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A note on a one-compartment model with clustering

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

James G. Booth
James G. Booth*
Affiliation:
The Australian National University
*
∗Postal address: Centre for Mathematics and its Applications, ANU, GPO Box 4, Canberra, ACT 2601, Australia.
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Abstract

The classical one-compartment model with no input or pure death process is shown to be a limiting case of a ‘binomial cascade' model which has the same mean and in which particles exit the compartment in binomial clusters. The transition probabilities of the binomial cascade process are derived in closed form. The model is easily modified to allow Poisson input into the compartment. Distributional results are given for this model also. In particular, it is shown that the M/M/∞ queue is a limiting case.

Keywords

MARKOV PROCESSM/M/∞ QUEUEPOISSON PROCESSSTOCHASTIC COMPARTMENTAL MODELWEAK CONVERGENCE

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 3 , September 1992 , pp. 535 - 542
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

On leave from the Department of Statistics, University of Florida, Gainesville, FL 32611, USA.

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