In a single channel manual soft cloth wash, cars arrive following Poisson distribution at the rate of 8 per hour. It takes an average of 6 minutes to wash a car, and the service time follows exponential distribution. The system utilization would be
A) $75 \%$
B) $80 \%$
C) $133.33 \%$
D) $125 \%$

Question

Quizplus · Accepted Answer

The system utilization ($\rho$) in a queuing system is given by $\rho = \lambda / \mu$, where $\lambda$ is the arrival rate and $\mu$ is the service rate. Here, $\lambda = 8$ cars per hour and the service time is 6 minutes per car, which translates to $\mu = 60 / 6 = 10$ cars per hour. Thus, $\rho = 8 / 10 = 0.8$ or $80\%$.

In a Single Channel Manual Soft Cloth Wash, Cars Arrive 75%75 \%75%

In a Single Channel Manual Soft Cloth Wash, Cars Arrive $75 \%$