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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: m_kobayashi@is.noda.tus.ac.jp
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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.

Information

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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