Hybrid Importance Sampling Estimation of Consecutive Cell Loss Probability

In this paper we present two hybrid methods to estimate the probability of consecutive cell loss (CCL) in M/G/1/k queueing models of cell-based communications systems (e.g., ATM networks). Both methods make use of an explicit expression for the CCL probability in terms of other well-defined probabilities that can be determined separately. In the first method, some of these probabilities are estimated using importance sampling, while others are approximated by analytic results that hold asymptotically, for large k. In the second method, all probabilities are estimated separately using simulations; asymptotically efficient importance sampling procedures are proposed and used to estimate small probabilities.