Efficiency of the Antithetic Variate Method for Simulating Stochastic Networks

This paper investigates the efficiency of antithetic variate simulation for estimating the expected completion time of stochastic networks. The method is compared with Monte Carlo simulation and considers both computation effort and the variance of the estimators. An efficiency ratio is first developed and then investigated within a theoretical framework. We then provide analytical proof of the superiority of the antithetic variate method for some networks whose activity durations are distributed symmetrically about their means. Next, experimental analysis of the efficiency ratio is carried out using test networks that are randomly structured and whose activity distributions are randomly assigned. The study shows that on the average the antithetic variate method can provide the same precision as Monte Carlo simulation, but with approximately 1/4 the computation effort. Furthermore, when activity distributions are symmetric, we can expect the antithetic variate method to require less than 1/10 the computation effort.