Stochastic comparisons for fork-join queues with exponential processing times

Esther Frostig, Tapani Lehtonen

Research output: Contribution to journalArticlepeer-review


Consider a fork-join queue, where each job upon arrival splits into k tasks and each joins a separate queue that is attended by a single server. Service times are independent, exponentially distributed random variables. Server i works at rate μi, Σki=1 μi = μ, where μ is constant. We prove that the departure process becomes stochastically faster as the service rates become more homogeneous in the sense of stochastic majorization. Consequently, when all k servers work with equal rates the departure process is stochastically maximized.

Original languageEnglish
Pages (from-to)487-497
Number of pages11
JournalJournal of Applied Probability
Issue number2
StatePublished - Jun 1997


  • Fork-join queues
  • Stochastic ordering
  • Weak majorization

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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