Consider the Jackson system below. The arrival rate into the emergency room is 1
ID: 3119590 • Letter: C
Question
Consider the Jackson system below. The arrival rate into the emergency room is 100 pa-tients per hour. The service rates for each station are as follows: µsign in = 60 [pa-tients/hr], µreg = 100 [patients/hr], µexam = 25 [patients/hr], µtrama = 100 [patients/hr],and µtreat = 110 [patients/hr]. The goal of this problem is to calculate various performancemetrics. Again, make use of tables where benecial 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 theservice-time at the sign-in desk)
(e) For trama patients that are mis-diagnosed at the sign-in and sent to the registration andexam room, how much time do they spend in the system until they nally access one ofthe trama rooms.
PLEASE ANSWER ALL OF THE QUESTIONS a THROUGH e WITH STEPS, THANKS!
Arrivals 0.9 0.1 Sign-in 1.0 Registration 0.2 1.0 Trauma Rooms Exam Rooms 0.3 Exit 0.5 0.7 0.3 Treatment roomExplanation / Answer
From the 100 entries coming along the way, the above table shows the number of patients going for each queue.
For per hour basis capacity of each queue, let us see in the given table,
(a) In one hour, only 60 patients can sign-in.
Those 60 will be sent to the registration.
Out of those 60, 54 will be sent to exam room and 6 to Trauma center.
Out of 54 to be sent to exam room, 27 will be sent to treatment room and 11 will be sent to trauma room.
The per hour capacity of exam room is 25, hence, in one hour only 12 will sent to treatment room and 5 will be sent to trauma room.
Throughput per hour of each queue can be given as in the below table:
b) Utilization of each queue can be given in percentage as below:
c) For every minute the average length of each queue can be given as:
The capacity of sign-in center and exam roo is less than number of patients entering. hence, the queue per minute is higher, The utilization of registration, trauma and treatment center is less.
d) In average, every one in ten patient goes to trauma center directly. For every 100, patients entering only 60 can sign in an hour. Hence, the service time is one minute for each patient. Waiting time is almost 2 minutes for each patient on an average. Hence, to reach trauma center they need 3 minutes.
Registration Exam Room Trauma Treatment 90 90 10 45Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.