Large deviations theory and efficient simulation of excessive backlogs in a GI/GI/m queue

Abstract

The problem of using importance sampling to estimate the average time to buffer overflow in a stable GI/GI/m queue is considered. Using the notion of busy cycles, estimation of the expected time to buffer overflow is reduced to the problem of estimating p/sub n/=P (buffer overflow during a cycle) where n is the buffer size. The probability p/sub n/ is a large deviations probability (p/sub n/ vanishes exponentially fast as n to infinity ). A rigorous analysis of the method is presented. It is demonstrated that the exponentially twisted distribution of S. Parekh and J. Walrand (1989) has the following strong asymptotic-optimality property within the nonparametric class of all GI/GI importance sampling simulation distributions. As n to infinity , the computational cost of the optimal twisted distribution of large deviations theory grows less than exponentially fast, and conversely, all other GI/GI simulation distributions incur a computational cost that grows with strictly positive exponential rate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>