Introduction to Discrete Event Systems pp 591-661 | Cite as

# 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 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.

## Keywords

Service Time Queue Length System Time Busy Period Interarrival Time## Preview

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