# Introduction to Discrete-Event Simulation

Chapter
Part of the The Kluwer International Series on Discrete Event Dynamic Systems book series (DEDS, volume 11)

## 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 πj(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
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Selected References

1. Banks, J., and J.S. Carson, Discrete Event System Simulation, Prentice-Hall, Englewood Cliffs, NJ, 1984.
2. Bratley, P., B.L. Fox, and L.E. Schrage, A Guide to Simulation, Springer-Verlag, New York, 1987.
3. Fishman, G.S, Principles of Discrete Event System Simulation, Wiley, New York, 1978.Google Scholar
4. Kiviat, P.J., R. Villanueva, and H.M. Markowitz, SIMSCRIPT 11.5 Programming Language, (edited by E.C. Russell ), CACI Inc., Los Angeles, 1973.Google Scholar
5. Knuth, D.E., The Art of Computer Programming: Vol. 2, Addison-Wesley, Reading, MA, 1981.
7. Law, A.M., and W.D. Kelton, Simulation Modeling and Analysis, McGraw-Hill, New York, 1991.Google Scholar
8. Lehmer, D.H., “Mathematical Methods in Large Scale Computing Units,” Annals Comput. Lab. Harvard University, Vol. 26, pp. 141–146, 1951.
9. Pegden, C.D., R.E. Shannon, and R.P. Sadowski, Introduction to Simulation Using SIMAN, McGraw-Hill, New York, 1990.Google Scholar
10. Pritsker, A.A.B., The GASP IV Simulation Language, Wiley, New York, 1974.
11. Pritsker, A.A.B., Introduction to Simulation and SLAM II, Halsted, New York, 1986.Google Scholar
12. Schriber, T.J., An Introduction to Simulation Using GPSS/H, Wiley, New York, 1990.Google Scholar
13. Zeigler, B.P., Theory of Modeling and Simulation, Wiley, New York, 1976.Google Scholar