On Poisson Traffic Processes in Discrete State Markovian Systems with Applications to Queueing Theory.
Abstract
A regular Markov process is considered with continuous parameter, countable state space, and stationary transition probabilities, over which a class of traffic processes is defined. The feasibility that multiple traffic processes constitute mutually independent Poisson processes is investigated in some detail. A variety of independence conditions on the traffic process and the underlying Markov process are shown to be equivalent or sufficient to ensure Poisson related properties; these conditions include independent increments, renewal, weak pointwise independence, and pointwise independence. Two computational criteria for Poisson traffic are developed: a necessary condition in terms of weak pointwise independence, and a sufficient condition in terms of pointwise independence. The utility of these criteria is demonstrated by sample applications to queueing-theoretic models. It follows that, for the class of traffic processes as per this paper in a queueing-theoretic context, Kelly's notion of quasi-reversibility and Gelenbe and Muntz's notion of completeness are essentially equivalent to pointwise independence of traffic and state. The latter concept, however, is the most general one. The relevance of the theory developed to queueing network decomposition is also pointed out.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1977
- Accession Number
- ADA043528
Entities
People
- Benjamin Melamed
Organizations
- University of Michigan