OR Spectrum

, Volume 34, Issue 3, pp 723–742 | Cite as

Mean sojourn times in two-queue fork-join systems: bounds and approximations

Open Access
Regular Article


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 Si denoting a job’s sojourn time in queue i, S is defined as max{S1, S2}. 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.


Queueing Fork-join network Simulation Parallel processing Synchronization Throughput time 



The authors would like to thank the editor and the referees for their useful and valuable comments.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Institute for Business and Industrial StatisticsUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of Quantitative Economics, Faculty of Economics and BusinessUniversity of AmsterdamAmsterdamThe Netherlands
  3. 3.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands
  4. 4.EURANDOMEindhovenThe Netherlands
  5. 5.CWIAmsterdamThe Netherlands

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