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.     

Route swapping in dynamic traffic networks

A dynamic traffic assignment (DTA) model typically consists of a traffic performance model and a route choice model. The traffic performance model describes how traffic propagates (over time) along routes connecting origin-destination (OD) pairs, examples being the cell transmission model, the vertical queueing model and the travel time model. This is implemented in a dynamic network loading (DNL) algorithm, which uses the given route inflows to compute the link inflows (and hence link costs), which are then used to compute the route travel times (and hence route costs). A route swap process specifies the route inflows for tomorrow (at the next iteration) based on the route inflows today (at the current iteration). A dynamic user equilibrium (DUE), where each traveller on the network cannot reduce his or her cost of travel by switching to another route, can be sought by iterating between the DNL algorithm and the route swap process. The route swap process itself takes up very little computational time (although route set generation can be very computationally intensive for large networks). However, the choice of route swap process dramatically affects convergence and the speed of convergence. The paper details several route swap processes and considers whether they lead to a convergent system, assuming that the route cost vector is a monotone function of the route inflow vector.     

Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model

Static traffic assignment models are still widely applied for strategic transport planning purposes in spite of the fact that such models produce implausible traffic flows that exceed link capacities and predict incorrect congestion locations. There have been numerous attempts to constrain link flows to capacity. Capacity constrained models with residual queues are often referred to as quasi-dynamic traffic assignment models. After reviewing the literature, we come to the conclusion that an important piece of the puzzle has been missing so far, namely the inclusion of a first order node model. In this paper we propose a novel path-based static traffic assignment model for finding a stochastic user equilibrium in general transportation networks. This model includes a first order (steady-state) node model that yields more realistic turn capacities, which are then used to determine consistent capacity constrained traffic flows, residual point (vertical) queues (upstream bottleneck links), and path travel times consistent with queuing theory. The route choice part of the model is specified as a variational inequality problem, while the network loading part is formulated as a fixed point problem. Both problems are solved using existing techniques to find a solution. We illustrate the model using hypothetical examples, and also demonstrate feasibility on large-scale networks.     

Routing aspects of electric vehicle drivers and their effects on network performance

This study investigates the routing aspects of battery electric vehicle (BEV) drivers and their effects on the overall traffic network performance. BEVs have unique characteristics such as range limitation, long battery recharging time, and recuperation of energy lost during the deceleration phase if equipped with regenerative braking system (RBS). In addition, the energy consumption rate per unit distance traveled is lower at moderate speed than at higher speed. This raises two interesting questions: (i) whether these characteristics of BEVs will lead to different route selection compared to conventional internal combustion engine vehicles (ICEVs), and (ii) whether such route selection implications of BEVs will affect the network performance. With the increasing market penetration of BEVs, these questions are becoming more important. This study formulates a multi-class dynamic user equilibrium (MCDUE) model to determine the equilibrium flows for mixed traffic consisting of BEVs and ICEVs. A simulation-based solution procedure is proposed for the MCDUE model. In the MCDUE model, BEVs select routes to minimize the generalized cost which includes route travel time, energy related costs and range anxiety cost, and ICEVs to minimize route travel time. Results from numerical experiments illustrate that BEV drivers select routes with lower speed to conserve and recuperate battery energy while ICEV drivers select shortest travel time routes. They also illustrate that the differences in route choice behavior of BEV and ICEV drivers can synergistically lead to reduction in total travel time and the network performance towards system optimum under certain conditions.     

Prediction of arrival times of freight traffic on US railroads using support vector regression

Variability of travel times on the United States freight rail network is high due to large network demands relative to infrastructure capacity, especially when traffic is heterogeneous. Variable runtimes pose significant operational challenges if the nature of runtime variability is not predictable. To address this issue, this article proposes a data-driven approach to predict estimated times of arrival (ETAs) of individual freight trains, based on the properties of the train, the properties of the network, and the properties of potentially conflicting traffic on the network. The ETA prediction problem from an origin to a destination is posed as a machine learning regression problem and solved using support vector regression trained and cross validated on over two years of detailed historical data for a 140 mile section of track located primarily in Tennessee, USA. The article presents the data used in this problem and details on feature engineering and construction for predictions made across the full route. It also highlights findings on the dominant sources of runtime variability and the most predictive factors for ETA. Improvement results for ETA exceed 21% over a baseline prediction method at some locations and average 14% across the study area.     

Driver response to variable message signs: a stated preference investigation

This paper uses a Stated Preference approach to undertake a detailed assessment of the effect on drivers’ route choice of information provided by variable message signs (VMS). Although drivers’ response to VMS information will vary according to the availability of alternative routes and the extent to which they are close substitutes, our findings show that route choice can be strongly influenced by the provision of information about traffic conditions ahead. This has important implications for the use of VMS systems as part of comprehensive traffic management and control systems. The principal findings are that the impact of VMS information depends on: the content of the message, such as the cause of delay and its extent; local circumstances, such as relative journey times in normal conditions; and drivers’ characteristics, such as their age, sex and previous network knowledge. The impact of qualitative indicators, visible queues and delays were examined. It was found that not only is delay time more highly valued than normal travel time, which is to be expected, but that drivers become more sensitive to delay time as delay times increased across the range presented.     

Day-to-day traffic dynamics considering social interaction: From individual route choice behavior to a network flow model

Social interaction is increasingly recognized as an important factor that influences travelers’ behaviors. It remains challenging to incorporate its effect into travel choice behaviors, although there has been some research into this area. Considering random interaction among travelers, we model travelers’ day-to-day route choice under the uncertain traffic condition. We further explore the evolution of network flow based on the individual-level route choice model, though that travelers are heterogeneous in decision-making under the random-interaction scheme. We analyze and prove the existence of equilibrium and the stability of equilibrium. We also analyzed and described the specific properties of the network flow evolution and travelers’ behaviors. Two interesting phenomena are found in this study. First, the number of travelers that an individual interacts with can affect his route choice strategy. However, the interaction count exerts no influence on the evolution of network flow at the aggregate-level. Second, when the network flow reaches equilibrium, the route choice strategy at the individual-level is not necessarily invariable. Finally, two networks are used as numerical examples to show model properties and to demonstrate the two study phenomena. This study improves the understanding of travelers’ route choice dynamics and informs how the network flow evolves under the influence of social interaction.     

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.     

Traffic signal timing problems with environmental and equity considerations

Traffic signal timings in a road network can not only affect total user travel time and total amount of traffic emissions in the network but also create an inequity problem in terms of the change in travel costs of users traveling between different locations. This paper proposes a multi‐objective bi‐level programming model for design of sustainable and equitable traffic signal timings for a congested signal‐controlled road network. The upper level of the proposed model is a multi‐objective programming problem with an equity constraint that maximizes the reserve capacity of the network and minimizes the total amount of traffic emissions. The lower level is a deterministic network user equilibrium problem that considers the vehicle delays at signalized intersections of the network. To solve the proposed model, an approach for normalizing incommensurable objective functions is presented, and a heuristic solution algorithm that combines a penalty function approach and a simulated annealing method is developed. Two numerical examples are presented to show the effects of reserve capacity improvement and green time proportion on network flow distribution and transportation system performance and the importance of incorporating environmental and equity objectives in the traffic signal timing problems. Copyright © 2013 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.     

Simultaneous determination of the equilibrium market penetration and compliance rate of advanced traveler information systems

We consider a specific advanced traveler information systems (ATIS) whose objective is to reduce drivers’ travel time uncertainty with recurrent network congestion through provision of traffic information. Since the provided information is still partial or imperfect, drivers equipped with an ATIS cannot always find the shortest travel time route and thus may not always comply with the advice provided by ATIS. Thus, there are three classes of drivers on a specific day: drivers without ATIS, drivers with ATIS but without compliance with ATIS advice, drivers with ATIS and in compliance with ATIS advice. All three classes of drivers make route choice in a stochastic manner, but with different degree of uncertainty of travel time on the network. In this paper we investigate the interactions among the three classes of drivers in an ATIS environment using a multiple behavior stochastic user equilibrium model. By assuming that the market penetration of ATIS is an increasing function of the actual private gain (time saving minus the cost associated with system use) derived from ATIS service, and the ATIS compliance rate of equipped drivers is given as the probability of the actual travel time of complied drivers being less than that of non-complied drivers, we determine the equilibrium market penetration and compliance rate of ATIS and the resulting equilibrium network flow pattern using an iterative solution procedure.     

The independence of volume-capacity ratio of private toll roads in general networks

In a general traffic network under some widely used assumptions, this paper proves that the level of service, represented by the volume-capacity (v/c) ratio, offered by a profit-maximizing private firm on a private toll road is independent of another competitor’s choice of capacity and toll rate for another private toll road. The v/c ratio will be the same as the one provided by a centralized welfare-maximizing traffic authority. Moreover, the ratio remains the same even in a regulated market where the authority imposes a cap for the generalized travel cost on the private toll road.     

Route Choice Models Used in the Stochastic User Equilibrium Problem: A Review

Several route choice models are reviewed in the context of the stochastic user equilibrium problem. The traffic assignment problem has been extensively studied in the literature. Several models were developed focusing mainly on the solution of the link flow pattern for congested urban areas. The behavioural assumption governing route choice, which is the essential part of any traffic assignment model, received relatively much less attention. The core of any traffic assignment method is the route choice model. In the wellknown deterministic case, a simple choice model is assumed in which drivers choose their best route. The assumption of perfect knowledge of travel costs has been long considered inadequate to explain travel behaviour. Consequently, probabilistic route choice models were developed in which drivers were assumed to minimize their perceived costs given a set of routes. The objective of the paper is to review the different route choice models used to solve the traffic assignment problem. Focus is on the different model structures. The paper connects some of the route choice models proposed long ago, such as the logit and probit models, with recently developed models. It discusses several extensions to the simple logit model, as well as the choice set generation problem and the incorporation of the models in the assignment problem.     

Consistent formulation of network equilibrium with stochastic flows

Traffic flows in real-life transportation systems vary on a daily basis. According to traffic flow theory, such variability should induce a similar variability in travel times, but this “internal consistency” is generally not captured by existing network equilibrium models. We present an internally-consistent network equilibrium approach, which considers two potential sources of flow variability: (i) daily variation in route choice and (ii) daily variation in origin–destination demand. We particularly aspire to a flexible formulation that permits alternative statistical assumptions, which allows the best fit to be made to observed variability data in particular applications. Joint probability distributions of route—and therefore link—flows are derived under several assumptions concerning stochastic driver behavior. A stochastic network equilibrium model with stochastic demands and route choices is formulated as a fixed point problem. We explore limiting cases which allow an equivalent convex optimization problem to be defined, and finally apply this method to a real-life network of Kanazawa City, Japan.     

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.     

Modeling the evolutions of day‐to‐day route choice and year‐to‐year ATIS adoption with stochastic user equilibrium

Suppose that in an urban transportation network there is a specific advanced traveler information system (ATIS) which acts for reducing the drivers' travel time uncertainty through provision of pre‐trip route information. Because of the imperfect information provided, some travelers are not in compliance with the ATIS advice although equipped with the device. We thus divide all travelers into three groups, one group unequipped with ATIS, another group equipped and in compliance with ATIS advice and the third group equipped but without compliance with the advice. Each traveler makes route choice in a logit‐based manner and a stochastic user equilibrium with multiple user classes is reached for every day. In this paper, we propose a model to investigate the evolutions of daily path travel time, daily ATIS compliance rate and yearly ATIS adoption, in which the equilibrium for every day's route choice is kept. The stability of the evolution model is initially analyzed. Numerical results obtained from a test network are presented for demonstrating the model's ability in depicting the day‐to‐day and year‐to‐year evolutions.     

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.     

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.     

Modeling the day-to-day traffic evolution process after an unexpected network disruption

Although various approaches have been proposed for modeling day-to-day traffic flow evolution, none of them, to the best of our knowledge, have been validated for disrupted networks due to the lack of empirical observations. By carefully studying the driving behavioral changes after the collapse of I-35W Mississippi River Bridge in Minneapolis, Minnesota, we found that most of the existing day-to-day traffic assignment models would not be suitable for modeling the traffic evolution under network disruption, because they assume that drivers’ travel cost perception depends solely on their experiences from previous days. When a significant network change occurs unexpectedly, travelers’ past experience on a traffic network may not be entirely useful because the unexpected network change could disturb the traffic greatly. To remedy this, in this paper, we propose a prediction-correction model to describe the traffic equilibration process. A “predicted” flow pattern is constructed inside the model to accommodate the imperfect perception of congestion that is gradually corrected by actual travel experiences. We also prove rigorously that, under mild assumptions, the proposed prediction-correction process has the user equilibrium flow as a globally attractive point. The proposed model is calibrated and validated with the field data collected after the collapse of I-35W Bridge. This study bridges the gap between theoretical modeling and practical applications of day-to-day traffic equilibration approaches and furthers the understanding of traffic equilibration process after network disruption.     

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.