Patients arrive to a 24-hour, 7-days-a-week outpatient clinic with interarrival times being distributed as exponential with mean 5.95 (all times are in minutes); the f rst patient arrives at time 0. The clinic has f ve different stations (like nodes in a network), where patients might be directed for service before leaving. All patients f rst sign in with a single receptionist; sign-in times have a triangular distribution with parameters 1, 4, and 8. From there, they might go to the nurses’ station (probability 0.9888) or to one of three exam rooms (probability 0.0112). The table below gives the f ve stations, service times at those stations, and transition probabilities out of each station into the next station for a patient (including out of the sign-in station, just described as an example): Next Station Probability (blank entries are zero probability) Station Service Time Sign In Nurses’ Station Exam Room Lab and X Ray Check Out Sign In TRIA(1, 4, 8) 0.9888 0.0112 Nurses’ Station TRIA(2, 5, 7) 0.9167 0.0833 Exam Room TRIA(4, 7, 13) 0.0428 0.4706 0.0214 0.4652 Lab and X-ray TRIA(15, 23, 38) 0.8333 0.1667 Check Out TRIA(3, 5, 8) From check out, all patients leave and go home . All patients eventually go through the checkout station and go home. Note that it is possible that, after a visit to an exam room, a patient is directed to an exam room again (but may have to queue for it). After a patient checks in but is queueing for either kel01315_ch04_121-206.indd 203 05/12/13 3:29 PM 204 Chapter 4 the nurses’ station or an exam room, regard that patient as being in the waiting room (and those patients leaving an exam room but again directed to an exam room are also regarded as being in the waiting room). There are three identical exam rooms, but only one resource unit at each of the other four stations. Queues for each station are f rst-in, f rst-out, and we assume that movement time between stations is negligible. Run a simulation of 30 round-the-clock 24-hour days and observe the average total time in system of patients, the average number of patients present in the clinic, as well as the throughput of the clinic (number of patients who leave the clinic and go home over the 30 days); also make a plot of the number of patients present in the clinic, and display a throughput counter. If you could afford to add resources, where is the need most pressing? (See Exercises6-24 and