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Achievable Stability in Redundancy Systems

Authors:

Youri Raaijmakers,

Sem BorstAuthors Info & Claims

Proceedings of the ACM on Measurement and Analysis of Computing Systems, Volume 4, Issue 3

Article No.: 46, Pages 1 - 21

https://doi.org/10.1145/3428331

Published: 30 November 2020 Publication History

Abstract

We consider a system with N~parallel servers where incoming jobs are immediately replicated to, say, d~servers. Each of the N servers has its own queue and follows a FCFS discipline. As soon as the first job replica is completed, the remaining replicas are abandoned. We investigate the achievable stability region for a quite general workload model with different job types and heterogeneous servers, reflecting job-server affinity relations which may arise from data locality issues and soft compatibility constraints. Under the assumption that job types are known beforehand we show for New-Better-than-Used (NBU) distributed speed variations that no replication $(d=1)$ gives a strictly larger stability region than replication $(d>1)$. Strikingly, this does not depend on the underlying distribution of the intrinsic job sizes, but observing the job types is essential for this statement to hold. In case of non-observable job types we show that for New-Worse-than-Used (NWU) distributed speed variations full replication ($d=N$) gives a larger stability region than no replication $(d=1)$.

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Cited By

Gast NVan Houdt B(2024)Approximations to Study the Impact of the Service Discipline in Systems with RedundancyProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/36390408:1(1-33)Online publication date: 21-Feb-2024
https://dl.acm.org/doi/10.1145/3639040
Gardner KMoyal P(2024)Editorial introduction: second part of the special issue on product forms, stochastic matching, and redundancyQueueing Systems10.1007/s11134-024-09922-1107:3-4(199-203)Online publication date: 9-Aug-2024
https://doi.org/10.1007/s11134-024-09922-1
Gardner KMoyal P(2024)Editorial introduction: special issue on product forms, stochastic matching, and redundancyQueueing Systems: Theory and Applications10.1007/s11134-024-09908-z106:3-4(193-198)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s11134-024-09908-z
Show More Cited By

Index Terms

Achievable Stability in Redundancy Systems
1. Computer systems organization
  1. Dependable and fault-tolerant systems and networks
    1. Redundancy

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Achievable Stability in Redundancy Systems
SIGMETRICS '21: Abstract Proceedings of the 2021 ACM SIGMETRICS / International Conference on Measurement and Modeling of Computer Systems

We investigate the achievable stability region for redundancy systems and a quite general workload model with different job types and heterogeneous servers, reflecting job-server affinity relations which may arise from data locality issues and soft ...
Achievable Stability in Redundancy Systems
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We investigate the achievable stability region for redundancy systems and a quite general workload model with different job types and heterogeneous servers, reflecting job-server affinity relations which may arise from data locality issues and soft ...
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We investigate the stability condition for redundancy-d systems where each of the servers follows a processor-sharing (PS) discipline. We allow for generally distributed job sizes, with possible dependence among the d replica sizes ...

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Published In

cover image Proceedings of the ACM on Measurement and Analysis of Computing Systems

Proceedings of the ACM on Measurement and Analysis of Computing Systems Volume 4, Issue 3

POMACS

December 2020

345 pages

EISSN:2476-1249

DOI:10.1145/3440131

Editors:
Augustin Chaintreau
Columbia University
,
Leana Golubchik
University of Southern California
,
Zhi-Li Zhang
University of Minnesota

Issue’s Table of Contents

Copyright © 2020 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 30 November 2020

Published in POMACS Volume 4, Issue 3

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Cited By

Gast NVan Houdt B(2024)Approximations to Study the Impact of the Service Discipline in Systems with RedundancyProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/36390408:1(1-33)Online publication date: 21-Feb-2024
https://dl.acm.org/doi/10.1145/3639040
Gardner KMoyal P(2024)Editorial introduction: second part of the special issue on product forms, stochastic matching, and redundancyQueueing Systems10.1007/s11134-024-09922-1107:3-4(199-203)Online publication date: 9-Aug-2024
https://doi.org/10.1007/s11134-024-09922-1
Gardner KMoyal P(2024)Editorial introduction: special issue on product forms, stochastic matching, and redundancyQueueing Systems: Theory and Applications10.1007/s11134-024-09908-z106:3-4(193-198)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s11134-024-09908-z
Anton ERighter RVerloop I(2024)Efficient scheduling in redundancy systems with general service timesQueueing Systems: Theory and Applications10.1007/s11134-024-09904-3106:3-4(333-372)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s11134-024-09904-3
Raaijmakers YBorst S(2022)Achievable Stability in Redundancy SystemsACM SIGMETRICS Performance Evaluation Review10.1145/3543516.345626749:1(27-28)Online publication date: 7-Jun-2022
https://dl.acm.org/doi/10.1145/3543516.3456267
Gardner K(2022)Correlation in redundancy systemsQueueing Systems: Theory and Applications10.1007/s11134-022-09829-9100:3-4(197-199)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1007/s11134-022-09829-9
Anselmi J(2022)Replication vs speculation for load balancingQueueing Systems: Theory and Applications10.1007/s11134-022-09809-z100:3-4(389-391)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1007/s11134-022-09809-z
Raaijmakers YBorst SHuang LGandhi AKiyavash NWang J(2021)Achievable Stability in Redundancy SystemsAbstract Proceedings of the 2021 ACM SIGMETRICS / International Conference on Measurement and Modeling of Computer Systems10.1145/3410220.3456267(27-28)Online publication date: 31-May-2021
https://dl.acm.org/doi/10.1145/3410220.3456267
Anselmi JWalton N(2021)Stability and Optimization of Speculative Queueing NetworksIEEE/ACM Transactions on Networking10.1109/TNET.2021.312877830:2(911-922)Online publication date: 24-Nov-2021
https://dl.acm.org/doi/10.1109/TNET.2021.3128778
Aktas MJoshi GKadhe SKazemi FSoljanin E(2021)Service Rate Region: A New Aspect of Coded Distributed System DesignIEEE Transactions on Information Theory10.1109/TIT.2021.311769567:12(7940-7963)Online publication date: Dec-2021
https://doi.org/10.1109/TIT.2021.3117695
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