5.1 M / G / 1 modified queue Apply (5.2) for the case of a rectangular (X_o-by-Y_o) service region with directions of travel parallel to the sides of the rectangle and with a single emergency repair unit garaged at the region's center, (x = X_o/2, y = Y_o/2). The emergency repair unit operates as in the third paragraph of Section 5.2.

1. Suppose that = 1 call per hour. Let us examine how several alternative service region designs having equal area (i.e., X_oY_o = A) can affect system performance. Let A = 4 square miles and response speed be 10 miles/hr. Further, suppose that the mean and variance of on-scene service time are 45 minutes and (45)² minutes², respectively. Find the mean time from calling until arrival of a service unit for X_o = Y_o, X_o= 2Y_o, and X_o = 20Y_o (assuming that we constrain X_oY_o = A = 4 square miles). Can the system be saturated (i.e., > 1) for some values of X_o, Y_o, and unsaturated for others?

2. Verify that with the constraint X_oY_o = A, minimum response time is always achieved by setting X_o = Y_o = A