Analytical solution of finite capacity M/D/1 queues

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 qu...

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Veröffentlicht in:	Journal of applied probability 2000-12, Vol.37 (4), p.1092-1098
Hauptverfasser:	Brun, Olivier, Garcia, Jean-Marie
Format:	Artikel
Sprache:	eng
Schlagworte:	60K25 68M20 Applied sciences average waiting time Coefficients Computer science control theory systems Computer systems performance. Reliability Determinism embedded Markov chain Exact sciences and technology Finite capacity M/D/1 queues Inference from stochastic processes time series analysis Markov analysis Markov chains Mathematics mean number of customers Modeling Operational research and scientific management Operational research. Management science Probability and statistics Probability distributions Probability theory and stochastic processes queue length distribution Queuing theory Queuing theory. Traffic theory Recursion Sciences and techniques of general use Short Communications Software Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) Statistics Studies Telecommunications systems Waiting rooms
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