Convergence results for harmonic gradient estimators

Sensitivity analysis of steady state simulation outputs typically involves estimating gradients. This paper presents convergence results for the harmonic gradient estimators. Sufficient conditions are formulated that validate the interchange of the derivative and the expectation operators for these estimators. The relationship between these estimators and finite differences gradient estimators is discussed. In particular, the harmonic estimators are shown to be variations of finite differences gradient estimators. Exploiting the orthogonal property of the trigonometric basis results in harmonic gradient estimation procedures requiring two simulation runs. Computational results with various queueing system simulation models are included to compare and illustrate the different estimators. These results suggest that the harmonic gradient estimation procedures requiring two simulation runs may be an alternative to forward (symmetric) finite differences gradient estimation procedures with common random number streams requiring p+1(2p) simulation runs.