Accession Number : ADA191217

Title :   Poisson Functionals of Markov Processes and Queueing Networks.

Descriptive Note : Interim rept. 1 Oct 86-25 Dec 87,

Corporate Author : NORTH CAROLINA UNIV AT CHAPEL HILL

Personal Author(s) : Serfozo, Richard F

PDF Url : ADA191217

Report Date : 25 Dec 1987

Pagination or Media Count : 26

Abstract : We present 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. We also present 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. We give several applications of queueing systems, and indicate how our results extend of functionals of non-Markovian processes.

Descriptors :   *MARKOV PROCESSES, *QUEUEING THEORY, FLOW, MULTIVARIATE ANALYSIS, NETWORKS, OUTPUT, POISSON DENSITY FUNCTIONS, POISSON EQUATION

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE