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Analysis of Fork/Join and Related Queueing Systems

Published: 25 August 2014 Publication History

Abstract

Fork/join (F/J) requests arise in contexts such as parallel computing, query processing in parallel databases, and parallel disk access in RAID. F/J requests spawn K tasks that are sent to K parallel servers, and the completion of all K tasks marks the completion of an F/J request. The exact formula for the mean response time of K = 2-way F/J requests derived under Markovian assumptions (RF/J2) served as the starting point for an approximate expression for RF/JK for 2 < K ≤ 32. When servers process independent requests in addition to F/J requests, the mean response time of F/J requests is better approximated by RmaxK, which is the maximum of the response times of tasks constituting F/J requests. RmaxK is easier to compute and serves as an upper bound to RF/JK. We discuss techniques to compute RmaxK and generally the maximum of K random variables denoting the processing times of the tasks of a parallel computation XmaxK. Graph models of computations such as Petri nets—a more general form of parallelism than F/J requests—are also discussed in this work. Jobs with precedence constraints may require multiple resources, which are represented by a queueing network model. We also discuss various queueing systems related to F/J queueing systems and outline their analysis.

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cover image ACM Computing Surveys
ACM Computing Surveys  Volume 47, Issue 2
January 2015
827 pages
ISSN:0360-0300
EISSN:1557-7341
DOI:10.1145/2658850
  • Editor:
  • Sartaj Sahni
Issue’s Table of Contents
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Published: 25 August 2014
Accepted: 01 May 2014
Revised: 01 May 2014
Received: 01 July 2012
Published in CSUR Volume 47, Issue 2

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Author Tags

  1. Fork-join queueing system
  2. MapReduce
  3. Markov chain model
  4. RAID5 disk array
  5. bulk arrivals
  6. characteristic maximum
  7. independent server model
  8. linear programming
  9. lock contention
  10. matrix geometric method
  11. mirrored disk
  12. order statistics
  13. parallel processing
  14. queueing network model
  15. replicated databases
  16. serialization delay
  17. split-merge queueing system
  18. stream processing
  19. task systems
  20. team service model
  21. vacationing server model

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