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

Tigran Nagapetyan; Evgenia Gasnikova

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arXiv · 1112.1628

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

Tigran Nagapetyan·Evgenia Gasnikova

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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.

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BibTeX RIS

Tigran Nagapetyan, Evgenia Gasnikova. 2011-12-23. About new dynamical interpretations of entropic model of correspondence matrix calculation and Nash-Wardrop's equilibrium in Beckmann's traffic flow distribution model. https://arxiv.org/abs/1112.1628

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