Application of RPA and the harmonic gradient estimators to a priority queueing system

We consider a queueing system with C customer classes under a nonpreemptive service discipline. The goal is to find gradient estimators for the stationary average sojourn time per customer of each class under admission control. Due to the service discipline, IPA (infinitesimal perturbation analysis) estimators are not applicable. We present the idea of harmonic gradient (HG) estimation, based on the Fourier decomposition of periodic functions. The canonical estimators can be used to obtain consistent estimators for all the control variables in a single run. However, the large number of values for each parameter required in the estimation can greatly affect the performance. We then describe the implementations of the phantom RPA (rare perturbation analysis) method. This method requires evaluating, in parallel, the dynamics of as many phantom systems as customers in each busy period. Since this number is random, the implementation of the method can be rather complex. We use the Fourier decomposition ideas to construct a hybrid estimator that we call the phantom HG method. We then give simulation results to compare the performance of the estimators and their complexity.