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.
    Let (X₁, Y₁) and (X₂, Y₂) denote the locations of the response unit and incident, respectively. Let S (S') denote the set of points within (outside) the central square.

    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?)