A bi-criterion dynamic user equilibrium traffic assignment model and solution algorithm for evaluating dynamic road pricing strategies (original) (raw)
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Transportation Research Record, 2006
This paper presents a dynamic traffic assignment model and its solution algorithm for solving bi-criterion dynamic user equilibrium (BDUE) that allows heterogeneous users with different value of time preferences. By assuming the value of time as a continuously distributed random variable across the population of trips, the BDUE problem is formulated as an infinite dimensional variational inequality (VI). Rather than solving the VI formulation directly, this study employs a generalized Frank-Wolfe algorithm to find the BDUE flow pattern. A bi-criterion time-dependent least cost path algorithm is applied to generate the extreme efficient path set, and the corresponding breakpoints naturally defines the multiple user classes, thereby generating the descent direction for a multi-class dynamic network loading. A traffic simulator is used to describe the traffic flow propagation and the spatial and temporal interactions. To circumvent the difficulty of storing the memory-intensive path set and routing policies for large-scale network applications, a simulation-based implementation technique is proposed to use the vehicle path set as a proxy for keeping track of the path assignment results. A set of numerical experiments are conducted to explore the convergence behavior of the BDUE algorithm and investigate how VOT distributions affect the path flow pattern and toll road usage under different dynamic road pricing schemes.
2007
This study develops a simulation-based dynamic traffic assignment, or dynamic user equilibrium (DUE), model for dynamic road pricing applications. This proposed model is considered as the bi-criterion DUE (BDUE) model, because it explicitly considers heterogeneous users with different values of time (VOT) choose paths that minimize the two path attributes: travel time and out-of-pocket cost. This study assumed trip-makers would select their respective least generalized cost paths, the generalized cost being the sum of travel cost and travel time weighted by the trip-maker's VOT. The VOT is modeled as a continuous random variable distributed across all users in a network. The BDUE problem is formulated as an infinite dimensional variational inequality (VI), and solved by a column generation-based algorithmic framework which embeds (i) a parametric analysis (PAM) to obtain the VOT breakpoints which determine multiple user classes, and find the set of extreme non-dominated paths, (ii) a simulator to determine experienced travel times, and (iii) a multi-class path flow equilibrating scheme to update path assignments. The idea of finding and assigning heterogeneous trips to the set of extreme non-dominated paths is based on the assumption that in the disutility minimization path choice model with convex utility functions, all trips would choose only among the set of extreme non-dominated paths. Moreover, to circumvent the difficulty of storing the grand path set and assignment results for large-scale network applications, a vehicle-based implementation technique is proposed. This BDUE model is generalized to the multi-criterion DUE (MDUE) model, in which heterogeneous users with different VOT and values of reliability (VOR) make path choices so as to minimize their path travel cost, travel time, and travel time variability. Another important extension of the BDUE model is the multi-criterion simultaneous route and departure time user equilibrium (MSRDUE) model, which considers heterogeneous trip-makers with different VOT and values of schedule delay (VOSD) making simultaneous route and departure time choices so as to minimize their respective trip costs, defined as the sum of travel cost, travel time weighted by VOT, and schedule delay weighted by VOSD. The MSRDUE problem is also solved by the column generation-based algorithmic framework. The Sequential Parametric Analysis Method (SPAM) is developed to find the VOT and VOSD breakpoints that define multiple user classes, and determine the least trip cost alternative (a combination of departure time and path) for each user class.
Modeling heterogeneous network user route and departure time responses to dynamic pricing
Transportation Research Part C: Emerging Technologies, 2011
The ability to realistically capture trip-makers' responses to time-varying road charges is essential for network equilibrium assignment models typically applied to predict network flows in the presence of dynamic road (congestion) pricing. User responses to pricing are governed by individual trip-makers' preferences, such as their value of time (VOT), and the cost they attach to late vs. early arrival relative to the destination. These behavioral characteristics vary across users. This paper presents a joint route and departure time network equilibrium assignment model explicitly considering heterogeneous users with different preferred arrival times at destinations, VOT, and values of early and late schedule delays (VOESD and VOLSD). The model is formulated as an infinite-dimensional variational inequality and solved by a column generation-based algorithmic framework that embeds: (i) an extreme non-dominated alternative-generating algorithm to obtain combinations of VOT, VOESD, and VOLSD subintervals (or breakpoints) that define multiple user classes, and the corresponding least trip cost alternative (joint departure time and path) for each user class, (ii) a traffic simulator to capture traffic flow dynamics and determine experienced travel costs; and (iii) a multi-class alternative flow updating scheme to solve the reduced multi-class simultaneous route and departure time user equilibrium problem defined by a subset of feasible alternatives. Application to an actual network illustrates the properties of the algorithm, and underscores the importance of capturing user heterogeneity and temporal shifts in the appraisal of dynamic pricing schemes.
Dynamic road pricing for optimizing network performance with heterogeneous users
Proceedings. 2005 IEEE Networking, Sensing and Control, 2005.
In transport networks, travelers individually make route and departure time choice decisions that may not be optimal for the whole network. By introducing (timedependent) tolls the network performance may be optimized. In the paper, the effects of time-dependent tolls on the network performance will be analyzed using a dynamic traffic model. The network design problem is formulated as a bi-level optimization problem in which the upper level describes the network performance with chosen toll levels while the lower level describes the dynamic network flows including userspecific route and departure time choice and the dynamic network loading. In case studies on a simple hypothetical network it is shown that network improvements can be obtained by introducing tolls. It is also shown that finding a global solution to the network design problem is complex as it is non-linear and non-convex.
Dynamic Pricing with Heterogeneous Users
Transportation Research Record: Journal of the Transportation Research Board, 2009
trip-maker path choice decisions in response to time-varying toll charges, VOT is assumed to be continuously distributed among trip makers, instead of the constant VOT adopted in existing dynamic user equilibrium (DUE) models. Numerical experiments conducted on several networks demonstrated how VOT distributions affect the path-flow pattern and toll road usage and highlights the necessity of addressing user heterogeneity in assignment models for road pricing. This BDUE model represents an attempt to accommodate greater behavioral and policy realism in applying DUE models to designing and evaluating dynamic pricing strategies, and it represents an advance in generalizing bicriterion user equilibrium models (2, 3) or cost-versus-time network equilibrium models (4) from the static regime to the dynamic traffic-assignment (DTA) context. A comprehensive review of assignment models under road pricing is available elsewhere (1).
Dynamic Toll Pricing Framework for Discrete-Time Dynamic Traffic Assignment Models
2006
This paper discusses a toll pricing framework for a traffic network in a dynamic setting. The model is based on a discrete-time dynamic traffic assignment problem, where the travel time is a function of density. We construct a set of time-varying toll vectors such that a solution (or an approximate solution) of the system problem is a solution of the corresponding tolled user equilibrium problem. In general, a valid time-varying toll vector is not unique and the set of valid toll vectors can be expressed algebraically. Then, a desired time-varying toll vector can be chosen to optimize a secondary objective. Illustrative numerical results from a small network are provided. Key words: congestion toll pricing, time-varying tolls, dynamic traffic assignment. 2