article

Fluid approximations for a processor-sharing queue

Authors:

Gideon WeissAuthors Info & Claims

Queueing Systems: Theory and Applications, Volume 27, Issue 1/2

Pages 99 - 125

https://doi.org/10.1023/A:1019105929766

Published: 14 December 1997 Publication History

Abstract

In this paper a fluid approximation, also known as a functional strong law of large numbers (FSLLN) for a GI/G/1 queue under a processor-sharing service discipline is established and its properties are analysed. The fluid limit depends on the arrival rate, the service time distribution of the initial customers, and the service time distribution of the arriving customers. This is in contrast to the known result for the GI/G/1 queue under a FIFO service discipline, where the fluid limit is piecewise linear and depends on the service time distribution only through its mean. The piecewise linear form of the limit can be recovered by an equilibrium type choice of the initial service distribution.

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Cited By

Lakshmikantha ASrikant RBeck C(2018)Differential equation models of flow-size based priorities in internet routersInternational Journal of Systems, Control and Communications10.1504/IJSCC.2010.0311632:1/2/3(170-196)Online publication date: 13-Dec-2018
https://dl.acm.org/doi/10.1504/IJSCC.2010.031163
Yashkov SYashkova A(2018)Processor sharingAutomation and Remote Control10.1134/S000511790709020268:9(1662-1731)Online publication date: 29-Dec-2018
https://dl.acm.org/doi/10.1134/S0005117907090202
Ben Tahar AJean-Marie A(2018)The fluid limit of the multiclass processor sharing queueQueueing Systems: Theory and Applications10.1007/s11134-012-9287-971:4(347-404)Online publication date: 29-Dec-2018
https://dl.acm.org/doi/10.1007/s11134-012-9287-9
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Published In

cover image Queueing Systems: Theory and Applications

Queueing Systems: Theory and Applications Volume 27, Issue 1/2

1997

199 pages

ISSN:0257-0130

Issue’s Table of Contents

Copyright © Copyright © 1997 Kluwer Academic Publishers.

Publisher

J. C. Baltzer AG, Science Publishers

United States

Publication History

Published: 14 December 1997

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Cited By

Lakshmikantha ASrikant RBeck C(2018)Differential equation models of flow-size based priorities in internet routersInternational Journal of Systems, Control and Communications10.1504/IJSCC.2010.0311632:1/2/3(170-196)Online publication date: 13-Dec-2018
https://dl.acm.org/doi/10.1504/IJSCC.2010.031163
Yashkov SYashkova A(2018)Processor sharingAutomation and Remote Control10.1134/S000511790709020268:9(1662-1731)Online publication date: 29-Dec-2018
https://dl.acm.org/doi/10.1134/S0005117907090202
Ben Tahar AJean-Marie A(2018)The fluid limit of the multiclass processor sharing queueQueueing Systems: Theory and Applications10.1007/s11134-012-9287-971:4(347-404)Online publication date: 29-Dec-2018
https://dl.acm.org/doi/10.1007/s11134-012-9287-9
Hampshire RHarchol-Balter MMassey W(2018)Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying ratesQueueing Systems: Theory and Applications10.1007/s11134-006-7584-x53:1-2(19-30)Online publication date: 29-Dec-2018
https://dl.acm.org/doi/10.1007/s11134-006-7584-x
Ben Tahar AJean-Marie AStea GMairesse JMendes J(2009)Population effects in multiclass processor sharing queuesProceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools10.4108/ICST.VALUETOOLS2009.7622(1-10)Online publication date: 20-Oct-2009
https://dl.acm.org/doi/10.4108/ICST.VALUETOOLS2009.7622

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