This article is cited in 19 papers

System Analysis and Operations Research

Asymmetrical resource networks. I. Stabilization processes for low resources

L. Yu. Zhilyakova

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: We consider dynamic resource allocation processes in two-sided asymmetrical resource networks with loops and study their stabilization conditions. We show that for a unit total resource, the resource reallocation process defines a regular Markov chain, and the limit state vector corresponds to the vector of limit probabilities and is an eigenvector of the stochastic matrix corresponding to the capacity matrix. We show that (a) for a resource not exceeding some threshold value, the limit state vector also exists, is unique, and is proportional to the limit probability vector; (b) for any connected network, the threshold value of total resource exists and is unique.

Presented by the member of Editorial Board: D. A. Novikov

Received: 09.06.2010

 English version: Automation and Remote Control, 2011, 72:4, 798–807

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