please answer the second, third, and fourth questions.

4. In the urgent care clinic of Figure 2.1, suppose that the patients arrive from outside into the clinic with interarrival times that are exponentially distributed with mean 6 minutes. The number of individual servers at each station and the branching probabilities are all as shown in Figure 2.1. The service times at cach node are exponentially distributed with means (all in minutes) of 3 for Sign In, 5 for Registration, 90 for Trauma Room, 16 for Exam Rooms, and 15 for Treatment Rooms. 1) For each of the five stations, compute the local traffic intensity (utilization) p there. Will this clinic be able to handle the external patient load? Why or why not? If you could add a single server to the system and add it to any of the five stations, where would you add it? (15 points) 2) For each of the five stations, compute each of W, W. Lq, L, and interpret in words. Would you still make the same decision about where to add that extra single resources unit that you did in the previous problem? Why and why not? Remember these are sick people, some of them seriously ill. (15 points) 3) How much higher could this inflow rate go and have the whole clinic still work (i.e., be able to handle the external patient load), even if only barely? (10 points) 4) The budget's been cut, and we need to eliminate one of the ten individual servers across the clinic; however, we have to keep at least one at each station. Where would this cut be least damaging to the system's operation? Could we cut two servers and expect the system still to work? More than two? (15 points) Amsal 100000 1.0 04 Registration OO Exam Rooms Normal Exit 0,1 Sign In 1.0 Trauma Rooms Treatment Rooms Figure 2.1: A queueing system representing an urgent-care clinic