OR Spectrum

, Volume 34, Issue 3, pp 723–742

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

Open AccessRegular Article

DOI: 10.1007/s00291-010-0235-y

Cite this article as:
Kemper, B. & Mandjes, M. OR Spectrum (2012) 34: 723. doi:10.1007/s00291-010-0235-y


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.


QueueingFork-join networkSimulationParallel processingSynchronizationThroughput time
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© 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