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A Note on Bounds and Error Bounds for Nonexponential Batch Arrival Systems

Published online by Cambridge University Press:  27 July 2009

Masakiyo Miyazawa  and
Nico M. van Dijk
Masakiyo Miyazawa
Affiliation:
Science University of Tokyo, Noda, Chiba 278, Japan
Nico M. van Dijk
Affiliation:
University of Amsterdam, Amsterdam, The Netherlands
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Abstract

This note studies the comparison of finite-buffer and nonexponential batch arrival systems of the form Gx/M/c/c + N with the corresponding systems, with N replaced by N', where N' can be smaller, larger, or infinite. If N' = ∞ the service times can be arbitrarily distributed. Both comparison and error bounds are obtained for performance measures such as the throughput, the idle probability, and the active server distribution. The results are of practical interest to establish computational reductions, either by infinite-space approximation or by reduced finite truncations. Two different proof techniques will be employed: the sample path approach and the Markov reward approach. The comparison of these two techniques is of interest in itself, showing the advantage and disadvantage of each.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 2 , April 1997 , pp. 189 - 201
Copyright
Copyright © Cambridge University Press 1997

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