Estimating small cell-loss ratios in ATM switches via importance sampling

Abstract

The cell-loss ratio at a given node in an ATM switch, defined as the steady-state fraction of packets of information that are lost at that node due to buffer overflow, is typically a very small quantity that is hard to estimate by simulation. Cell losses are rare events, and importance sampling is sometimes the appropriate tool in this situation. However, finding the right change of measure is generally difficult. In this article, importance sampling is applied to estimate the cell-loss ratio in an ATM switch modeled as a queuing network that is fed by several sources emitting cells according to a Markov-modulated ON/OFF process, and in which all the cells from the same source have the same destination. The charge of measure is obtained via an adaptation of a heuristic proposed by Chang et al. {1994} for intree networks. The numerical experiments confirm important efficiency improvements even for large nonintree networks and a large number of sources. Experiments with different variants of the importance sampling methodology are also reported, and a number of practical issues are illustrated and discussed.