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):

Report Date:

1987-12-25

Pagination or Media Count:

26.0

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 MM1 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.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE