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MONOTONICITY RESULTS FOR SINGLE-SERVER FINITE-CAPACITY QUEUES WITH RESPECT TO DIRECTIONALLY CONVEX ORDER

Published online by Cambridge University Press:  01 July 2004

Shigeo Shioda  and
Daisuke Ishii
Shigeo Shioda
Affiliation:
Urban Environment Systems, Faculty of Engineering, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan, E-mail: shioda@faculty.chiba-u.jp
Daisuke Ishii
Affiliation:
Urban Environment Systems, Faculty of Engineering, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan, E-mail: shioda@faculty.chiba-u.jp
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Abstract

In this article, we investigate single-server finite-capacity queues where the partial acceptance rule is applied. In particular, we focus on the monotonicity of the amount of lost (processed) work in the queues with respect to the directionally convex order of work or interarrival processes. We first compare the queues that differ only in their work processes and show that if the work processes are directionally convex ordered, so is the amount of work lost (or processed) in the systems. Next, we compare the queues that differ only in their interarrival processes and show that if the interarrival processes are directionally convex ordered, so is the amount of work lost (or processed) in the systems. Using these results, we establish the formula that gives the upper bound of work-loss probability based only on the marginal distributions of work and interarrival processes. Numerical experiments using the data of actual-LAN (local area network) traffic show that the derived formula gives tight bounds sufficient for practical use.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 18 , Issue 3 , July 2004 , pp. 369 - 393
Copyright
© 2004 Cambridge University Press

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