10. Consider the Jackson system below 0.4 Registration .95 . Arrivals Exam Rooms

Question

10. Consider the Jackson system below 0.4 Registration .95 . Arrivals Exam Rooms 0.9 0.5 Exit 0.05 0.1 0.9 Sign-in 0.1 1.0 0.1 Treatment roo Trauma Rooms Figure 2: Jackson network The arrival rate into the emergency room is 100 patients per hour. The service rates for each station are as follows: sign-in-60 [patients/hr], reg 100 [patients/hr], ezam-30 [pa- tients/hr], trama-50 [patients/hr], and treat-30 [patients/hr]. The goal of this problem is to calculate various performance metrics. Again, make use of tables where beneficial to clearly present the results (a) What is the average throughput of each queue? (b) What is the utilization of each queue? (c) What is the average queue length of each queue? (d) For trama patients sent directly to the trama room, on average how much time does it take for the patient to enter the trama room (account for all queue-times and the service-time at the sign-in desk) (e) For trama patients that are mis-diagnosed at the sign-in and sent to the registration and exam room, how much time do they spend in the system until they finally access one of the trama rooms

Explanation / Answer

mean Service rate Mean Service rate required in the queue Max throughput=max of mean service rate and queue created utilization=max throughput/mean Service rate arrival 100 Sign -In 60 100 60 100% Trauma room 50 23 12 23% registration 100 90 54 54% Exam Roon 30 86 30 100% Treatment room 30 57 24 79% Exit 52

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