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On the subcritical Bellman-Harris process with immigration

Published online by Cambridge University Press:  14 July 2016

A. G. Pakes  and
Norman Kaplan
A. G. Pakes
Affiliation:
Monash University
Norman Kaplan
Affiliation:
University of California, Berkeley
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Abstract

Some necessary and sufficient conditions are found for the existence of a proper non-degenerate limiting distribution for a Bellman-Harris age-dependent branching process with a compound renewal immigration component. A number of these results are applicable to the batch arrival GI/G/∞ queueing process. Some aspects of the situation when there is no such limiting distribution are considered. The situation when the immigration component is a nonhomogeneous compound Poisson process is briefly considered.

Keywords

BRANCHING PROCESSESIMMIGRATIONAGE-DEPENDENCELIMITING DISTRIBUTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 652 - 668
Copyright
Copyright © Applied Probability Trust 1974 

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