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Evaluation of the total time in system in a preempt/resume priority queue via a modified Lindley process

Published online by Cambridge University Press:  01 July 2016

J. Keilson  and
U. Sumita
J. Keilson*
Affiliation:
University of Rochester
U. Sumita*
Affiliation:
University of Rochester
*
∗Postal address: The Graduate School of Management, The University of Rochester, Rochester, NY 14627, U.S.A.
∗Postal address: The Graduate School of Management, The University of Rochester, Rochester, NY 14627, U.S.A.
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Abstract

A Poisson stream of arrival rate λI and service-time distribution AI(x) has preempt/resume priority over a second stream of rate λII and distribution AII(x). Abundant theoretical results exist for this system, but severe numerical difficulties have made many descriptive distributions unavailable. Moreover, the distribution of total time in system of low-priority customers has not been discussed theoretically. It is shown that the waiting-time sequences of such customers before first entry into service is a Lindley process modified by replacement. This leads to the total time distribution needed. A variety of descriptive distributions, transient and stationary, is obtained numerically via the Laguerre transform method.

Keywords

NUMERICAL DISTRIBUTIONSLAGUERRE TRANSFORM
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 4 , December 1983 , pp. 840 - 856
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

This paper was supported in part by GTE Laboratories, Waltham, MA 02154, U.S.A.

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