Infinitesimal perturbation analysis of a queueing system with bursty traffic

We study aG/G/1 queueing system with a bursty arrival process. Based on a general model for such a bursty process, we derive infinitesimal perturbation analysis (IPA) derivative estimators of the mean system time with respect to various parameters of interest. The cases of both complete and partial state information are considered. To ensure unbiasedness and strong consistency of the estimators, different sample path representations are developed such that sample functions are continuous with respect to the particular parameter of interest. Some of these representations are applicable to a wider class of gradient estimation problems where sample path discontinuities arise. Simulation results are included to compare the convergence rates and variance properties of the different IPA estimators developed.