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A Unifying Conservation Law for Single-Server Queues

Part of: Special processes Operations research and management science Computer system organization

Published online by Cambridge University Press:  14 July 2016

Urtzi Ayesta
Urtzi Ayesta*
Affiliation:
LAAS-CNRS
*
∗Postal address: LAAS-CNRS, 7 Avenue Colonel Roche, Toulouse, 31077, France. Email address: urtzi@laas.fr
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Abstract

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We develop a conservation law for a multi-class GI/GI/1 queue operating under a general work-conserving scheduling discipline. For single-class single-server queues, conservation laws have been obtained for both nonanticipating and anticipating disciplines with general service time distributions. For multi-class single-server queues, conservation laws have been obtained for (i) nonanticipating disciplines with exponential service time distributions and (ii) nonpreemptive nonanticipating disciplines with general service time distributions. The unifying conservation law we develop generalizes already existing conservation laws. In addition, it covers popular nonanticipating multi-class time-sharing disciplines such as discriminatory processor sharing (DPS) and generalized processor sharing (GPS) with general service time distributions. As an application, we show that the unifying conservation law can be used to compare the expected unconditional response time under two scheduling disciplines.

Keywords

Queueing theoryperformance evaluationscheduling

MSC classification

Secondary: 60K25: Queueing theory 68M20: Performance evaluation; queueing; scheduling 90B36: Scheduling theory, stochastic
Type
Research Papers
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 1078 - 1087
Copyright
Copyright © Applied Probability Trust 2007 

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