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During the early morning hours, customers arrive at a branch post office at the average rate of 45 per hour (exponential interarrival times), while clerks can handle transactions on an average of 4 minutes each (exponential). What is the minimum number of clerks needed to keep the average time in the system under 5 minutes?

a. 2
b. 3
c. 4
d. 5
e. 6

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Answer: B. 3

Explanation:

The expected arrival rate at service point is 45 customers per hour and reasonable service rate is 4 minutes.

The total numbers of customers each clerk can handled per hour is calculated below,

= (60 minutes)/ 4(minutes) = 15 customers

At the arrival rate of 45 customers per hour. The required number of clerks needed to handle 45 customers per hour is;

= customer arrived / customer served

= 45/15 =3

Therefore 3 clerks are required to keep the pace steady at an average time under 5 minutes.

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