Accession Number : AD0775212

Title :   The Superposition of Two Independent Markov Renewal Processes,

Corporate Author : MICHIGAN UNIV ANN ARBOR DEPT OF INDUSTRIAL AND OPERATIONS ENGINEERING

Personal Author(s) : Cherry,W. Peter

Report Date : 15 SEP 1973

Pagination or Media Count : 29

Abstract : In the paper the author investigates a problem arising in the theory of queueing networks, namely, the superposition of two independent Markov renewal processes defined on countable state spaces. It is shown by suitably defining random variables that the superposed process is a Markov renewal process defined on a state space which is essentially the cross product of a countable set with the non-negative real numbers. For the superposed process, the author obtains results dealing with recurrence properties of events, exhibits a stationary probability measure for the underlying Markov chain, and investigates the existence of a limit of the probability measure of the associated semi-Markov process. Finally, the author briefly discusses the implications of these results to the theory of queueing networks. (Modified author abstract)

Descriptors :   *Queueing theory, *Stochastic processes, Networks, Random variables, Distribution functions, Measure theory

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE