Efficient Rare Event Simulation Using DPR for Multidimensional Parameter Spaces

Performance constraints in communication systems and networks require the error or fault probabilities to be very low. Analytical and numerical models are often too restrictive and Monte Carlo simulation is computationally prohibitive for low probabilities. Importance sampling (IS) has been used to estimate rare event probabilities but is increasingly difficult to apply to complex systems where there is an indirect relationship between the inputs and the system response. Splitting is an alternative rare event simulation method that can overcome some of the difficulties associated with IS techniques, and has produced satisfactory results for systems for which the splitting parameter space is one dimensional. However, when the efficient simulation of the rare event requires that splitting is controlled by multiple system parameters, incorrect choice of the splitting parameters can lead to estimates with poor statistical accuracy. In this paper, we show that the important regions of the multidimensional parameter space can be correctly and easily identified when the system parameters are selected depending to the nature of the rare event. The equalization of the raw or unweighted steady state probabilities within the important region yields statistically accurate rare event estimates. The probability equalization can be achieved using the readily available Direct Probability Redistribution (DPR) method, by mapping the multidimensional parameter space to a one dimensional DPR control parameter. In this paper, we discuss alternative ways to perform this mapping, and demonstrate multidimensional splitting using two illustrative example systems.