In the urgent-care clinic of Figure 2.1, suppose that the patients arrive from outside into the clinic (coming from the upper right corner of the figure and always into the Sign In station) 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 each node are exponentially distributed with means (all in minutes) of 3 for Sign In, 5 for Registration, 90 for Trauma Rooms, 16 for Exam Rooms, and 15 for Treatment Rooms. For each of the five stations, compute the "local" traffic intensity ?Station there. Will this clinic "work," i.e., 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? Why? Hint: Unless you like using your calculator, a spreadsheet or computer program might be good, or perhaps use mmc.exe.

O Arrival 10 -0000 O) 0.4 1.0 O O O 0.9 Registration O 10.6 OO Exam Normal O Rooms Exit 0.1 O Sign In 1.0 (1.0 O Trauma O Rooms Treatment Rooms Figure 2.1: A queueing system representing an urgent-care clinic