Question

Pls answer!!!!!!

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.

1. What is the queuing model of this company? (2 Points)

2. What is the probability that a caller receives a busy signal? (4 Points)

3. What is the probability that a caller is put on hold before receiving service? (4 Points)

4. On average, how long must a caller wait before speaking with the staff? (5 Points)

5. 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)

Answer 1

d) Average time caller wait would be calculated as followed:

Arrival rate ()=60

Service rate ()= 5

p= = 60/5= 12%

W_sys= 1/ ()= 1/60-5 = 0.018

Avg. time caller wait would be W= p*W_sys.

W= 0.12*0.018= 0.00216hr. = 2mins 16 secs.

a) M/M/1 queuing model(multiple serving points)

b) Probability that caller recieves busy signal would be as followed: