At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes.The car wash takes exactly 4 minutes (this is constant).On average, how long would each driver have to wait before receiving service?
A)28 minutes
B)32 minutes
C)17 minutes
D)24 minutes

Question

Quizplus · Accepted Answer

The average arrival rate is 7 cars per 30 minutes, or 1 car every 4.29 minutes. Since the service rate is 1 car every 4 minutes, the system is stable. The average wait time in the queue can be calculated using the formula Wq = λ/(2μ(μ-λ)), where λ is the arrival rate (1/4.29 cars per minute) and μ is the service rate (1/4 cars per minute). Plugging in the values, we get Wq = (1/4.29)/(2*(1/4)*(1/4 - 1/4.29)) = 28 minutes.

At an Automatic Car Wash, Cars Arrive Randomly at a Rate