A small credit has a small branch with two tellers. Arrival rate of customers to the branch is 12 customers per hour and the average service time is 6 minutes. Both inter-arrival time and service time follow exponential distribution (that is, the coefficient of variation is 1).
what is the utilization rate.
My answer is 6/5. Is this corect?
To calculate the utilization rate, we need to determine the ratio of the average service rate to the arrival rate.
The average service rate can be calculated as the reciprocal of the average service time. In this case, the average service time is given as 6 minutes, so the average service rate would be 1/6 customers per minute.
The arrival rate is given as 12 customers per hour. To convert it to customers per minute, we divide by 60, resulting in an arrival rate of 12/60 = 1/5 customers per minute.
Now we can calculate the utilization rate by dividing the average service rate by the arrival rate:
Utilization rate = (1/6) / (1/5)
= (1/6) * (5/1)
= 5/6
So the correct answer for the utilization rate is 5/6, not 6/5.