Equilibrium characterizations of solutions to side constrained asymmetric traffic assignment models

In order to refine the basic model of traffic assignment to capture supplementary flow relationships, the traditional modelling strategy is to modify the travel cost mapping. This strategy is well suited for capturing relationships such as interactions among vehicles on different road links and turning priorities in junctions, and it usually results in nonseparable and asymmetric travel cost functions. It is, however, not the proper approach for incorporating traffic flow restrictions such as those imposed by joint capacities on two-way streets or in junctions, or the presence of a traffic control policy. We consider the introduction of side constraints to describe those flow relationships that have more natural interpretations as flow restrictions than as additional travel costs. Such a refinement should be easier to construct and calibrate as well as lead to more reliable traffic models than that using the traditional refinement strategy only. The utilization of the appropriate combination of these two modelling strategies results, in general, in a variational inequality model of the traffic assignment problem augmented with a set of side constraints. We establish characterizations of its solutions as Wardrop and queueing delay equilibria in terms of well-defined and natural generalized travel costs, and derive stability results for the model. The results obtained may, for example, be applied to derive link tolls for achieving traffic management goals without using centralized traffic control.

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

[2]  C. B. Mcguire,et al.  Studies in the Economics of Transportation , 1958 .

[3]  Niels O Jorgensen,et al.  Some aspects of the urban traffic assignment problem , 1963 .

[4]  G. Stampacchia,et al.  On some non-linear elliptic differential-functional equations , 1966 .

[5]  Leon S. Lasdon,et al.  Optimization Theory of Large Systems , 1970 .

[6]  U. Mosco.  Dual variational inequalities , 1972 .

[7]  M. Beckmann,et al.  TRAVELER DECISIONS AND TRAFFIC FLOWS: A BEHAVIORAL THEORY OF NETWORK EQUILIBRIUM , 1974 .

[8]  R. Rockafellar.  MONOTONE OPERATORS AND AUGMENTED LAGRANGIAN METHODS IN NONLINEAR PROGRAMMING , 1978 .

[9]  David E. Boyce,et al.  The effect on equilibrium trip assignment of different link congestion functions , 1981 .

[10]  D. Bertsekas.  Network Flows and Monotropic Optimization (R. T. Rockafellar) , 1985 .

[11]  H. Inouye.  TRAFFIC EQUILIBRIA AND ITS SOLUTION IN CONGESTED ROAD NETWORKS , 1987 .

[12]  M J Smith.  TRAFFIC CONTROL AND TRAFFIC ASSIGNMENT IN A SIGNAL-CONTROLLED NETWORK WITH QUEUEING , 1987 .

[13]  Contributions a la decomposition et a l'agregation dans les problemes variationnels , 1990 .

[14]  Patrick T. Harker,et al.  Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

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

[16]  A. Nagurney.  Network Economics: A Variational Inequality Approach , 1992 .

[17]  Thomas L. Magnanti,et al.  Sensitivity Analysis for Variational Inequalities , 1992, Math. Oper. Res..

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

[19]  Hai Yang,et al.  Traffic Assignment and Traffic Control in General Freeway-arterial Corridor Systems , 1994 .

[20]  Terry L. Friesz,et al.  Day-To-Day Dynamic Network Disequilibria and Idealized Traveler Information Systems , 1994, Oper. Res..

[21]  David Bernstein,et al.  Equilibria for Networks with Lower Semicontinuous Costs: With an Application to Congestion Pricing , 1994, Transp. Sci..

[22]  James V. Burke,et al.  Exposing Constraints , 1994, SIAM J. Optim..

[23]  Torbjörn Larsson,et al.  On side constrained models of traffic equilibria , 1995 .

[24]  Antonino Maugeri.  Optimization problems with side constraints and generalized equilibrium principles , 1995 .

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

[26]  Patrice Marcotte,et al.  Co-Coercivity and Its Role in the Convergence of Iterative Schemes for Solving Variational Inequalities , 1996, SIAM J. Optim..