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.
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    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].

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c. Finally, find W(a). As a check, W(0) = 2/3, W(1) = 11/12. (Why?)