Antithetic Variates, Common Random Numbers and Optimal Computer Time Allocation in Simulation

Two simple variance reduction techniques are discussed, viz. antithetic variates and common random numbers. Their joint application creates undesirable negative correlations between the responses of two simulated systems. Therefore three alternatives are considered: antithetics only, common random numbers only, antithetic and common random numbers combined. No alternative is always best as is shown by analytical results for extremely simple systems and simulation results for simple queuing systems. Therefore a procedure is derived that starts with some pilot runs for both systems and estimates which alternative minimizes the variance; at the same time this procedure allocates the limited amount of computer time to the two systems in an optimal way. Results of the application of the procedure to several queuing systems are presented. Because of certain disadvantages of the procedure we may decide to select alternative 1 (antithetics only) a priori. Then the procedure can still be used for the optimal computer time allocation.