Simulation of the asymptotic constant in some fluid models

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 sup(tgreater than or equal to0)(integral(0)(t)Z(s) ds - ct) and P(V > u) = Ce (-gammau)(1 + o(l)). 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 Z(t) = Sigma(j=1)(n)X(j)(t), 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.