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

Sung‐Seok Ko and Richard F. Serfozo

Naval Research Logistics (NRL), 2008, vol. 55, issue 5, 432-443

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

Date: 2008
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:55:y:2008:i:5:p:432-443

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