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March 3, 2021
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March 3, 2021

What is the probability that a caller is put on hold before receiving service?

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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