Primal-dual method for searching equillibriums in mixed traffic assignment problems

TL;DR

This paper develops a primal-dual mirror descent method for finding equilibria in large-scale mixed traffic assignment problems, comparing two solution recovery techniques and analyzing their respective advantages.

Contribution

It introduces a primal-dual approach for traffic equilibrium problems and compares two methods for recovering primal solutions, enhancing solution strategies for complex traffic models.

Findings

The primal-dual mirror descent method effectively finds traffic equilibria.

Two solution recovery techniques have distinct advantages and drawbacks.

The approach applies to large network traffic models like BMW and SD.

Abstract

We consider mixed model of traffic flow distribution in large networks (BMW model, 1954 & Stable Dynamic model, 1999). We build dual problem and consider primal-dual mirror descent method for the dual problem. There are two ways to recover the solution of the primal problem. First technique is based on "models" approach and second one is based on Lagrange multiplyers technique. Both approaches have its own advantages and drawbacks. We discuss them.