A grocery store has two identical checkouts; each can serve an average of 20 customers per hour following an exponential distribution. Customers ready to check out arrive at a common checkout line following Poisson distribution with a rate of 30 per hour. The utilization of the system will be:
A) 1.5
B) 0.75
C) 0.667
D) 0.25

Question

Quizplus · Accepted Answer

The utilization ($U$) of the system can be calculated using the formula $U = \frac{\lambda}{s \mu}$, where $\lambda$ is the arrival rate, $s$ is the number of servers, and $\mu$ is the service rate of each server. Given $\lambda = 30$ customers per hour, $s = 2$ checkouts, and $\mu = 20$ customers per hour per checkout, the utilization is $U = \frac{30}{2 \times 20} = 0.75$.

A Grocery Store Has Two Identical Checkouts; Each Can Serve