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Comparing counting processes and queues

Published online by Cambridge University Press:  01 July 2016

Ward Whitt
Ward Whitt*
Affiliation:
Bell Laboratories
*
∗Postal address: Bell Laboratories, Holmdel, NJ 07733, U.S.A.
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Abstract

Several partial orderings of counting processes are introduced and applied to compare stochastic processes in queueing models. The conditions for the queueing comparisons involve the counting processes associated with the interarrival and service times. The two queueing processes being compared are constructed on the same probability space so that each sample path of one process lies below the corresponding sample path of the other process. Stochastic comparisons between the processes and monotone functionals of the processes follow immediately from this construction. The stochastic comparisons are useful to obtain bounds for intractable systems. For example, the approach here yields bounds for queues with time-dependent arrival rates.

Keywords

QUEUEINGSTOCHASTIC ORDERSTOCHASTIC COMPARISONSCOUNTING PROCESSPOINT PROCESS ON THE LINEBOUNDS
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 1 , March 1981 , pp. 207 - 220
Copyright
Copyright © Applied Probability Trust 1981 

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