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The impact of reneging in processor sharing queues

Authors
Publisher
Eurandom
Publication Date
Keywords
  • Queuing Theory
  • Measurement Techniques For Computer Systems
  • Time Sharing
Disciplines
  • Mathematics

Abstract

The Impact of Reneging in Processor Sharing Queues H. Christian Gromoll ∗ Department of Mathematics Stanford University Stanford, CA 94305-2125, USA [email protected] Philippe Robert INRIA-Rocquencourt RAP project Domaine de Voluceau 78153 Le Chesnay, France [email protected] Bert Zwart † Eindhoven University Department of Mathematics and Computer Science P.O. Box 513 5600 MB Eindhoven, the Netherlands [email protected] Richard Bakker Eindhoven University Department of Mathematics and Computer Science P.O. Box 513 5600 MB Eindhoven, the Netherlands [email protected] ABSTRACT We investigate an overloaded processor sharing queue with renewal arrivals and generally distributed service times. Im- patient customers may abandon the queue, or renege, be- fore completing service. The random time representing a customer’s patience has a general distribution and may be dependent on his initial service time requirement. We pro- pose a scaling procedure that gives rise to a fluid model, with nontrivial yet tractable steady state behavior. This fluid model captures many essential features of the under- lying stochastic model, and we use it to analyze the impact of impatience in processor sharing queues. We show that this impact can be substantial compared with FCFS, and we propose a simple admission control policy to overcome these negative impacts. Categories and Subject Descriptors C.4 [Computer System Organization]: Performance of Systems General Terms Algorithms,Performance ∗Research supported in part by an NSF Mathematical Sci- ences Postdoctoral Research Fellowship, a European Union Marie Curie Postdoctoral Research Fellowship, and EU- RANDOM†Research supported by an NWO-VENI grant Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on t

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