Accession Number : ADA194289

Title :   Poisson Functionals of Markov Processes and Queueing Networks,

Corporate Author : NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Serfozo, R F

PDF Url : ADA194289

Report Date : Dec 1987

Pagination or Media Count : 29

Abstract : The author presents conditions under which a point process of certain jump times of a Markov process is a Poisson process. One result is that if the Markov process is stationary and the compensator of the point process in reverse time has a constant intensity a, then the point process is Poisson with rate a. A classical example is that the output flow from a M/M/1 queueing system is Poisson. Also presented are similar Poisson characterizations of more general marked point process functionals of a Markov process. These results yield easy-to-use criteria for a collection of such processes to be multi-variate Poisson or marked Poisson with a specified dependence or independence. This document gives several applications to queueing systems, and indicates how the results extend to functionals of non-Markovian processes.

Descriptors :   *MARKOV PROCESSES, *POISSON DENSITY FUNCTIONS, *QUEUEING THEORY, *POINT THEOREM, FLOW, INTENSITY, MULTIVARIATE ANALYSIS, NETWORKS, OUTPUT, POISSON EQUATION, REVERSIBLE, TIME, MATHEMATICAL FILTERS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE