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Sojourn times in G/M/1 fork‐join networks
Author(s) -
Ko SungSeok,
Serfozo Richard F.
Publication year - 2008
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.20294
Subject(s) - fork (system call) , join (topology) , fork–join queue , node (physics) , computer science , queueing theory , task (project management) , queue , mathematics , combinatorics , computer network , queue management system , operating system , structural engineering , management , engineering , economics
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