimodal model, the mean and variance of total travel time are analytical estimated for setting up the NDP. A sensitivity‐based solution algorithm is proposed for solving the NDP, and two numerical examples are adopted to demonstrate the characteristics of the proposed model. Copyright © 2014 John Wiley & Sons, Ltd.     

Modeling Travel Time Under ATIS Using Mixed Linear Models

The objective of this paper is to model travel time when drivers are equipped with pre-trip and/or en-route real-time traffic information/advice. A travel simulator with a realistic network and real historical congestion levels was used as a data collection tool. The network included 40 links and 25 nodes. This paper presents models of the origin-to-destination travel time and en-route short-term route (link) travel time under five different types and levels of advanced traveler information systems (ATIS). Mixed linear models with the repeated observation's technique were used in both models. Different covariance structures (including the independent case) were developed and compared. The effect of correlation was found significant in both models. The trip travel time analysis showed that as the level of information increases (adding en-route to the pre-trip and advice to the advice-free information), the average travel time decreases. The model estimates show that providing pre-trip and en-route traffic information with advice could result in significant savings in the overall travel time. The en-route short-term (link) travel time analysis showed that the en-route short-term (link) information has a good chance of being used and followed. The short-term qualitative information is more likely to be used than quantitative information. Learning and being familiar with the system that provides the information decreases en-route short-term delay.     

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.     

Travel time estimation for urban road networks using low frequency probe vehicle data

The paper presents a statistical model for urban road network travel time estimation using vehicle trajectories obtained from low frequency GPS probes as observations, where the vehicles typically cover multiple network links between reports. The network model separates trip travel times into link travel times and intersection delays and allows correlation between travel times on different network links based on a spatial moving average (SMA) structure. The observation model presents a way to estimate the parameters of the network model, including the correlation structure, through low frequency sampling of vehicle traces. Link-specific effects are combined with link attributes (speed limit, functional class, etc.) and trip conditions (day of week, season, weather, etc.) as explanatory variables. The approach captures the underlying factors behind spatial and temporal variations in speeds, which is useful for traffic management, planning and forecasting. The model is estimated using maximum likelihood. The model is applied in a case study for the network of Stockholm, Sweden. Link attributes and trip conditions (including recent snowfall) have significant effects on travel times and there is significant positive correlation between segments. The case study highlights the potential of using sparse probe vehicle data for monitoring the performance of the urban transport system.     

An adaptive information fusion model to predict the short-term link travel time distribution in dynamic traffic networks

As intelligent transportation systems (ITS) approach the realm of widespread deployment, there is an increasing need to robustly capture the variability of link travel time in real-time to generate reliable predictions of real-time traffic conditions. This study proposes an adaptive information fusion model to predict the short-term link travel time distribution by iteratively combining past information on link travel time on the current day with the real-time link travel time information available at discrete time points. The past link travel time information is represented as a discrete distribution. The real-time link travel time is represented as a range, and is characterized using information quality in terms of information accuracy and time delay. A nonlinear programming formulation is used to specify the adaptive information fusion model to update the short-term link travel time distribution by focusing on information quality. The model adapts good information by weighing it higher while shielding the effects of bad information by reducing its weight. Numerical experiments suggest that the proposed model adequately represents the short-term link travel time distribution in terms of accuracy and robustness, while ensuring consistency with ambient traffic flow conditions. Further, they illustrate that the mean of a representative short-term travel time distribution is not necessarily a good tracking indicator of the actual (ground truth) time-dependent travel time on that link. Parametric sensitivity analysis illustrates that information accuracy significantly influences the model, and dominates the effects of time delay and the consistency constraint parameter. The proposed information fusion model bridges key methodological gaps in the ITS deployment context related to information fusion and the need for short-term travel time distributions.     

A hybrid scheme for real‐time prediction of bus trajectories

The uncertainty associated with public transport services can be partially counteracted by developing real‐time models to predict downstream service conditions. In this study, a hybrid approach for predicting bus trajectories by integrating multiple predictors is proposed. The prediction model combines schedule, instantaneous and historical data. The contribution of each predictor as well as values of respective parameters is estimated by minimizing the prediction error using a linear regression heuristic. The hybrid method was applied to five bus routes in Stockholm, Sweden, and Brisbane, Australia. The results indicate that the hybrid method consistently outperforms the timetable and delay conservation prediction method for different route layouts, passenger demands and operation practices. Model validation confirms model transferability and real‐time applicability. Generating more accurate predictions can help service users adjust their travel plans and service providers to deploy proactive management and control strategies to mitigate the negative effects of service disturbances. Copyright © 2017 John Wiley & Sons, Ltd.     

A framework for neighbour links travel time estimation in an urban network

This paper proposes a solution to the problem of limited network sensor coverage caused by insufficient sample size of probe vehicles or inadequate numbers of fixed sensors. A framework is proposed to estimate link travel times using available data from neighbouring links. Two clues are used for real-time travel time estimation: link historical travel time data and online travel time data from neighbour links. In the absence of online travel time data from neighbour links, historical records only have to be relied upon. However, where the two types of data are available, a data fusion scheme can be applied to make use of the two clues. The proposed framework is validated using real-life data from the City of Vancouver, British Columbia. The estimation accuracy is found to be comparable to the existing literature. Overall, the results demonstrate the feasibility of using neighbour links data as an additional source of information that might not have been extensively explored before.     

Short‐term travel time forecasts for transport information system in hong kong

In this paper, a case study is carried out in Hong Kong for demonstration of the Transport Information System (TIS) prototype. A traffic flow simulator (TFS) is presented to forecast the short‐term travel times that can be served as a predicted travel time database for the TIS in Hong Kong. In the TFS, a stochastic deviation coefficient is incorporated to simulate the minute‐by‐minute fluctuation of traffic flows within the peak hour period. The purposes of the case study are: 1) to show the applicability of the TFS for larger‐scale road network; and 2) to illustrate the short‐term forecasting of path travel times in practice. The results of the case study show that the TFS can be applied to real network effectively. The predicted travel times are compared with the observed travel times on the selected paths for an OD pair. The results show that the observed path travel times fall in the 90% confidence interval of the predicted path travel times.