Parameter Perturbation Analysis through Stochastic Petri Nets: Application to an Inventory System

Abstract

Sensitivity analysis is used to determine how “sensitive” a performance measure of a model is with respect to a change in the value of the parameters of the model. Parameter sensitivity analysis of a model is usually performed as a series of tests in which the model analyst sets different values for the parameters of the model to see how a change in the parameters causes a change in the dynamic behavior of the model. Broadly speaking, this analysis is to see what happens when the value of some crucial parameters of a model changes. If a small change in the value of a parameter leads to a big change in the performance of the model, the parameter needs a closer look. It is a useful tool for performance evaluation of a model as well as its model building. Hence, sensitivity analysis can help the modeler to understand the dynamics of a system. Sensitivity analysis is often used to estimate the sensitivity of a performance measure of a system with respect to its decision variables (parameters) by evaluating the gradient (derivatives) of the performance measure at each given value of the parameters. With the gradient, the system performance measure can be optimized by using a gradient method. Moreover, sensitivity analysis can be used to identify key parameters of a system by discovering the parameters whose small change in value leads to a big change in the behavior of the system. In model building, sensitivity analysis can be used to validate a model with unkown parameters by studying the uncertainties of the model associated with the parameters. In the past, sensitivity analysis was usually based on simulation. One of the major research fields in this area is perturbation analysis (PA). The approach firstly applied to an engineering problem was proposed by Ho, Eyler and Chien in 1979. With great efforts made by many researchers in more than one decade, fundamental results for PA have been obtained. Currently, formal sensitivity analysis approaches based on stochastic processes were proposed in the literature. Particularly, efficient algorithms were developed to compute the performance derivates of Markov processes with respect to infinitesimal changes of their parameters (infinitesimal generators) (Cao et al., 1998, 1997). Besides the fundamental works in developing its theory and algorithms, perturbation analysis has also