Abstract

The purpose of this chapter is to promote and encourage the modeling of stochastic systems with analytical models. “War is the realm of chance” (von Clausewitz, 1976, p. 101), and discrete event simulation (DES) is a very common method to model the chances of war, not to mention the uncertainties of support and peacetime operations. DES has many advantages. It has flexibility that makes it adaptable to virtually any system that can be mathematically defined. Its relationship to the modeled system is easy to explain. On the other hand, DES also has some disadvantages, most basically that the output of a simulation is one sample from an unknown distribution, so multiple runs and statistical treatment of the results are required. DES models also have a seemingly inevitable tendency to grow in detail and complexity, making them harder and harder to interpret. Analytical models, such as Markov chains and queuing models, have their own strengths and weaknesses. They give instant and exact answers. However, they require that the system modeled have a certain mathematical structure, at least approximately, that is perhaps not always present. They are also more abstract and harder to explain to someone unfamiliar with the method. Despite this balance of advantages and disadvantages, it seems that simulation is much more widely used than analytical models in the practice of military operations research. This chapter will explore why that might be so, and propose some reasons why analysts might want to try to develop an analytical model for the problem at hand rather than turning at once to discrete event simulation. The reader is assumed to be broadly familiar with these methods, but not too familiar to find a review of the basics useful for this discussion.