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STRUCTURE-REVERSIBILITY OF A TWO-DIMENSIONAL REFLECTING RANDOM WALK AND ITS APPLICATION TO QUEUEING NETWORK

Published online by Cambridge University Press:  29 September 2014

Masahiro Kobayashi ,
Masakiyo Miyazawa  and
Hiroshi Shimizu
Masahiro Kobayashi
Affiliation:
Department of Information Sciences, Tokyo University of Science, 2641 Yamazaki, Noda City, Chiba 278-8510, Japan
Masakiyo Miyazawa
Affiliation:
Department of Information Sciences, Tokyo University of Science, 2641 Yamazaki, Noda City, Chiba 278-8510, Japan
Hiroshi Shimizu
Affiliation:
Nihon Unisys, Ltd., 1-1-1 Toyosu, Koto-ku, Tokyo 135-8560, Japan E-mail: [email protected]
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Abstract

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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 1 , January 2015 , pp. 1 - 25
Copyright
Copyright © Cambridge University Press 2014 

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