Much of geometrical probability deals with points distributed uniformly and independently over some region R. At first the uniformity assumption may appear quite restrictive, and although this is true to some extent, it is not as restrictive as one may think. The spatial uniformity assumption plays a role analogous to the assumption of negative exponential service times in queueing systems (Chap. 4):

  1. It provides for a tractable model.

  2. It yields a good "first cut" at the interrelationships among model parameters.

  3. It provides a reasonable approximation for some situations in which the assumption does not hold exactly.

  4. For situations that are not adequately approximated directly, it provides a "building block" upon which to structure a system whose performance adequately reflects the true complexities encountered.