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The depletion time for M/G/1 systems and a related limit theorem

Published online by Cambridge University Press:  01 July 2016

Julian Keilson  and
Ushio Sumita
Julian Keilson*
Affiliation:
University of Rochester
Ushio Sumita*
Affiliation:
University of Rochester
*
Postal address for both authors: The Graduate School of Management, The University of Rochester, Rochester, NY 14627, U.S.A.
Postal address for both authors: The Graduate School of Management, The University of Rochester, Rochester, NY 14627, U.S.A.
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Abstract

Waiting-time distributions for M/G/1 systems with priority dependent on class, order of arrival, service length, etc., are difficult to obtain. For single-server multipurpose processors the difficulties are compounded. A certain ergodic post-arrival depletion time is shown to be a true maximum for all delay times of interest. Explicit numerical evaluation of the distribution of this time is available. A heavy-traffic distribution for this time is shown to provide a simple and useful engineering tool with good results and insensitivity to service-time distribution even at modest traffic intensity levels. The relationship to the diffusion approximation for heavy traffic is described.

Keywords

M/G/1 QUEUESPRIORITYSERVER BACKLOGWAITING TIMESDEPLETION TIMESHEAVY TRAFFIC
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 2 , June 1983 , pp. 420 - 443
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

∗

During part of the development of the paper, U. Sumita was in the Department of Industrial Engineering and Operations Research at Syracuse University.

Research partly supported by GTE Laboratories.

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