Simulation of the Asymptotic Constant in Some Fluid Models

Abstract

Let Z(t) be a stationary centered Gaussian process with a Markovian structure. In some fluid models, the stationary buffer content V can be expressed as and P(V>u)=Ce −γu (1+o(1)). The asymptotic constant C can be expressed by the so called generalized Pickands constants H. In most cases no formula or approximation for C are known. In this paper we show a method of simulation of C by the use of change of measure technique. The method is applicable when Z(t) is a stationary Ornstein-Uhlenbeck process or where (X 1(t),…,X n (t)) is a Gauss-Markov process. Two examples of simulations are included. Moreover we give a formula for a lower bound for generalized Pickands constants.