Poisson Functionals of Markov Processes and Queueing Networks,
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1987
- Accession Number
- ADA194289
Entities
People
- R. F. Serfozo
Organizations
- University of North Carolina at Chapel Hill