Poisson Traffic Processes in RGSMP and Generalized Networks

In this paper, we present conditions under which the traffic processes in a generalized semi-Markov process with reallocation (RGSMP) are Poison processes, and givean easy-to-use criterion for the quasi-reversibility of queues which can be described byRGSMP's. By applying these results to a multiple class generalized network with generalservice time distributions, we prove that its stationary state distribution is of a productform and the traffic processes which represent the customers exiting the network arePoisson processes.