2011•Wiley Encyclopedia of Operations Research and Management ScienceRequires access

Markov Renewal Processes

Serhan Ziya

Abstract

Abstract A Markov renewal process is a vector valued counting process that keeps track of the number of certain types of events associated with a stochastic process. It is a generalization of a renewal process in that a Markov renewal process with a single‐dimensional state representation is a renewal process. In this article, we first define Markov renewal sequences, which are at the core of Markov renewal processes. Then, we give a formal description of Markov renewal processes and provide a number of examples where these processes appear.

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Key concepts: Markov renewal process, Renewal theory, Markov chain, Markov process, Markov property, Markov model, Computer science, Process (computing)