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An approximate analysis of waiting time in multi-class M/G/1/./EDF queues

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Laurent DecreusefondAuthors Info & Claims

ACM SIGMETRICS Performance Evaluation Review, Volume 24, Issue 1

Pages 190 - 199

https://doi.org/10.1145/233008.233043

Published: 15 May 1996 Publication History

Abstract

The Earliest-Deadline-First (EDF) queueing discipline is being more and more widely used for handling time-sensitive applications in computer systems and networks. In this paper, we consider an arbitrary number of traffic classes with class-specific soft-deadline. A soft-deadline is a target waiting-time limit that can be missed. EDF queueing has been proved to minimize the maximum delay overflow related to this limit. We propose a quantitative analysis, through the metric of mean waiting time, on the behavior of EDF queueing. This analysis gives also insight on the correlation between traffic classes with different time-constraints. Technically speaking, we have proven that the mean waiting times for an arbitrary set of N classes of traffic streams with soft deadlines are the unique solution of a system of non-linear equations under the constraint of the Kleinrock's conservation law. We then provide an O (N²) algorithm to get the solution. Simulation suggests that the theoretical approximation we made is quite acceptable.

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Chen MYen H(2016)A two-stage approach in solving the state probabilities of the multi-queue M/G/1 modelInternational Journal of Systems Science10.1080/00207721.2014.91942747:5(1230-1244)Online publication date: 1-Apr-2016
https://dl.acm.org/doi/10.1080/00207721.2014.919427
Kim KLee J(2013)Topology-aware fanout set division scheme for QoS-guaranteed multicast transmissionJournal of Communications and Networks10.1109/JCN.2013.00011115:6(614-634)Online publication date: Dec-2013
https://doi.org/10.1109/JCN.2013.000111
Chen MYen H(2013)A probabilistic approach to estimate the mean waiting times in the earliest deadline first pollingComputers and Industrial Engineering10.1016/j.cie.2012.12.01964:3(817-826)Online publication date: 1-Mar-2013
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An approximate analysis of waiting time in multi-class M/G/1/./EDF queues

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An approximate analysis of waiting time in multi-class M/G/1/./EDF queues
SIGMETRICS '96: Proceedings of the 1996 ACM SIGMETRICS international conference on Measurement and modeling of computer systems

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Published In

cover image ACM SIGMETRICS Performance Evaluation Review

ACM SIGMETRICS Performance Evaluation Review Volume 24, Issue 1

May 1996

273 pages

ISSN:0163-5999

DOI:10.1145/233008

Editors:
Blaine E. Gaither
Hewlett-Packard, Fort Collins, CO
,
Daniel A. Reed
Univ. of Illinois, Urbana

Issue’s Table of Contents

SIGMETRICS '96: Proceedings of the 1996 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
May 1996
279 pages
ISBN:0897917936
DOI:10.1145/233013
Chairman:
Daniel A. Reed
Univ. of Illinois, Urbana
,
Editor:
Blaine D. Gaither
Hewlett-Packard, Fort Collins, CO

Copyright © 1996 ACM.

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 the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 15 May 1996

Published in SIGMETRICS Volume 24, Issue 1

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Chen MYen H(2016)A two-stage approach in solving the state probabilities of the multi-queue M/G/1 modelInternational Journal of Systems Science10.1080/00207721.2014.91942747:5(1230-1244)Online publication date: 1-Apr-2016
https://dl.acm.org/doi/10.1080/00207721.2014.919427
Kim KLee J(2013)Topology-aware fanout set division scheme for QoS-guaranteed multicast transmissionJournal of Communications and Networks10.1109/JCN.2013.00011115:6(614-634)Online publication date: Dec-2013
https://doi.org/10.1109/JCN.2013.000111
Chen MYen H(2013)A probabilistic approach to estimate the mean waiting times in the earliest deadline first pollingComputers and Industrial Engineering10.1016/j.cie.2012.12.01964:3(817-826)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1016/j.cie.2012.12.019
Chen MYen H(2012) A state diagram analysis of the multi-queue M / M /1 model with finite lengths Journal of the Chinese Institute of Engineers10.1080/02533839.2012.63851435:2(165-179)Online publication date: Mar-2012
https://doi.org/10.1080/02533839.2012.638514
Singhoff FLegrand JNana LMarcé L(2005)Scheduling and memory requirements analysis with AADLACM SIGAda Ada Letters10.1145/1104011.1103847XXV:4(1-10)Online publication date: 13-Nov-2005
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Muwumba AJusto GMassawe LNgubiri J(2020)Priority EDF Scheduling Scheme for MANETsCommunications and Networking10.1007/978-3-030-41114-5_6(66-76)Online publication date: 27-Feb-2020
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Gamini Abhaya VTari ZZeephongsekul PZomaya A(2014)Performance Analysis of EDF Scheduling in a Multi-Priority Preemptive M/G/1 QueueIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2013.17125:8(2149-2158)Online publication date: Aug-2014
https://doi.org/10.1109/TPDS.2013.171

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