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Line Reversibility of Multiserver Systems

Published online by Cambridge University Press:  27 July 2009

Dinah W. Cheng
Dinah W. Cheng
Affiliation:
Leonard N. Stern School of Business, Department of Statistics/Operations Research, 704 Tisch Hall, New York University, New York, New York 10012-1138
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Abstract

The line reversibility property of a two-stage multiserver system with manufacturing blocking has previously been established using a duality argument between the blocked state and the idle state. In this paper, we provide counterexamples that show this argument does not apply to systems with more than two stages. A focus of this paper is to provide a new proof for the result. Our argument is based on the duality between the service initiation and the service completion events.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 2 , April 1997 , pp. 177 - 188
Copyright
Copyright © Cambridge University Press 1997

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References

1.Chao, X. & Pinedo, M. (1992). On reversibility of tandem queues with blocking. Naval Research Logistics 39: 957–974.3.0.CO;2-3>CrossRefGoogle Scholar
2.Cheng, D.W. (1995). Line reversibility of tandem queues with general blocking. Management Science 41: 864–873.CrossRefGoogle Scholar
3.Cheng, D.W. & Righter, R. (1995). On the order of tandem queues. Queueing Systems: Theory and Applications 21: 143–160.CrossRefGoogle Scholar
4.Dattatreya, E.S. (1978). Tandem queueing systems with blocking. Ph.D. dissertation, Operations Research Center, University of California, Berkeley.Google Scholar
5.Meester, L. & Shanthikumar, J.G. (1990). Concavity of the throughput and optimal buffer space allocation for tandem queueing systems with finite buffer storage space. Advances in Applied Probability 36: 1548–1566.Google Scholar
6.Melamed, B. (1986). A note on the reversibility and duality of some tandem blocking queueing systems. Management Science 32: 1648–1650.CrossRefGoogle Scholar
7.Muth, E.J. (1979). The reversibility property of production lines. Management Science 25: 152–158.Google Scholar
8.Ross, S. (1983). Stochastic processes. New York: John Wiley & Sons.Google Scholar
9.Kawashima, Yamazaki G. & Sakasegawa, H. (1983). Reversibility of tandem blocking queueing systems. Kogakuin University, Tokyo.Google Scholar
10.Yamazaki, G., Sakasegawa, H. & Shanthikumar, J.G. (1992). On optimal arrangement of stations in a tandem queueing system with blocking. Management Science 38: 137–153.CrossRefGoogle Scholar