Relations entre distribution stationnaire et distribution aux instants d’arrivée pour des files d’attente usuelles

In queueing theory, three probability distributions naturally arise: arriving customer’s distribution, departing customer’s distribution and stationary queue length distribution. The aim of this paper is to generalize the PASTA property by using a martingale formulation, so to obtain easily relations between these probability distributions. This approach is applied to queues arising when modelling networks based upon the asynchronous transfer mode, namely those composed of a Markov jump process, an Erlang process or a renewal process whose interarrivai time has a Cox distribution.