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An algorithm for the equilibrium assignment problem with random link times
Author(s) -
Sheffi Yosef,
Powell Warren B.
Publication year - 1982
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230120209
Subject(s) - uniqueness , convergence (economics) , link (geometry) , mathematical optimization , minification , assignment problem , algorithm , computer science , mathematics , order (exchange) , combinatorics , mathematical analysis , finance , economics , economic growth
In this article we offer an equivalent minimization formulation for the traffic assignment problem when the link travel times are flow‐dependent random variables. The paper shows the equivalency between the first‐order conditions of this program and the stochastic equilibrium conditions as well as the uniqueness of the solution. The paper also describes an algorithmic approach to the solution of this program, including a proof of convergence. Finally, we conduct some limited numerical experiments on the rate of convergence of the algorithm and the merits of the stochastic equilibrium model, in general, as compared with deterministic approaches.