Variance and bias reduction techniques for the harmonic gradient estimator¹ 1 This research was partially supported by an Ohio Board of Regents Research Initiation Grant, and a summer research fellowship from the Weatherhead School of Management at Case Western Reserve University through the Dean's Research Fellowship Fund.

Gradient estimation techniques are useful for the optimization and sensitivity analysis of discrete-event simulation. Techniques to improve the quality of such estimators are needed to make efficient use of simulation data. This paper discusses variance and bias reduction techniques for the steady state simulation response harmonic gradient estimator. The variance reduction techniques incorporate two control variates. The first control variate is obtained from a noise simulation run output process (i.e., the input parameters are kept fixed during the run). The second control variate is obtained from a signal simulation run output process (i.e., the input parameters are varied in sinusoidal patterns during the run). Two bias reduction techniques are proposed. The first approach involves fitting a quadratic regression model to the harmonic coefficient estimates at frequencies in a neighborhood of zero. The second approach involves sinusoidally varying the simulation input parameters in batches. Procedures incorporating these techniques, requiring a fixed number of simulation runs independent of the number of input parameters, are discussed. Computational results on simulation models of a M/M/1 queueing system and a (S, s) inventory system are included to illustrate the effectiveness and the limitations of these procedures.