Mathematical Modeling in the Social and Life Sciences

CHAPTER 15

Roulette Wheels and Hospital Beds: A Computer Simulation of Operating and Recovery Room Usage

We are more than half what we are by imitation. The great point is to choose good models and to study them with care.

—Philip Dormer Stanhope, Earl of Chesterfield

I. Introduction

A. The Need for Simulation

In previous chapters we have seen that we can successfully attack a wide variety of problems by modeling their essential features with mathematical concepts and then using the analytical tools of the mathematician to make predictions about a system's behavior. There are many problems in the social and physical sciences, however, that do not appear to be amenable to solution by currently available analytic methods.

The mathematical modeling approach can break down in two essentially different ways. If we re-examine the basic diagram for model building (Fig. 15.1), we note where the difficulties may arise.

In the first place, we must translate the important features of the real-world phenomenon into mathematics. But which branch of mathematics do we choose? For some problems, there seem to exist several different classes of techniques from which we can choose. A deterministic approach using differential equations may suggest itself, or perhaps a probabilistic scheme using Markov chains. The history of scientific thought reveals many instances when a branch of pure mathematics was seized upon as the proper vehicle for a study of real-world phenomena. To develop his theory of ...