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Two Extremal Autocorrelated Arrival Processes

Published online by Cambridge University Press:  27 July 2009

Hiroshi Toyoizumi ,
J. George Shanthikumar  and
Ronald W. Wolff
Hiroshi Toyoizumi
Affiliation:
NTT Multimedia Networks Laboratories, Midori-cho 3-9-11 Musashino-shi, Tokyo 180, Japan
J. George Shanthikumar
Affiliation:
Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, California 94720
Ronald W. Wolff
Affiliation:
Faculty of Economics, Tokyo Metropolitan University, 1-1 Minami Oosawa, Hachioji-shi, Tokyo, 192-03, Japan and Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, California 94720
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Abstract

Extremal arrival processes, in the sense of increasing convex order of waiting time of queueing systems, are investigated. Two types of extremal processes are proposed: one in the class of processes that have identical marginal distributions and the other in the class of bounded stochastic processes that have the same mean and covariance structure. The worst performance with regard to waiting time in the sense of increasing convex order is guaranteed when these extremal processes are fed into a first in-first out single-server queue.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 4 , October 1997 , pp. 441 - 450
Copyright
Copyright © Cambridge University Press 1997

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References

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