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The number of overtakes in an M/M/2 queue

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  • Baumann, Hendrik
  • Neumann, Berenice Anne

Abstract

The phenomenon of overtaking in queueing systems and queueing networks has been addressed by several authors with various motivations in the last decades. Nevertheless, up to now, for the relatively simple M/M/2/FCFS queue, the distribution of the number of overtakes a stationary customer suffers from was not known. In this paper, we characterize this distribution by its probability generating function. As a consequence, we derive the expectation (which is well-known) and the variance.

Suggested Citation

  • Baumann, Hendrik & Neumann, Berenice Anne, 2018. "The number of overtakes in an M/M/2 queue," Operations Research Perspectives, Elsevier, vol. 5(C), pages 280-287.
    • Handle: RePEc:eee:oprepe:v:5:y:2018:i:c:p:280-287
    DOI: 10.1016/j.orp.2018.09.001
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    References listed on IDEAS

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    1. Richard C. Larson, 1987. "OR Forum—Perspectives on Queues: Social Justice and the Psychology of Queueing," Operations Research, INFORMS, vol. 35(6), pages 895-905, December.
    2. Neumann, Berenice Anne & Baumann, Hendrik, 2018. "The expected discrimination frequency for two-server queues," Operations Research Perspectives, Elsevier, vol. 5(C), pages 145-149.
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