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English version:
Journal of Applied and Industrial Mathematics, 2016, 10:2, 243-256

Volume 23, No 2, 2016, P. 63-87

UDC 519.8
A. Yu. Krylatov
Network flow assignment as a fixed point problem

Abstract:
This paper deals with the user equilibrium problem (flow assignment with equal journey time by alternative routes) and system optimum (flow assignment with minimal average journey time) in a network consisting of parallel routes with a single origin-destination pair. The travel time is simulated by arbitrary smooth nondecreasing functions. We prove that the equilibrium and optimal assignment problems for such a network can be reduced to the fixed point problem expressed explicitly. A simple iterative method of finding equilibrium and optimal flow assignment is developed. The method is proved to converge geometrically; under some fairly natural conditions the method is proved to converge quadratically.
Bibliogr. 30.

Keywords: user-equilibrium, system optimum, fixed point, network routes.

DOI: 10.17377/daio.2016.23.503

Alexander Yu. Krylatov 1,2
1. Saint Petersburg State University,
7/9 Universitetskaya Nab., 199034 St. Petersburg, Russia
2. Solomenko Institute of Transport Problems of the RAS,
13 12th Line VO, 199178 St. Petersburg, Russia
e-mail: a.krylatov@spbu.ru, aykrylatov@yandex.ru

Revised 24 November 2015

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