C) average time in the system Bill Youngdahl has been collecting data at the TU
ID: 346476 • Letter: C
Question
C) average time in the system Bill Youngdahl has been collecting data at the TU student grill. He has found that, between 5:00 P.M. and 7:00 P.M., students arrive at the grill at a rate of 20 per hour (Poisson distributed) and service time takes an average of 2.0 minutes (negative exponential distribution). There is only 1 server, who can work on only 1 order at a time. a) The average number in the line = 1.33 customers (round your response to two decimal places). b) The average time in the system 6 minutes (round your response to one decimal place). c) Suppose that a second server can be added to team up with the first (and, in effect, act as one faster server). This would reduce the average service time to 90 seconds. The average time in the system = minutes round your response to two decimal placesExplanation / Answer
Arrival rate, = 20 per hour
Service rate, = 60/2 = 30 per hour
This M/M/1 queue model
a) Average number in the line, Lq = 2/(*(-)) = 202/(30*(30-20)) = 1.33
b) Average time in the system, W = 1/(-) = 1/(30-20) = 0.1 hour = 6 minutes
c) This is still M/M/1 queue model, with new service rate, = 3600 seconds per hour / 90 seconds = 40 per hour
Average time in the system, W = 1/(-) = 1/(40-20) = 0.05 hour = 3 minutes
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