Markov Renewal Processes with Finitely Many States

1961/12/01 by Ronald Pyke
Mathematics · Business, Management and Accounting · Decision Sciences · #Stochastic processes and statistical mechanics #Advanced Queuing Theory Analysis #Probability and Risk Models

paper · pdf · doi:10.1214/aoms/1177704864

Abstract

In this paper, Markov Renewal processes having a finite number of states are studied. Explicit expressions are derived for the distribution functions of first passage times, as well as for the marginal distribution function of the corresponding Semi-Markov process. Double generating functions are obtained for the distribution functions of the N_j-processes. The limiting behavior of a Markov Renewal process is discussed, the stationary probabilities being derived completely. General Markov Renewal processes are introduced, and a related stationary process is determined. Several examples are given.

Citations

• Markov Renewal Processes: Definitions and Preliminary Properties

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