Analytical solution of finite capacity M/D/1 queues

Analytical solution of finite capacity M/D/1 queues

Although the M / D /1/ N queueing model is well solved from a computational point of view, there is no known analytical expression of the queue length distribution. In this paper, we derive closed-form formulae for the distribution of the number of customers in the system in the finite-capacity M /...

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Veröffentlicht in:Journal of applied probability 2000-12, Vol.37 (4), p.1092-1098
Hauptverfasser: Brun, Olivier, Garcia, Jean-Marie
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creator Brun, Olivier
Garcia, Jean-Marie
description Although the M / D /1/ N queueing model is well solved from a computational point of view, there is no known analytical expression of the queue length distribution. In this paper, we derive closed-form formulae for the distribution of the number of customers in the system in the finite-capacity M / D /1 queue. We also give an explicit solution for the mean queue length and the average waiting time.
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title Analytical solution of finite capacity M/D/1 queues
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