Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. On average, how long (in minutes) does it take to service each student?
Given,
Arrival rate a = 12 students per hour
Service rate s = 20 students per hour
Utilization p = a/s = 12/20 = 0.6
Number of customers in the queueL_{q} = p^{2}/(1-p)
L_{q} = (0.6)^{2}/(1-0.6)
L_{q} = 0.9
Time one has to wait in the queue to get service W_{q} = L_{q}/a = 0.9/12 = 0.075 hours
W = W_{q} + 1/s
W = 0.075 + 1/20
W = 0.125 hours or
Time that each customer will be served W = 7.5 minutes