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June 2016 Random walks in a queueing network environment
M. Gannon, E. Pechersky, Y. Suhov, A. Yambartsev
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J. Appl. Probab. 53(2): 448-462 (June 2016).

Abstract

We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The environment is cast in terms of a Jackson/Gordon–Newell network although alternative interpretations are possible. The main tool is the detailed balance equations. The difference compared to earlier works is that the position of the random walk influences the transition intensities of the network environment and vice versa, creating strong correlations. The form of the stationary distribution is closely related to the well-known product formula.

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M. Gannon. E. Pechersky. Y. Suhov. A. Yambartsev. "Random walks in a queueing network environment." J. Appl. Probab. 53 (2) 448 - 462, June 2016.

Information

Published: June 2016
First available in Project Euclid: 17 June 2016

zbMATH: 1344.60086
MathSciNet: MR3514290

Subjects:
Primary: 60J27
Secondary: 60J28

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 2 • June 2016
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