On Traffic Equilibrium Models with a Nonlinear Time/Money Relation

Torbjörn Larsson · Per Olov Lindberg · Michael Patriksson · Clas Rydergren

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Transportation Planning and Optimization Complexity and Algorithms in Graphs Optimization and Variational Analysis

Abstract

We consider a traffic equilibrium problem in which each route has two attributes, time delay and monetary outlay, which are combined into a generalized time through a nonlinear relation. It is shown that this problem can be stated as a convex optimization model. Two simplicial decomposition type methods are proposed for its solution. The subproblem of these methods, which is a two-attribute shortest route problem, can be efficiently solved by the multi-labelling technique which has previously been applied to resource-constrained shortest path problems. Our numerical experiments show that both methods are feasible approaches to the equilibrium problem.

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References

1986Urban transportation networks: Equilibrium analysis with mathematical programming methods 1994The Traffic Assignment Problem: Models and Methods 1992Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem 1997The Traffic Equilibrium Problem with Nonadditive Path Costs

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