Characterizations of Poisson Traffic Streams in Jackson Queueing Networks.

摘要

The equilibrium behavior of Jackson queueing networks (Poisson arrivals, exponential servers and Bernoulli switches) has recently been investigated in some detail. In particular, it was found that in equilibrium, the traffic processes on the so-called exit arcs of a Jackson network with single server nodes constitute Poisson processes. This result may be viewed as an extension of Burke's Theorem from single queues to networks of queues. A conjecture made by Burke and others contends that the traffic processes on nonexit arcs cannot be Poisson in equilibrium. This paper proves this conjecture to be true for a variety of Jackson networks with single server nodes. Subsequently, a number of characterizations of the equilibrium traffic streams on the arcs of open Jackson networks emerge, whereby stochastic properties of traffic streams are shown to be equivalent to a simple graph-theoretic property of the underlying arcs. These results then help to identify some inherent limitations on the feasibility of equilibrium decompositions of Jackson networks. (Author)