Simultaneous Events in General Queueing Systems and their Impact on Perturbation Analysis Derivative Estimation

Abstract

Queueing theory is a widespread approach for analyzing complex stochastic networks, such as flexible manufacturing systems or communication networks. Actually, the goal of system analysis is to optimize or at least to improve the performance of the system. Typical performance measures are throughput, utilization or mean sojourn times. In optimizing, the derivative of the performance measure with respect to a system parameter is of interest. One approach, known as Infinitesimal Perturbation Analysis, is to estimate the derivative via the sample derivatives of the performance measure.

We study simultaneous events in a general queueing system setting and thereby derive sufficient and necessary conditions for the existence of sample path derivatives. Having stated the relationship between simultaneous events and the existence of sample derivatives, we extend significantly the area of problems in which the sample path derivative provides an unbiased estimator for the derivative of the performance. Our results extend to queueing systems with discrete service time or interarrival distributions.