## 7.5.1 Advantages of Simulation

In deciding whether simulation should be part of a project aimed at understanding, modifying, or designing the operation of an urban system, it is important to keep in mind what this technique can offer, over and beyond the analytical approaches described in Chapters 2-6. First, simulation can be a method of last resort for problems that are mathematically intractable by any other techniques. In Section 7.3 we described a simple problem with a single server and a (very natural) shortest-distance dispatching strategy for which there are no results from queueing theory, exact or otherwise-even under steady-state conditions. One does not have to think hard to identify a large number of similarly difficult but important problems. Second, even for problems that are mathematically tractable, simulation can often provide a higher level of detail than can other techniques. For instance, while queueing theory might provide good approximations to many aggregate (fleet-wide) statistics for a fleet of spatially distributed urban service vehicles, we might still wish to simulate that fleet in order to study, say, specific vehicles in specific parts of the city. Finally, simulation can sometimes provide (approximate) answers at a lesser cost (or effort) to some problems which are fully tractable mathematically but whose solution may be cumbersome and timeconsuming. It may sometimes be easier, for example, to estimate the average distance between two random points in an area with a complicated shape through simulation (by generating many random pairs of points and "measuring" the distance between them) than through the geometrical probability techniques of Chapter 3.

One should also not lose track of the fact that simulation is based on experiments. In this respect the two main advantages of simulation, by comparison to experiments in the "real world," are that it abbreviates time immensely and that it makes it possible to perform what would in reality be very expensive experiments with very expensive systems. "Expensive" is used here not only in the sense of "costly" but also of "high risk," both in a physical and in a political respect. It is next to impossible for a fire department administrator, for example, to ever authorize drastic modifications in the allocation of fire companies in a borough as a temporary experimental measure. However, one can simulate these modifications and observe in a few seconds how, in an approximate way, the modified system would have reacted to a sequence of fire alarms that is an exact duplicate of all the fires that took place in a city in a whole year [IGNA 78]. Actual experiments with urban service systems are becoming increasingly unusual and costly (see, e.g., [KELL 74] for a description of a recent one). Moreover, unless such experiments are predesigned with meticulous care, they are bound to raise more questions than they answer [LARS 75]. Simulation packages, therefore, may soon be providing the only available preliminary testing ground for some of these experiments. In this respect, other advantages of simulation include that it permits modification or design of urban service systems by trial and error, allows for easy exploration of the system's sensitivity to changes in the input parameters, and provides a highly controllable environment for experiments (allowing duplication of probabilistic sequences of events through the repetition of random number sequences) to an extent unparalleled even in the traditional physics or chemistry laboratory.

Last but not least, simulation can be valuable to the urban operations researcher as a means of testing the applicability and validity of mathematical models and expressions. Throughout this book we have developed mathematical expressions for quantities of interest in the urban environment which were often derived from idealized models of what actually happens in practice. An excellent way to see how valid these expressions are is to compare their predictions with the results of more realistic and detailed simulation models. We have seen several instances [e.g., expressions (3.93) and (5.64)] where simple mathematical expressions that might have seemed to provide only the crudest approximations to reality were shown by simulation to provide highly accurate and reliable predictions [IGNA 78].