Variance Reduction by Antithetic Variates in GI/G/1 Queuing Simulations

This paper considers the use of antithetic variates to reduce the variance of estimates obtained in the simulation of a GI/G/1 queue. Two experimental configurations are considered: in the first, 2n observations are taken in a single run; in the second, n observations are taken in each of two runs. If the sequences of uniform random variables that generate the realizations of the queuing system in the two runs are antithetic, we show that the variance of estimates of the mean and distribution of stationary waiting time and number in the queue is less in the second configuration than in the first. We also obtain sufficient conditions for the covariance of functions of a vector of uniform random variables to be nonnegative. Experimental results are given for M/M/1 queuing simulations to illustrate the magnitude of the variance reduction.