A single-bay car wash with a Poisson arrival rate and an exponential service time has cars arriving at an average of 10 minutes apart with an average service time of 4 minutes. What is the system utilization?
A) 0.3
B) 0.4
C) 0.5
D) 0.6

Question

Quizplus · Accepted Answer

System utilization ($\rho$) in a queuing system is calculated as the ratio of the arrival rate ($\lambda$) to the service rate ($\mu$). Given that cars arrive every 10 minutes, $\lambda = 1/10$ cars per minute. The service time is 4 minutes, so $\mu = 1/4$ cars per minute. Thus, $\rho = \lambda / \mu = (1/10) / (1/4) = 0.4$.

A Single-Bay Car Wash with a Poisson Arrival Rate and an Exponential