User-equilibrium properties of fixed points in dynamic traffic assignment

Kaufman, David W.; Smith, Robert L.; Wunderlich, Karl

doi:10.1016/s0968-090x(98)00005-9

Cited by 27 publications

(21 citation statements)

References 16 publications

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“…The authors investigated the impact such (limited) route guidance had on the individual travel times of the vehicles as well as the system average travel times. The results and performance of the sampled fictitious play algorithm were compared with those of the heretofore best method SAVaNT (Kaufman, Smith and Wunderlich, 1998). When the guided vehicles constituted 5% of the total number of vehicles, their average travel times were approximately 10% better than those of the unguided vehicles, with the system-wide average travel time of 17.22 minutes.…”

Section: Dynamic Traffic Routing Assignmentmentioning

confidence: 99%

A Fictitious Play Approach to Large-Scale Optimization

Lambert

Epelman²,

Smith

2005

Operations Research

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In this paper we investigate the properties of the sampled version of the fictitious play algorithm, familiar from game theory, for games with identical payoffs, and propose a heuristic based on fictitious play as a solution procedure for discrete optimization problems of the form max{u(y) : y = (y 1 , . . . , y n ) ∈ Y 1 × · · · × Y n }, i.e., in which the feasible region is a Cartesian product of finite sets Y i , i ∈ N = {1, . . . , n}. The contributions of this paper are two-fold. In the first part of the paper we broaden the existing results on convergence properties of the fictitious play algorithm on games with identical payoffs to include an approximate fictitious play algorithm which allows for errors in players' best replies. Moreover, we introduce sampling-based approximate fictitious play which possesses the above convergence properties, and at the same time provides a computationally efficient method for implementing fictitious play. In the second part of the paper we motivate the use of algorithms based on sampled fictitious play to solve optimization problems in the above form with particular focus on the problems in which the objective function u(·) comes from a "black box," such as a simulation model, where significant computational effort is required for each function evaluation.

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Section: Dynamic Traffic Routing Assignmentmentioning

confidence: 99%

A Fictitious Play Approach to Large-Scale Optimization

Lambert

Epelman²,

Smith

2005

Operations Research

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“…Though this method can be proven to converge to a solution, it cannot be adapted to the user-optimal problem. Computational tests showed this algorithm to converge much more quickly than that of Kaufman et al [29].…”

Section: Centralized and Predictive Route Guidancementioning

confidence: 78%

“…Kaufman et al [29] considers the computation of user-equilibrium Dynamic Traffic Assignment. It uses a model that combines an assignment mapping of flows to paths and a routing mapping that computes resulting sets of fastest paths.…”

Section: Dynamic Traffic Assignmentmentioning

confidence: 99%

Hybrid Vehicle-Centric Route Guidance 1

Farver

Chabini

2003

IFAC Proceedings Volumes

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“…The models for dynamic traffic assignment can be classified into five categories according to research methods: Computer simulating [1,2]; Mathematical programming [3,4]; Optimal control theory [5,6]; Variational inequality (VI) and non-linear complementarity [7,8,9,10]; Fixed point theory [11]. The dynamic traffic assignment model based on computer simulating gives route choices of travellers by iteration, but it cannot guarantee the convergence and precision of solutions.…”

Section: Introductionmentioning

confidence: 99%