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Sojourn times in G/M/1 fork‐join networks

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  • Sung‐Seok Ko
  • Richard F. Serfozo

Abstract

We consider a processing network in which jobs arrive at a fork‐node according to a renewal process. Each job requires the completion of m tasks, which are instantaneously assigned by the fork‐node to m task‐processing nodes that operate like G/M/1 queueing stations. The job is completed when all of its m tasks are finished. The sojourn time (or response time) of a job in this G/M/1 fork‐join network is the total time it takes to complete the m tasks. Our main result is a closed‐form approximation of the sojourn‐time distribution of a job that arrives in equilibrium. This is obtained by the use of bounds, properties of D/M/1 and M/M/1 fork‐join networks, and exploratory simulations. Statistical tests show that our approximation distributions are good fits for the sojourn‐time distributions obtained from simulations. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

Suggested Citation

  • Sung‐Seok Ko & Richard F. Serfozo, 2008. "Sojourn times in G/M/1 fork‐join networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(5), pages 432-443, August.
    • Handle: RePEc:wly:navres:v:55:y:2008:i:5:p:432-443
    DOI: 10.1002/nav.20294
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    Cited by:

    1. Yonit Barron, 2023. "The Delay Time Profile of Multistage Networks with Synchronization," Mathematics, MDPI, vol. 11(14), pages 1-30, July.
    2. Hongyuan Lu & Guodong Pang, 2016. "Gaussian Limits for a Fork-Join Network with Nonexchangeable Synchronization in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 560-595, May.

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