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)