Accession Number : AD0755234

Title :   The Superposition of Two Independent Markov Renewal Processes.

Descriptive Note : Technical rept. Jun-Dec 72,

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

Personal Author(s) : Cherry,William Peter

Report Date : 30 DEC 1972

Pagination or Media Count : 145

Abstract : The importance of Markov renewal processes in the analysis of queueing networks by decomposition into components has become evident in research carried out during the past ten years. The departure processes from M/G/1 and GI/G/1 queues are Markov renewal processes as are the output streams produced by certain stochastic switches operating on Markov renewal input processes. In the report the superposition of two independent Markov renewal processes is investigated. The resulting stochastic process is a Markov renewal process defined on a state space which is the cross product of a countable set with the non-negative real numbers. The resulting process represents the merging of the outputs of two independent M/G/1 queues. The properties of the superposed process including transition probabilities, recurrence properties and limiting probabilities are derived. (Author)

Descriptors :   (*QUEUEING THEORY, *STOCHASTIC PROCESSES), MATHEMATICAL MODELS, NETWORKS, RANDOM VARIABLES, MULTIPLE OPERATION, DISTRIBUTION FUNCTIONS, MEASURE THEORY, RELIABILITY, THEOREMS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE