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Random walks in a queueing network environment

Part of: Markov processes

Published online by Cambridge University Press:  21 June 2016

M. Gannon ,
E. Pechersky ,
Y. Suhov  and
A. Yambartsev
M. Gannon*
Affiliation:
University of Sao Paulo
E. Pechersky*
Affiliation:
University of Sao Paulo and IITP, Moscow
Y. Suhov*
Affiliation:
IITP, Moscow, University of Sao Paulo, University of Cambridge, and Penn State University
A. Yambartsev*
Affiliation:
University of Sao Paulo and Oregon State University
*
* Postal address: IME, University of Sao Paulo (USP), Sao Paulo 05508-090, SP, Brazil.
* Postal address: IME, University of Sao Paulo (USP), Sao Paulo 05508-090, SP, Brazil.
**** Postal address: Statistical Laboratory, DPMMS, University of Cambridge, Cambridge CB3 0WB, UK. Email address: yms@statslab.cam.ac.uk
* Postal address: IME, University of Sao Paulo (USP), Sao Paulo 05508-090, SP, Brazil.
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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.

Keywords

Continuous-time Markov processqueueing networkJackson networksimple exclusionzero rangereversibilitystationary probabilityproduct formula

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J28: Applications of continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 448 - 462
Copyright
Copyright © Applied Probability Trust 2016 

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