Application of extreme value theory to the analysis of a network simulation

In this paper we present an application of the extreme value theory to the results of a GPSS simulation of a network of queues which is not suitable to be modeled by a product form and, so, to be treated by operational analysis. The objective of this work is to estimate the finite buffer size of the queues such that packets (elements) arriving to the system at a lower rate than one fixed have a very low probability — usually, less than 10-8 — to be rejected (because the buffer is full). To carry out this task only by means of simulation would require a large amount of computational effort. Extreme value theory is employed to estimate, from the results of a reduced simulation, which buffer size corresponds to this loss probability. The extreme value theory is presented and the way it can be applied to the simulation analysis is explained. Further refinements, in order to extend its extrapolative capability, are introduced, and also the way to calculate confidence intervals. Numerical results are presented.