There is only one copying machine in the student lounge of the business school S

Question

There is only one copying machine in the student lounge of the business school Students arrive at the tale of lambda = 45 per bout (according to a Poisson distribution) Copying takes an average of 45 seconds, or mu = 80 per how (according to an exponential distribution) The percentage of tine the machine is used = 56 percent The average length of the queue 0 72 students The average number of students in the system = 1.29 students The average time spent waiting in the queue The average time in the system

Explanation / Answer

Answer:

Lambda = mean arrival rate of students = 45 students per hour

Mu = mean service time = 80 students per hour

Appropriate measures of the service:

1.     The average utilization of the system= p = lambda/mu = 45/80 = 0.5625 per customer

2.     The average number of students in the service system = L = lambda/(mu-lambda) = 45/(80-45) = 1.2857students

3.     Average customer waiting in the line = pL = 0.5625 x 1.2857 = 0.7232

4.     Average time spent waiting in the line = W = 1/(mu-lambda) = 1/35 = 0.02857 hours per student

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