5.1 M / G / 1 modified queue Apply (5.2) for the case of a rectangular (Xo-by-Yo) 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 = Xo/2, y = Yo/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., XoYo = 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 Xo = Yo, Xo= 2Yo, and Xo = 20Yo (assuming that we constrain XoYo = A = 4 square miles). Can the system be saturated (i.e., > 1) for some values of Xo, Yo, and unsaturated for others?

  2. Verify that with the constraint XoYo = A, minimum response time is always achieved by setting Xo = Yo = A