A non parametric estimate of performance in queueing models with long-range correlation, with applications to telecommunications

A discrete-time G/G/1 (General arrivals/General service times/single server) queueing model is considered, useful for performance evaluation of asynchronous communication systems, in particular ATM (Asynchronous Transfer Mode) systems. The attention is focused on the unfinished work tail probability. In fact it is equivalent to the overflow probability, and hence closely related to the Cell Loss Probability, one of the most important performance parameter in ATM networks. In this paper a non-parametric estimate and related asymptotic confidence intervals of an approximation of the equilibrium unfinished work tail probability is first proposed. Opposite to the usual assumptions, a general correlation function (including Long Range Dependence - LRD) for the arrival process is allowed. Then the presence of LRD is validated by making use of a semiparametric technique. Data come from measurements made by Telecom Italia in the framework of the European ATM Pilot Project. Finally, the obtained estimate of the unfinished work tail probability is evaluated on the available data to assess the performance of a Cell Switch Router (an IP router employing ATM as data link and switching technology) fed by a possibly LRD arrival process.