Generating function analysis of some joint distributions for Poisson loss systems

Generating function analysis of some joint distributions for Poisson loss systems

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Article ID: iaor20013053
Country: Netherlands
Volume: 34
Issue: 1/4
Start Page Number: 183
End Page Number: 198
Publication Date: Jan 2000
Journal: Queueing Systems
Authors: ,
Keywords: M/M/c queues
Abstract:

We present a new approach to derive joint distributions for stationary Poisson loss systems. In particular, for M/M/m/0 and M/M/1/n we find the Laplace transforms (with respect to time t) of the probability that at time t there are i customers in the system and during [0,t], j customers are refused admission; for M/M/m/0 we further determine the LT of the probability that the system was full for less than s time units during [0,t] and serves i customers at time t. Explicit formulas for the corresponding moments are also given.

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