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Monotonicity of the Loss Probabilities of Single Server Finite Queues with Respect to Convex Order of Arrival or Service Processes

Published online by Cambridge University Press:  27 July 2009

Masakiyo Miyazawa  and
J. George Shanthikumar
Masakiyo Miyazawa
Affiliation:
Science University of Tokyo
J. George Shanthikumar
Affiliation:
University of California, Berkeley
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Abstract

The loss probabilities of customers in the Mx/GI/1/k, GI/Mx/l/k and their related queues such as server vacation models are compared with respect to the convex order of several characteristics, for example, batch size, of the arrival or service process. In the proof, we give a characterization of a truncation expression for a stationary distribution of a finite Markov chain, which is interesting in itself.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 1 , January 1991 , pp. 43 - 52
Copyright
Copyright © Cambridge University Press 1991

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References

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