Your company employs several sales personnel who create Purchase Orders and one

Question

Your company employs several sales personnel who create Purchase Orders and one operator who enters the PO information into the computer system. The sales personnel create PO's at the rate of 25 per hour . The operator can enter the information with an average exponentially distributed time of 2 minutes. Assume the population is infinite and arrivals are poission. a. calducate the percentage utilization of he operator b. calcualte the average number of documents in the system c. calculate the average time in the system. d. calculate the probablity of 4 or more documents being in the system. Your company employs several sales personnel who create Purchase Orders and one operator who enters the PO information into the computer system. The sales personnel create PO's at the rate of 25 per hour . The operator can enter the information with an average exponentially distributed time of 2 minutes. Assume the population is infinite and arrivals are poission. a. calducate the percentage utilization of he operator b. calcualte the average number of documents in the system c. calculate the average time in the system. d. calculate the probablity of 4 or more documents being in the system.

Explanation / Answer

Arrival rate (A or lambda) = 25 per hour

Service rate (S or Mu) = 2 minutes or 60/2 = 30 per hour

a) Utilization = A/S*100 = 25/30*100 = 83.3%

b) Average number of documents (Lq) = A^2/(S*(S-A)) = 25^2/(30*(30-20)) = 2.08

c) Average total time in system = Lq/A + 1/S = (2.08/25 + 1/30)*60 = 6.99 minutes

d) Probability of 4 or more documents = (A/S)^4 = (25/30)^4 = 0.48

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