Counter Intuitive Aspects of Statistical Independence in Steady State Distributions

Stochastic processes that differ materially from one another can sometimes possess exactly the same steady state distribution. This makes it dangerous to draw certain inferences about the nature of a stochastic process by analysing the properties of its associated steady state distribution. Product form queuing networks provide a concrete example of this phenomenon by demonstrating that statistical independence among the states of individual queues does not necessarily imply that these queues operate independently in the associated stochastic process. The distinction between statistical independence and dynamic independence is introduced clarify the issues involved.