Moment formulas for the Markov renewal branching process
- 1 December 1976
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 8 (4), 690-711
- https://doi.org/10.2307/1425930
Abstract
There are many queueing models in which there appears a semi-Markov matrix G(·), whose entries are absorption-time distributions in a Markov renewal branching process. The role of G(·) is similar to that of the busy period in the simple M/G/1 model. The computation of various quantities associated with G(·) is however much more complicated. The moment matrices, and particularly the mean matrix of G(·), are essential in the construction of general and mathematically well-justified algorithms for the steady-state distributions of such queues.This paper discusses the moment matrices of G(·) and algorithms for their numerical computation. Its contents are basic to the algorithmic solutions to several queueing models, which are to be presented in follow-up papers.Keywords
This publication has 13 references indexed in Scilit:
- A queue with poisson input and semi-Markov service times: busy period analysisJournal of Applied Probability, 1975
- The M/M/1 Queue in a Markovian EnvironmentOperations Research, 1974
- A Queuing-Type Birth-and-Death Process Defined on a Continuous-Time Markov ChainOperations Research, 1973
- Non-linear matrix integral equations of Volterra type in queueing theoryJournal of Applied Probability, 1973
- A queue subject to extraneous phase changesAdvances in Applied Probability, 1971
- Two servers in series, studied in terms of a Markov renewal branching processAdvances in Applied Probability, 1970
- Two queues in series with a finite, intermediate waitingroomJournal of Applied Probability, 1968
- Time dependence of queues with semi-Markovian servicesJournal of Applied Probability, 1967
- Time dependence of queues with semi-Markovian servicesJournal of Applied Probability, 1967
- The single server queue with Poisson input and semi-Markov service timesJournal of Applied Probability, 1966