CASE-STUDIES ON MULTIDIMENSIONAL RESTART SIMULATIONS

Rare event simulation studies are usually time consuming, therefore se veral techniques have been proposed to speed them up. Parallelization, variance reduction, importance sampling, and splitting are the most p opular methods for simulation acceleration. An approach to multilevel splitting is called RESTART (REpetitive Simulation Trials After Reachi ng Thresholds) and allows the simulation of probabilities even smaller than 10(-10) in a reasonable amount of simulation runtime. However, m ost known applications of RESTART are limited to cases, where only one state variable Is observed, even if the model has a complex structure . In this paper we give examples on how to define multivariate thresho ld functions and how to set up RESTART simulations with them. In our c ontext, multivariate threshold functions use information from many sys tem variables to optimize simulation path splitting for one measure of interest. This contrasts the approach of multiple measures, e.g. the simultaneous simulation of loss probabilities in more than one queue. Simulation results for different models demonstrate the speed-up with RESTART and the additional speed-up with our multivariate approach. Fo r the more complex models the gain is smaller than in models with only one state variable, hence raising the question hom to find an optimal multivariate threshold function.