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The second moments of the absorption times in the Markov renewal branching process

Published online by Cambridge University Press:  14 July 2016

Marcel F. Neuts
Marcel F. Neuts*
Affiliation:
University of Delaware
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Abstract

We derive explicit formulas for the second moments of the absorption time matrices in the Markov renewal branching process. These formulas may easily be computationally implemented and are useful in the iterative computation of the semi-Markov matrices, which give the distributions of the duration and of the number of customers served in a busy period of a great variety of complex queueing models.

Keywords

MARKOV RENEWAL BRANCHING PROCESSQUEUESSEMI-MARKOV SERVICE TIMESCOMPUTATIONAL PROBABILITYBUSY PERIOD
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 4 , December 1978 , pp. 707 - 714
Copyright
Copyright © Applied Probability Trust 1978 

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References

[1] Neuts, M. F. (1976) Moment formulas for the Markov renewal branching process. Adv. Appl. Prob. 8, 690–711.CrossRefGoogle Scholar
[2] Neuts, M. F. (1977) Some explicit formulas for the steady-state behavior of the queue with semi-Markovian service times. Adv. Appl. Prob. 9, 141–157.Google Scholar