Poisson Functionals of Markov Processes and Queueing Networks.
Interim rept. 1 Oct 86-25 Dec 87,
NORTH CAROLINA UNIV AT CHAPEL HILL
Pagination or Media Count:
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.
- Statistics and Probability