Stability of Redundancy Systems with Processor Sharing

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2 Citations (Scopus)

Abstract

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 being governed by an arbitrary joint distribution. We establish that the stability condition for the associated fluid-limit model is characterized by the expectation of the minimum of d replica sizes being less than the mean interarrival time per server. In the special case of identical replicas, the stability condition is insensitive to the job size distribution given its mean, and the stability condition is inversely proportional to the number of replicas. In the special case of i.i.d. replicas, the stability threshold decreases (increases) in the number of replicas for job size distributions that are NBU (NWU). We also discuss extensions to scenarios with heterogeneous servers.

Original languageEnglish
Title of host publicationProceedings of the 13th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2020
PublisherAssociation for Computing Machinery, Inc
Pages120-127
Number of pages8
ISBN (Electronic)9781450376464
DOIs
Publication statusPublished - 18 May 2020
Event13th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2020 - Tsukuba, Japan
Duration: 18 May 202020 May 2020

Publication series

NameACM International Conference Proceeding Series

Conference

Conference13th EAI International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2020
CountryJapan
CityTsukuba
Period18/05/2020/05/20

Keywords

  • Parallel-server systems
  • processor-sharing
  • redundancy
  • stability

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