Conditional importance sampling and its application to ATM switch analysis

Abstract

In communication systems and networks, important performance measures include the error or fault probabilities related to the inability of the system to sustain a desirable operating state. These probabilities are typically low, in the range of 10 ;6 or less. In many cases, it is not possible to nd analytical expressions for such probabilities. Monte Carlo simulation quickly becomes intractable due to the low probabilities involved, although Importance Sampling (IS) techniques have been used as a means of increasing simulation e ciency. P arametric IS methods are not very e ective in cases where the input processes are characterized by uniform input distributions (e.g., random delays), which arise frequently in communication systems and networks. In this paper, we present a conditional IS scheme for systems with input processes that can be characterized by uniform input distributions. The scheme adaptively modi es an initial biasing strategy as samples are taken and also incorporates a problem speci c component that enables the algorithm to be applied to a diverse set of problems. The overall approach i s m o r e e e c t i v e than parametrically biasing the uniform input distributions. We use the conditional biasing algorithm to estimate rare jitter probabilities in ATM switches for CBR sources multiplexed with heterogeneous background VBR and CBR sources. For the experimental systems considered, we observe that the improvement in simulation e ciency is inversely proportional to the probability being estimated. 1

Simulation of rare events in communications networks

“…Parametric IS methods are not very effective when the randomness in the system is described by a uniform probability distributions. Conditional biasing is an impor- tance sampling technique that has been shown to be effective in such cases [10,11]. However, conditional biasing does require some prior knowledge of the system behavior that causes the important event of interest.…”

“…The occurrence of each important event is weighted by a factor Now if C = C*, then the improvement obtained would be 1/w (r, θ) = 40, but since this is not the case (i.e., there is room for samples to be located at the corners of C* which are not in C) the improvement will be somewhat less. See [11] for a more complete development of conditional biasing.…”

“…The simulation overhead involved with the technique is negligible. See [10,11] for more complete descriptions of the use of conditional biasing in estimating cell loss, cell delay, and cell delay variation, respectively, in ATM networks.…”