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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 A I(x) has preempt/resume priority over a second stream of rate λII and distribution A II(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

Information

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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