Perturbation analysis explained

Abstract

This note provides a simple explanation of the ideas behind perturbation analysis. Perturbation Analysis (PA) is a technique for the computation of the gradient of performance measure (PM) of a discrete event dynamic system with respect to its parameters (e) using only one sample path or Monte Carlo experiment of the system. When first presented, one's immediate reaction has often been incredulity stemming from the belief that "one cannot get something for nothing". Later this disbelief may be developed into a more sophisticated and technical objection involving the legitimacy of interchanging differentiation and expectation operators or the probabilistic convergence of the PA estimate to its true value (more about these later). In nontechnical terms, these translate to "How can you squeeze out information about a trajectory / sample-path operating under one value of the system parameter from that of another operating under a different value? Don't the two trajectories behave entirely dissimilarly?" We shall offer below a simple explanation. This explanation covers the essence of PA in the simplest terms stripped of all of its computational trappings, efficiency tricks, etc. Once the basic ideas are made clear, we leave the question of "how efficient" to other papers and potential implementors. For similar tutorial reasons, the example used below is not at all the most general case for which PA can be applied. The purpose here is to convey the fundamental idea behind this approach in terms accessible to the largest audience. Interested readers are referred to other PA papers which at this point total over 40 (see [7],[8]).