Journal of Applied Probability

Analytical solution of finite capacity M/D/1 queues

Olivier Brun and Jean-Marie Garcia

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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.

Article information

J. Appl. Probab. Volume 37, Number 4 (2000), 1092-1098.

First available in Project Euclid: 27 February 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]

Finite capacity M/D/1 queues embedded Markov chain queue length distribution mean number of customers average waiting time


Brun, Olivier; Garcia, Jean-Marie. Analytical solution of finite capacity M / D /1 queues. J. Appl. Probab. 37 (2000), no. 4, 1092--1098. doi:10.1239/jap/1014843086.

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