Introduction to Discrete-Event Simulation

Abstract

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 Chap. 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 Chap. 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 Sect. 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.

It is helpful to think of computer simulation as the electronic equivalent of a good old-fashioned laboratory experiment. The only hardware involved is a computer, and instead of physical devices connected with each other we have software capturing all such interactions. Randomness (noise) is also replaced by appropriate software driven by what we call a “random number generator.” Simulation is still not the “real thing”, but it is the next best thing we have to actually building some very expensive and complicated systems just to experiment with them. In the case of DES, simulation is widely used in a number of applications. Examples include designing manufacturing systems and evaluating their performance, designing communication networks and testing various protocols for handling messages contending for network resources, and designing airports, road networks, or subways to handle projected traffic loads. Note that these are all highly complex stochastic systems. Thus, building a “laboratory” consisting of highways and cars dedicated to just doing experiments before building the real thing is truly unrealistic. At the same time, it is simply too risky to go ahead and just build such a system based on rough approximations or “gut feeling” alone, given the cost and complexity involved. Finally, one should not exclude the possibility of using approximate solutions for these DES; in this case, simulation becomes a means for testing their accuracy before we can gain any real confidence in them.