Sensitivity Analysis and Concurrent Estimation

Abstract

After going through all the previous chapters, it would be natural for readers to conclude that DES are inherently complex and hard to analyze, regardless of the modeling framework adopted. It would also be natural to wonder whether there are any properties at all in DES that we can exploit in our effort to develop mathematical techniques for analysis, design, and control.

In Chap.1, we saw that systems with event-driven dynamics cannot be modeled through differential (or difference) equations, leaving us with inadequate mathematical tools to analyze their behavior. In Chaps. 2–5, we developed a number of models, both timed and untimed. Although these models certainly enhance our understanding of DES and give us solid foundations for analysis, one cannot help but notice that they involve rather elaborate notation and sometimes intricate definitions. In fact, the complexity of these models was such that in order to proceed with any manageable analysis of stochastic DES we were forced, in Chaps. 7–9, to work with the special class of Markov chains. Even within this class, simple formulae in closed form are hard to come by; in Chap. 8, we saw that outside some simple queueing systems at steady state, analysis becomes extremely complicated. This complexity has led to discrete-event simulation as the only universal tool at this point for studying DES, especially stochastic ones. However, as we saw in Chap. 10, simulation has its own limitations. First, it is based on statistical experiments whose validity must always be checked; we saw, for example, that the problem of selecting the length of simulation runs in seeking estimates of steady-state performance measures is far from simple. Second, even with a new generation of very fast computers, simulation remains a slow and costly approach, certainly not suited for real-time applications. A typical problem one faces in the design or control of a system is that of determining how performance is affected as a function of some parameter θ. In the absence of analytical expressions of the form J(θ), where J(θ) is a performance measure, one is forced to simulate the system repeatedly, at least once for each value of θ of interest. It is easy to see how tedious a process this becomes for complex systems where θ is in fact a vector of parameters or perhaps a list of alternative designs or control policies to be explored.