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Analytical Solution of Finite Capacity M/D/1 Queues

Olivier Brun and Jean-Marie Garcia
Journal of Applied Probability
Vol. 37, No. 4 (Dec., 2000), pp. 1092-1098
Stable URL: http://www.jstor.org/stable/3215497
Page Count: 7
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Analytical Solution of Finite Capacity M/D/1 Queues
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Abstract

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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