3.13 Zero-demand zone Consider a
unit-square response area,
as shown in Figure P3.13(a). We assume that a response unit and
incident (i.e., requests
for service) are distributed uniformly, independently over that part
of the unit square
not contained within the central square having area a2. Travel
occurs according to the
right-angle metric, and travel is allowed through the zero-demand
zone. We want to use
conditioning arguments to derive the expected travel distance W(a)
to a random incident.
Now focus on a unit square on which incidents and the response unit are uniformly, independently distributed over the entire square, yielding an expected travel distance E[D].
c. Finally, find W(a). As a check, W(0) = 2/3, W(1) = 11/12. (Why?)