article

Tail asymptotics for policies favoring short jobs in a many-flows regime

Authors:

Chang-Woo Yang,

Sanjay Shakkottai,

Mor Harchol-BalterAuthors Info & Claims

ACM SIGMETRICS Performance Evaluation Review, Volume 34, Issue 1

Pages 97 - 108

https://doi.org/10.1145/1140103.1140290

Published: 26 June 2006 Publication History

Abstract

Scheduling policies that prioritize short jobs have received growing attention in recent years. The class of SMART policies includes many such disciplines, e.g. Shortest-Remaining-Processing-Time (SRPT) and Preemptive-Shortest-Job-First (PSJF). In this work, we study the delay distribution of SMART policies and contrast this distribution with that of the Least-Attained-Service (LAS) policy, which indirectly favors short jobs by prioritizing jobs with the least attained service (age).We study the delay distribution (rate function) of LAS and the SMART class in a discrete-time queueing system under the many sources regime. Our analysis in this regime (large capacity and large number of flows) hinges on a novel two dimensional queue representation, which creates tie-break rules. These additional rules do not alter the policies, but greatly simplify their analysis. We demonstrate that the queue evolution of all the above policies can be described under this single two dimensional framework.We prove that all SMART policies have the same delay distribution as SRPT and illustrate the improvements SMART policies make over First-Come-First-Served (FCFS). Furthermore, we show that the delay distribution of SMART policies stochastically improves upon the delay distribution of LAS. However, the delay distribution under LAS is not too bad -- the distribution of delay under LAS for most jobs sizes still provides improvement over FCFS. Our results are complementary to prior work that studies delay-tail behavior in the large buffer regime under a single flow.

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Zhou DFang VXie TPan WKesavan RLin TPatel N(2018)Empirical Evaluation and Enhancement of Enterprise Storage System Request SchedulingACM Transactions on Storage10.1145/319374114:2(1-27)Online publication date: 27-Apr-2018
https://dl.acm.org/doi/10.1145/3193741
Gourhant YGouta APhilip V(2012)Fair Usage and Capping for Providing Internet for All in Developing Countriese-Infrastructure and e-Services for Developing Countries10.1007/978-3-642-29093-0_4(35-48)Online publication date: 2012
https://doi.org/10.1007/978-3-642-29093-0_4
Subramanian VJavidi TKittipiyakul S(2011)Many-Sources Large Deviations for Max-Weight SchedulingIEEE Transactions on Information Theory10.1109/TIT.2011.211085057:4(2151-2168)Online publication date: Apr-2011
https://doi.org/10.1109/TIT.2011.2110850
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Index Terms

Tail asymptotics for policies favoring short jobs in a many-flows regime
1. Mathematics of computing
  1. Probability and statistics
    1. Statistical paradigms
      1. Queueing theory
    2. Stochastic processes

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Published In

cover image ACM SIGMETRICS Performance Evaluation Review

ACM SIGMETRICS Performance Evaluation Review Volume 34, Issue 1

Performance evaluation review

June 2006

388 pages

ISSN:0163-5999

DOI:10.1145/1140103

Issue’s Table of Contents

SIGMETRICS '06/Performance '06: Proceedings of the joint international conference on Measurement and modeling of computer systems
June 2006
404 pages
ISBN:1595933190
DOI:10.1145/1140277
General Chair:
Raymond Marie
University of Rennes 1/IRISA, France
,
Program Chairs:
Peter Key
Microsoft Research, Cambridge, U.K.
,
Evgenia Smirni
College of William and Mary, USA

Copyright © 2006 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

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Publication History

Published: 26 June 2006

Published in SIGMETRICS Volume 34, Issue 1

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Cited By

Zhou DFang VXie TPan WKesavan RLin TPatel N(2018)Empirical Evaluation and Enhancement of Enterprise Storage System Request SchedulingACM Transactions on Storage10.1145/319374114:2(1-27)Online publication date: 27-Apr-2018
https://dl.acm.org/doi/10.1145/3193741
Gourhant YGouta APhilip V(2012)Fair Usage and Capping for Providing Internet for All in Developing Countriese-Infrastructure and e-Services for Developing Countries10.1007/978-3-642-29093-0_4(35-48)Online publication date: 2012
https://doi.org/10.1007/978-3-642-29093-0_4
Subramanian VJavidi TKittipiyakul S(2011)Many-Sources Large Deviations for Max-Weight SchedulingIEEE Transactions on Information Theory10.1109/TIT.2011.211085057:4(2151-2168)Online publication date: Apr-2011
https://doi.org/10.1109/TIT.2011.2110850
Kittipiyakul SJavidi TSubramanian V(2008)Many-sources large deviations for max-weight scheduling2008 46th Annual Allerton Conference on Communication, Control, and Computing10.1109/ALLERTON.2008.4797739(1495-1502)Online publication date: Sep-2008
https://doi.org/10.1109/ALLERTON.2008.4797739
Grandl RAnanthanarayanan GKandula SRao SAkella A(2014)Multi-resource packing for cluster schedulersACM SIGCOMM Computer Communication Review10.1145/2740070.262633444:4(455-466)Online publication date: 17-Aug-2014
https://dl.acm.org/doi/10.1145/2740070.2626334
Grandl RAnanthanarayanan GKandula SRao SAkella ABustamante FHu YKrishnamurthy ARatnasamy S(2014)Multi-resource packing for cluster schedulersProceedings of the 2014 ACM conference on SIGCOMM10.1145/2619239.2626334(455-466)Online publication date: 17-Aug-2014
https://dl.acm.org/doi/10.1145/2619239.2626334
Yang CWierman AShakkottai SHarchol-Balter M(2012)Many Flows Asymptotics for SMART Scheduling PoliciesIEEE Transactions on Automatic Control10.1109/TAC.2011.217341857:2(376-391)Online publication date: Feb-2012
https://doi.org/10.1109/TAC.2011.2173418
Wierman ANuyens M(2008)Scheduling despite inexact job-size informationACM SIGMETRICS Performance Evaluation Review10.1145/1384529.137546136:1(25-36)Online publication date: 2-Jun-2008
https://dl.acm.org/doi/10.1145/1384529.1375461
Wierman ANuyens MLiu ZMisra VShenoy P(2008)Scheduling despite inexact job-size informationProceedings of the 2008 ACM SIGMETRICS international conference on Measurement and modeling of computer systems10.1145/1375457.1375461(25-36)Online publication date: 2-Jun-2008
https://dl.acm.org/doi/10.1145/1375457.1375461
Harchol-Balter M(2008)Scheduling for Server Farms: Approaches and Open ProblemsPerformance Evaluation: Metrics, Models and Benchmarks10.1007/978-3-540-69814-2_1(1-3)Online publication date: 2008
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