Perturbation analysis is exact for the M/G/1/ queue

The perturbation analysis technique has recently been developed as an effective method for sensitivity analysis of complex discrete event systems. It enables the sensitivity of a performance measure to be calculated while observing a single sample path of the system. It therefore offers computational savings for computer simulations, and it also has the ability to be applied directly on actual systems. Thus far, much of the research on perturbation analysis has focused on experimental results demonstrating its accuracy for various complex systems. It is clear that for a practically useful new approach such as this, it is also important to study its theoretical properties. As a step in this direction we study here perturbation analysis applied to an M/G/1 queue. While this is a simple and analytically well understood system from the point of queueing theory, it nevertheless is nontrivial, and provides a good test case for perturbation analysis techniques. Only by understanding the behavior of perturbation analysis for simpler systems can we hope to study its properties for more complex cases.