Algorithms for Computing Traffic Equilibria

This paper surveys the most basic traffic models based on the concept of traffic equilibria. It describes the most fruitful formulations that have been used, together with characterizations and properties of equilibria that can be derived from them. It further discusses the structural properties of these models that can be beneficially utilized, either directly or through model manipulations, in iterative algorithms, as well as some of the most successful such representatives. Extensions to traffic equilibrium models with side constraints and with non-additive route costs are provided.

[1]  Yosef Sheffi,et al.  Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods , 1985 .

[2]  Ronald E. Bruck On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space , 1977 .

[3]  Hillel Bar-Gera,et al.  Origin-Based Algorithm for the Traffic Assignment Problem , 2002, Transp. Sci..

[4]  Torbjörn Larsson,et al.  Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem , 1992, Transp. Sci..

[5]  M. Patriksson,et al.  SIDE CONSTRAINED TRAFFIC EQUILIBRIUM MODELS: TRAFFIC MANAGEMENT THROUGH LINK TOLLS. , 1998 .

[6]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[7]  David Bernstein,et al.  The Traffic Equilibrium Problem with Nonadditive Path Costs , 1995, Transp. Sci..

[8]  C. Fisk Some developments in equilibrium traffic assignment , 1980 .

[9]  Anthony Chen,et al.  Computational study of state-of-the-art path-based traffic assignment algorithms , 2002, Math. Comput. Simul..

[10]  D. Bertsekas,et al.  TWO-METRIC PROJECTION METHODS FOR CONSTRAINED OPTIMIZATION* , 1984 .

[11]  J. Baillon Un theoreme de type ergodique pour les contractions non lineaires dans un espace de Hilbert , 1975 .

[12]  M. Patriksson,et al.  Equilibrium characterizations of solutions to side constrained asymmetric traffic assignment models , 1995 .

[13]  D. Bertsekas On the Goldstein-Levitin-Polyak gradient projection method , 1974, CDC 1974.

[14]  L. Escudero A motivation for using the truncated Newton approach in a very large scale nonlinear network problem , 1986 .

[15]  Michael Patriksson,et al.  A Mathematical Model and Descent Algorithm for Bilevel Traffic Management , 2002, Transp. Sci..

[16]  J. Dunn On recursive averaging processes and Hilbert space extensions of the contraction mapping principle , 1973 .

[17]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[18]  Hillel Bar-Gera,et al.  Origin-based Network Assignment , 2002 .

[19]  Michael C. Ferris,et al.  Engineering and Economic Applications of Complementarity Problems , 1997, SIAM Rev..

[20]  P. Brucker Review of recent development: An O( n) algorithm for quadratic knapsack problems , 1984 .

[21]  M. Patriksson,et al.  An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems , 1995 .

[22]  Eitan Altman,et al.  Non-cooperative routing in loss networks , 2002, Perform. Evaluation.

[23]  A. Iusem On some properties of paramonotone operators. , 1998 .

[24]  Torbjörn Larsson,et al.  A dual scheme for traffic assignment problems , 1997 .

[25]  Suzanne P. Evans,et al.  DERIVATION AND ANALYSIS OF SOME MODELS FOR COMBINING TRIP DISTRIBUTION AND ASSIGNMENT , 1976 .

[26]  Eitan Altman,et al.  Analysis of two competing TCP/IP connections , 2002, Perform. Evaluation.

[27]  J. Hammond Solving asymmetric variational inequality problems and systems of equations with generalized nonlinear programming algorithms , 1984 .

[28]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[29]  Naihua Xiu,et al.  Unified Framework of Extragradient-Type Methods for Pseudomonotone Variational Inequalities , 2001 .

[30]  Larry J. LeBlanc,et al.  AN EFFICIENT APPROACH TO SOLVING THE ROAD NETWORK EQUILIBRIUM TRAFFIC ASSIGNMENT PROBLEM. IN: THE AUTOMOBILE , 1975 .

[31]  Patrice Marcotte,et al.  Conditions ensuring the applicability of cutting-plane methods for solving variational inequalities , 2000, Math. Program..

[32]  Torbjörn Larsson,et al.  On traffic equilibrium models with a nonlinear time/money relation , 2002 .

[33]  James V. Burke,et al.  Characterization of solution sets of convex programs , 1991, Oper. Res. Lett..

[34]  Torbjörn Larsson,et al.  Side constrained traffic equilibrium models: analysis, computation and applications , 1999 .

[35]  John G. Klincewicz,et al.  A Newton method for convex separable network flow problems , 1983, Networks.

[36]  R. Rockafellar Monotone Operators and the Proximal Point Algorithm , 1976 .