ATM system buffer design under very low cell loss probability constraints

This paper deals with a general method for buffer design in an ATM system in which the target loss probability should be very low (e.g. less than 10-9). This method is based on the application of the Generalized Extreme Value Theory (GEVT) on results arising from simulation runs. This theory allows the estimation of very small probabilities which would not be evaluable with traditional Montecarlo approach. An advantage of 4/5 decades with respect to Montecarlo limits can be obtained utilizing the same sample set. The extension of the theory to the case of distribution functions of discrete random variables is here discussed. The applicability of the method is here demonstrated with reference to known probability distribution functions (Exponential, Normal, Weibull, Iperexponential, Geometric, Bernoulli and Poissonian). Moreover, the GEVT is applied in the cases of classical queueing systems, i.e. M/D/I, Geo/D/1 and MMPP/D/l. Finally, the general criteria for the evaluation of the basic GEVT parameters are discussed.