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Superposition of Markov renewal processes and applications

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

C. Teresa Lam
C. Teresa Lam*
Affiliation:
The University of Michigan
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Abstract

In this paper, we study the superposition of finitely many Markov renewal processes with countable state spaces. We define the S-Markov renewal equations associated with the superposed process. The solutions of the S-Markov renewal equations are derived and the asymptotic behaviors of these solutions are studied. These results are applied to calculate various characteristics of queueing systems with superposition semi-Markovian arrivals, queueing networks with bulk service, system availability, and continuous superposition remaining and current life processes.

Keywords

S-MARKOV RENEWAL EQUATIONSUPERPOSITION MARKOV RENEWAL THEOREMQUEUES WITH SUPERPOSITION SEMI-MARKOVIAN ARRIVALSQUEUEING NETWORKS WITH BULK SERVICESTATE DEPENDENT SERVICE RATESSYSTEM AVAILABILITYCONTINUOUS SUPERPOSITION REMAINING AND CURRENT LIFE PROCESSES

MSC classification

Primary: 60K15: Markov renewal processes, semi-Markov processes
Secondary: 60K10: Applications (reliability, demand theory, etc.) 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 3 , September 1993 , pp. 585 - 606
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Research supported in part by a fellowship from Horace H. Rackham School of Graduate Studies, The University of Michigan.

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