there is only one copying machine in the student lounge of the business school.
ID: 376496 • Letter: T
Question
there is only one copying machine in the student lounge of the business school. Students arrive at the rate of lambda = 50 students per hour. It takes each student a minute on average to make their copies. Compute:
(a) the percentage of time that the machine is used
(b) the average length of the queue
(c) the average time spent in the queue
(d) the average number of students in the system
(e) the average time each student spends in the system
Please make sure the answer is right, im having problems with this question in class
Explanation / Answer
Lambda = 50 per hour
Mu = 60 per hour
Rho = lambda / mu = 5/6
(a) Percentage of time the machine is used = 5/6 = 83.33%
(b) Avg queue length = ( Lambda)2 / mu ( mu- lambda)
= 50x50 / 60 x(60-50)
= 2500 / 600 =4.16
(c) Avg time spent in queue =Lambda / mu ( mu- lambda)
= 50 / 60 (10) =0.0833 hour =4.99 = 5 min.
(e) Avg time spent by a student in system = 1/ mu-lambda = 1/60-50 = 1/10 hour = 6 min.
(d) Avg no. of students in system = lambda / mu- lambda = 50 /10 = 5
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