3.2 PERTURBATION METHODS

Sometimes the probabilistic behavior of random variables that we analyze is complicated by elements found in a realistic urban environment. These elements could be barriers to travel (e.g., parks, cemeteries, rivers), complications to travel (detours, one-way streets), variations in district design due to irregularities in a city's topology, variations in spatial distribution, and so on. In each case it may be possible to solve a simpler problem that ignores the complication(s) and then sequentially add the complication(s) as perturbations to the original problem. We have already seen an illustrative use of the perturbation method in solving one part of the "pedestrian crossing" problem in Chapter 2. We treat separately three different (but related) situations: (1) perturbations to the random variable, (2) perturbations to the pdf, and (3) geometrical perturbations to the region over which objects are uniformly distributed.