Analytical Modeling of Stochastic Systems

Contributing USMA Research Unit(s)

Systems Engineering

Publication Date


Publication Title

Handbook of Military and Defense Operations Research

Document Type



This chapter is to promote and encourage the modeling of stochastic systems with analytical models rather than discrete event simulation (DES). DES has many advantages, including flexibility and ease of explanation, but it also requires multiple runs and statistical treatment of their results. DESs also tend to grow in detail and complexity, making them harder and harder to interpret. Analytical models, such as Markov chains and queuing models, give quick answers, but they require a mathematical structure, and they are more abstract and harder to explain. Despite this balance of advantages and disadvantages, simulation is more widely used than analytical models in the practice of military operations research. A brief review of DES and analytical modeling is given, including a sample of some fundamental results and the particular advantages and disadvantages of each. This is followed by a direct comparison, including results from modeling a system that is easily modeled each way. Two examples are presented of analytical modeling of military systems that one might expect to be modeled in a DES. There is a discussion of the imprecision in results from assumptions required to fit a real situation into an analytical framework, with a numerical example.

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