Filtering formulas and the ./M/1 queue in a quasireversible network

Abstract

This paper proposes an elementary justification of the filtering formulas for a Markov chain and an analysis of the arrival and departure processes at a ./M/1 queue in a quasireversible network. It is shown that the interarrival time distributions of the two above mentioned processes are always identical under equilibrium. This generalizes the corresponding result proved for Jackson networks in [1]. An example shows that the those two prrcesses do not necessarily have the same law even if the network outside of the o M,T node is reversible and if there is no immediate feedback on that node. This contradicts a conjecture made in [2].

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