3.14 Square barrier Suppose that the conditions of Problem 3.13 apply, except that in addition, no travel is allowed through the central square. We wish to derive

W'(a) = expected travel distance to a random incident

We use perturbation arguments to write

W"(a) = W(a) + W_E,(a)

where W(a) is the mean travel distance from Problem 3.13 and W_E(a) is the mean extra (perturbation) distance due to the barrier.

As a check, verify the reasonableness of the result W'(l) = 1.