Queuing Theory. (20 Points).
Company ABC wants to hire seasonal workers to answer phone calls. Suppose that calls to the phone center occur at a rate of 60 per hour and follow a Poisson distribution and each staff can answer an average of 5 calls per hour that follows exponential distribution. Right now, 10 workers are working at the phone center and when all the lines are busy, the phone system can keep 5 additional calls on hold.
a) What is the queuing model of this company? (2 Points)
b) What is the probability that a caller receives a busy signal? (4 Points)
c) What is the probability that a caller is put on hold before receiving service? (4 Points)
d) On average, how long must a caller wait before speaking with the staff? (5 Points)
e) How many additional staff would be required if the Company ABC wants no more than a 5% chance of a caller receiving a busy signal? (5 Points)
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