Question

at an automatic car was, cars arrive randomly at a rate of 7 cars every 30 minutes. the car wash takes exactly 4 minutes (this is constant). on average, what would be the legnth of the line

Answer 1

6.53

Explanation:

Given that :

Mean Arrival rate (λ) = 7 cars / 30 minutes

time = 30 minutes

Mean time taken to wash = 4 minutes

Length of line =?

Service rate (μ) = 30 / 4 = 7.5

Length of queue (Lq) = λ² / μ(μ - λ)

Length of queue = 7² / 7.5(7.5 - 7)

Length of queue = 49 / 7.5(0.5)

Length of queue = 49 / 3.75

Length of queue = 13.0667

Length of queue on average = 13.0667/2 = 6.533