The method of Common Random Numbers is a technique used to reduce the variance of difference estimates in simulation optimization problems. These differences are commonly used to estimate gradients of objective functions as part of the process of determining optimal values for parameters of a simulated system. Asymptotic results exist which show that using the Common Random Numbers method in the iterative Finite Difference Stochastic Approximation optimization algorithm (FDSA) can increase the optimal rate of convergence of the algorithm from the typical rate of k -1/3 to the faster k -1/2 , where k is the algorithm's iteration number. Simultaneous Perturbation Stochastic Approximation (SPSA) is a newer and often much more efficient optimization algorithm, and we will show that this algorithm, too, converges faster when the Common Random Numbers method is used. We will also provide multivariate asymptotic covariance matrices for both the SPSA and FDSA errors.Common Random Numbers, Simultaneous Perturbation Stochastic Approximation (SPSA), Finite Difference Stochastic Approximation (FDSA), discrete event dynamic systems

The cost of delay i s a serious and increasing problem in the airline industry. Air travel is increasing, and already domestic airports incur thousands of hours of delay daily, costing the industry $2 billion a year. One strategy for reducing total delay costs is to hold planes for a short time at the gate in order to reduce costly airborne congestion. In a network of airports involving hundreds of ights, it is dicult to determine the amount to hold each ight at the gate. This paper discusses how the optimization procedure simultaneous perturbation stochastic approximation (SPSA) can be used to process delay cost measurements from air trac simulation packages and produce an optimal gate holding schedule. As a test case, the SIMMOD air trac simulation package was used to model a simple four-airport network. Initial delay costs are reduced up to 10.3%.