Abstract
This paper considers a fork-join system (or: parallel queue), which is a two-queue network in which any arrival generates jobs at both queues and the jobs synchronize before they leave the system. The focus is on methods to quantify the mean value of the ‘system’s sojourn time’ S: with S i denoting a job’s sojourn time in queue i, S is defined as max{S 1, S 2}. Earlier work has revealed that this class of models is notoriously hard to analyze. In this paper, we focus on the homogeneous case, in which the jobs generated at both queues stem from the same distribution. We first evaluate various bounds developed in the literature, and observe that under fairly broad circumstances these can be rather inaccurate. We then present a number of approximations, that are extensively tested by simulation and turn out to perform remarkably well.
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The authors would like to thank the editor and the referees for their useful and valuable comments.
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Part of this work was done while M. Mandjes was at Stanford University, Stanford, CA 94305, USA.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Kemper, B., Mandjes, M. Mean sojourn times in two-queue fork-join systems: bounds and approximations. OR Spectrum 34, 723–742 (2012). https://doi.org/10.1007/s00291-010-0235-y
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DOI: https://doi.org/10.1007/s00291-010-0235-y