Generating function analysis of some joint distributions for Poisson loss systems

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...

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Veröffentlicht in:	Queueing systems 2000, Vol.34 (1-4), p.183-197
Hauptverfasser:	STADJE, W, PARTHASARATHY, P. R
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Exact sciences and technology Laplace transforms Mathematical models Mathematics Operational research and scientific management Operational research. Management science Probability Probability and statistics Probability theory and stochastic processes Queuing Queuing theory. Traffic theory Sciences and techniques of general use Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) Studies
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Zusammenfassung:	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.[PUBLICATION ABSTRACT]
ISSN:	0257-0130 1572-9443
DOI:	10.1023/a:1019157019655