On the equivalence of flows in networks of queues

Abstract

Consider a network of queues in equilibrium. When are the flows observed on two given links of that network equivalent, i.e., when do they have the same law?The verification of the equivalence of two such point processes is first reduced to an algebraic problem by a technique based on the filtering theory.This method is then used to show that the arrival and departure processes at an M/M/1 node in a Jackson network are not always equivalent, thereby contradicting a conjecture made in [8]. An example where that equivalence holds is also given; it provides new results on the time reversibility of some familiar processes.