Poisson Functionals of Markov Processes and Queueing Networks.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 25, 1987
- Accession Number
- ADA191217
Entities
People
- Richard F. Serfozo
Organizations
- University of North Carolina at Chapel Hill