STRUCTURE-REVERSIBILITY OF A TWO-DIMENSIONAL REFLECTING RANDOM WALK AND ITS APPLICATION TO QUEUEING NETWORK
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Published:2014-09-29
Issue:1
Volume:29
Page:1-25
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ISSN:0269-9648
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Container-title:Probability in the Engineering and Informational Sciences
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language:en
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Short-container-title:Prob. Eng. Inf. Sci.
Author:
Kobayashi Masahiro,Miyazawa Masakiyo,Shimizu Hiroshi
Abstract
We consider a two-dimensional reflecting random walk on the non-negative integer quadrant. It is assumed that this reflecting random walk has skip-free transitions. We are concerned with its time-reversed process assuming that the stationary distribution exists. In general, the time-reversed process may not be a reflecting random walk. In this paper, we derive necessary and sufficient conditions for the time-reversed process also to be a reflecting random walk. These conditions are different from but closely related to the product form of the stationary distribution.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
Reference10 articles.
1. Latouche G. & Miyazawa M. (2013). Product form characterization for a two dimensional reflecting random walk and its applications, To appear Queueing systems, http://link.springer.com/article/10.1007/s11134-013-9381-7
2. Introduction to Stochastic Networks
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