7 Simulation in the Urban Context

In urban operations research we often encounter the following situation: a new operational strategy has been proposed (e.g., a new strategy for allocating fire engines among firehouses or a different set of rules for ambulance dispatching) and we wish to investigate its implications for several indices of an urban service system's performance. In attempting to use for this purpose some of the analytical techniques that we have presented so far, either of two things may happen: the problem may prove to be too complicated to solve analytically; or the problem may be tractable in some respects but the level of detail provided by the analytical answers may be insufficient for our needs.

In either event, it is clear that we would like to learn much more about our problem. One possible solution is to put the new concept into practice on an experimental basis and see if it produces the desired results. However, many constraints of an economic, technical, legal, or political nature very often make such experiments infeasible. Only very rarely does one have an opportunity to perform large-scale experiments in the "real world" with an urban service system. The risks and the costs are usually so high that responsible administrators refuse to give permission or provide the resources necessary for such "trial runs."

Faced with an inability to use an analytical approach or to perform a real-world, real-time experiment with the actual system, the analyst or the planner might then resort to the technique of simulation.

Simulation is a term that has been used to describe many different kinds of activities. For instance, the military exercises that armed forces all over the world perform on a more-or-less regular basis can be considered as examples of simulation (of actual war conditions in this case). So, for that matter, can that part of the training program of airline pilots which involves flying the mock version of an airplane (the "simulator") in a laboratory under "simulated" traffic conditions. Here, however, we shall use a considerably stricter definition:

Definition: Simulation is the procedure in which a computer-based mathematical model of a physical system is used to perform experiments with that system by generating external stimuli ("demands") and observing how the system reacts to them over a period of time.

Thus, central to the idea of simulation-in this interpretation, at leastis the notion of a mathematical model. Almost equally important is the presence of the digital computer as the device which, through its prodigious computational abilities and speed, provides attractive and powerful features to simulation. In fact, it is because simulation is so closely linked with the computer as its tool that this technique did not really come on its own until after the second generation of computers came into existence in the early 1960s. Also central to the concept of simulation is the idea of learning from "empirical" evidence (i.e., from observation of the outcomes of experiments). This is in contrast to the classical approach in mathematics, in which problems are solved once and for all for some given set of assumptions. For this reason simulation is sometimes referred to as the experimental branch of mathematics.

The use of simulation in urban operations research is already considerable and is likely to continue growing in the future. In this chapter we shall examine those specific aspects of simulation which are particularly important in this area of application.

One such aspect is the simulation of probabilistic events. The importance of analyzing urban service systems from a probabilistic point of view is one of the central themes of this book: as we have already noted many times, it is the probabilistic nature of demand and of service requirements for most urban services that makes them difficult to manage and ultimately contributes heavily to their high cost. Thus, the ability to simulate random events is essential to simulation in urban operations research. Section 7.1 will deal in some detail with this topic.

The second area of emphasis in this chapter concerns techniques for working with two-dimensional geometrical relationships in the computer. Obviously, the ability to work with such relationships is essential to simulations of urban services. As we shall see, solutions to problems that appear "natural" and straightforward to human beings require careful analysis and delineation when programmed for a computer.

We shall also discuss briefly simulation languages and the technique of event-paced simulation, which is very convenient for simulating queueing systems of any kind. Finally, simulation is, in some instances, a rather controversial technique. We shall therefore conclude this chapter with a discussion of the advantages, disadvantages, and misuse of simulation as an urban operations research technique.