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Transient Analytical Solution of M/D/1/N Queues

Jean-Marie Garcia, Olivier Brun and David Gauchard
Journal of Applied Probability
Vol. 39, No. 4 (Dec., 2002), pp. 853-864
Stable URL: http://www.jstor.org/stable/3216008
Page Count: 12
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Transient Analytical Solution of M/D/1/N Queues
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Abstract

An analytical expression of the time-dependent probability distribution of M/D/1/N queues initialised in an arbitrary deterministic state is derived. We also obtain a simple analytical expression of the differential equation governing the transient average traffic which only involves probabilities of boundary states. As a by-product, a closed form solution of the departure rate from the system is also determined.

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