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Network flow assignment as a fixed point problem. / Krylatov, A. Yu.

In: Journal of Applied and Industrial Mathematics, Vol. 10, No. 2, 2016, p. 243-256.

Research output: Contribution to journal › Article

Harvard

Krylatov, AY 2016, 'Network flow assignment as a fixed point problem', Journal of Applied and Industrial Mathematics, vol. 10, no. 2, pp. 243-256. <http://link.springer.com/article/10.1134/S1990478916020095>

APA

Krylatov, A. Y. (2016). Network flow assignment as a fixed point problem. Journal of Applied and Industrial Mathematics, 10(2), 243-256. http://link.springer.com/article/10.1134/S1990478916020095

Vancouver

Krylatov AY. Network flow assignment as a fixed point problem. Journal of Applied and Industrial Mathematics. 2016;10(2):243-256.

Author

Krylatov, A. Yu. / Network flow assignment as a fixed point problem. In: Journal of Applied and Industrial Mathematics. 2016 ; Vol. 10, No. 2. pp. 243-256.

BibTeX

@article{3ac2fb0efeb04a11808aaa0fc0772e12,
title = "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 equilibriumand optimal flow assignment is developed. The method is proved to converge geometrically; under some fairly natural conditions the method is proved to converge quadratically.",
keywords = "user equilibrium, system optimum, fixed point, network routes",
author = "Krylatov, {A. Yu.}",
year = "2016",
language = "English",
volume = "10",
pages = "243--256",
journal = "Journal of Applied and Industrial Mathematics",
issn = "1990-4789",
publisher = "МАИК {"}Наука/Интерпериодика{"}",
number = "2",

}

RIS

TY - JOUR

T1 - Network flow assignment as a fixed point problem

AU - Krylatov, A. Yu.

PY - 2016

Y1 - 2016

N2 - 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 equilibriumand optimal flow assignment is developed. The method is proved to converge geometrically; under some fairly natural conditions the method is proved to converge quadratically.

AB - 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 equilibriumand optimal flow assignment is developed. The method is proved to converge geometrically; under some fairly natural conditions the method is proved to converge quadratically.

KW - user equilibrium

KW - system optimum

KW - fixed point

KW - network routes

M3 - Article

VL - 10

SP - 243

EP - 256

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 2

ER -

ID: 7568542