Introduction to Discrete-Event Simulation

In our study of dynamic systems, our first goal is to obtain a model. For our purposes, a model consists of mathematical equations which describe the behavior of a system. For example, in Chapter 5 we developed the set of equations (5.7)–(5.12) which describe how the state of a DES evolves as a result of event occurrences over time. Our next goal is to use a model in order to obtain explicit mathematical expressions for quantities of interest. For example, in Chapter 7 our model was a Markov chain and the main quantities of interest were the state probabilities π_j(k) = P[X_k = j], j= 0, 1, ... In some cases, we can indeed obtain such expressions, as we did with birth-death chains at steady state in Section 7.4.3. In general, however, “real world” systems either do not conform to some assumptions we make in order to simplify a model, or they are just too complex to yield analytical solutions. Our mathematical model may still be valid; the problem is that we often do not have the tools to solve the equations which make up such a model. Simulation is a process through which a system model is evaluated numerically, and the data from this process are used to estimate various quantities of interest. As we have repeatedly pointed out in previous chapters, analytical solutions for DES are particularly hard to come by, making simulation a very attractive tool for their study.