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Insensitive Bounds for the Moments of the Sojourn Times in M/GI Systems Under State-Dependent Processor Sharing

Part of: Operations research and management science Stochastic processes Computer system organization Distribution theory - Probability Special processes

Published online by Cambridge University Press:  01 July 2016

Andreas Brandt  and
Manfred Brandt
Andreas Brandt*
Affiliation:
Humboldt-Universität zu Berlin
Manfred Brandt*
Affiliation:
Zuse Institute Berlin
*
∗ Postal address: Institut für Operations Research, Humboldt-Universität zu Berlin, Spandauer Strasse 1, D-10178 Berlin, Germany. Email address: brandt@wiwi.hu-berlin.de
∗∗ Postal address: Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Takustrasse 7, D-14195 Berlin, Germany. Email address: brandt@zib.de
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Abstract

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We consider a system with Poisson arrivals and independent and identically distributed service times, where requests in the system are served according to the state-dependent (Cohen's generalized) processor-sharing discipline, where each request receives a service capacity that depends on the actual number of requests in the system. For this system, we derive expressions as well as tight insensitive upper bounds for the moments of the conditional sojourn time of a request with given required service time. The bounds generalize and extend corresponding results, recently given for the single-server processor-sharing system in Cheung et al. (2006) and for the state-dependent processor-sharing system with exponential service times by the authors (2008). Analogous results hold for the waiting times. Numerical examples for the M/M/m-PS and M/D/m-PS systems illustrate the given bounds.

Keywords

Poisson arrivalgeneral service timestate-dependent processor sharingCohen's generalized processor sharingconditional sojourn timeconditional waiting timemomentsinsensitive boundsmany serverM/GI/m-PSLaplace-Stieltjes transform

MSC classification

Primary: 60K25: Queueing theory 68M20: Performance evaluation; queueing; scheduling 90B22: Queues and service 60E15: Inequalities; stochastic orderings 60G10: Stationary processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 1 , March 2010 , pp. 246 - 267
Copyright
Copyright © Applied Probability Trust 2010 

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