About new dynamical interpretations of entropic model of correspondence matrix calculation and Nash-Wardrop's equilibrium in Beckmann's traffic flow distribution model

TL;DR

This paper introduces a new dynamical interpretation of the entropic model for correspondence matrix calculation and demonstrates how a best response dynamic converges to Nash-Wardrop's equilibrium in traffic flow models, using a statistical physics approach.

Contribution

It provides a novel dynamical perspective on the static entropic model and proposes a best response dynamic that converges to Nash-Wardrop's equilibrium in traffic flow.

Findings

The new dynamic converges to Nash-Wardrop's equilibrium under general conditions.

Demonstrated the approach with two example cases.

Extended statistical physics methods to traffic flow modeling.

Abstract

In this work we widespread statistical physics (chemical kinetic stochastic) approach to the investigation of macrosystems, arise in economic, sociology and traffic flow theory. The main line is a definition of equilibrium of macrosystem as most probable macrostate of invariant measure of Markov dynamic (corresponds to the macrosystem). We demonstrate new dynamical interpretations for the well known static model of correspondence matrix calculation. Based on this model we propose a best response dynamics for the Beckmann's traffic flow distribution model. We prove that this "natural" dynamic under quite general conditions converges to the Nash-Wardrop's equilibrium. After that we consider two interesting demonstration examples.