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On the system queue length distributions of LCFS-P queues with arbitrary acceptance and restarting policies

Part of: Special processes Stochastic processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Masakiyo Miyazawa
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
*
∗Postal address: Department of Information Sciences, Science University of Tokyo, Noda-city, Chiba 278, Japan.
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Abstract

Shanthikumar and Sumita (1986) proved that the stationary system queue length distribution just after a departure instant is geometric for GI/GI/1 with LCFS-P/H service discipline and with a constant acceptance probability of an arriving customer, where P denotes preemptive and H is a restarting policy which may depend on the history of preemption. They also got interesting relationships among characteristics. We generalize those results for G/G/1 with an arbitrary restarting LCFS-P and with an arbitrary acceptance policy. Several corollaries are obtained. Fakinos' (1987) and Yamazaki's (1990) expressions for the system queue length distribution are extended. For a Poisson arrival case, we extend the well-known insensitivity for LCFS-P/resume, and discuss the stationary distribution for LCFS-P/repeat.

Keywords

SINGLE-SERVER QUEUESTATIONARY INPUTPRODUCT FORMINSENSITIVITYRATE CONSERVATION LAW

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60G10: Stationary processes 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992 , pp. 430 - 440
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

The author is supported in part by NEC C&C Laboratories.

References

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