Joint queue length distribution of multi-class, single-server queues with preemptive priorities

Andrei Sleptchenko, Jori Selen, Ivo Adan, Geert Jan van Houtum

    Research output: Contribution to journalArticlepeer-review

    18 Scopus citations


    In this paper we analyze an M/M/1 queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a multi-dimensional Markov process, where the coordinates keep track of the number of customers of each class in the system. Based on matrix-analytic techniques and probabilistic arguments, we develop a recursive method for the exact determination of the equilibrium joint queue length distribution. The method is applied to a spare parts logistics problem to illustrate the effect of setting repair priorities on the performance of the system. We conclude by briefly indicating how the method can be extended to an M/M/1 queueing system with non-preemptive priorities between customer classes.

    Original languageBritish English
    Pages (from-to)379-395
    Number of pages17
    JournalQueueing Systems
    Issue number4
    StatePublished - 23 Sep 2015


    • Equilibrium distribution
    • Matrix-analytic method
    • Multi-dimensional Markov process
    • Static priority


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