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Analysis of a finite buffer model with two servers and two nonpreemptive priority classes


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  • Feng, Wei
  • Umemura, Masataka
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    In this paper, we analyze a finite buffer queueing model with two servers and two nonpreemptive priority service classes. The arrival streams are independent Poisson processes, and the service times of the two classes are exponentially distributed with different means. One of the two servers is reserved exclusively for one class with high priority and the other server serves the two classes according to a nonpreemptive priority service schedule. For the model, we describe its dynamic behavior by a four-dimensional continuous-time Markov process. Applying recursive approaches we present the explicit representation for the steady-state distribution of this Markov process. Then, we calculate the Laplace-Stieltjes Transform and the steady-state distribution of the actual waiting times of two classes of customers. We also give some numerical comparison results with other queueing models.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 192 (2009)
    Issue (Month): 1 (January)
    Pages: 151-172

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    Handle: RePEc:eee:ejores:v:192:y:2009:i:1:p:151-172

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    Keywords: Two-class and two-server queueing model Nonpreemptive priority Waiting time Steady-state distribution Blocking probability;


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    1. Feng, Wei & Adachi, Kouichi & Kowada, Masashi, 2002. "A two-queue and two-server model with a threshold-based control service policy," European Journal of Operational Research, Elsevier, vol. 137(3), pages 593-611, March.
    2. Wagner, Dietmar, 1997. "Waiting times of a finite-capacity multi-server model with non-preemptive priorities," European Journal of Operational Research, Elsevier, vol. 102(1), pages 227-241, October.
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    Cited by:
    1. Walraevens, Joris & Maertens, Tom & Bruneel, Herwig, 2013. "A semi-preemptive priority scheduling discipline: Performance analysis," European Journal of Operational Research, Elsevier, vol. 224(2), pages 324-332.
    2. Bruneel, Herwig & Maertens, Tom & Walraevens, Joris, 2014. "Class clustering destroys delay differentiation in priority queues," European Journal of Operational Research, Elsevier, vol. 235(1), pages 149-158.


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