A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day.
-On average, how long does a plow wait before the mechanic begins the repair?
A) 0.19 hour
B) 1.25 hours
C) 1.52 hours
D) 2.64 hours

Question

Quizplus · Accepted Answer

We need to use the M/M/1 queuing formula where:
λ = arrival rate = 4 plows per day
μ = service rate = 7 plows per day
Using the formula:
Lq = λ^2 / (μ(μ-λ)) = (16/49) plows
Wq = Lq / λ = (4/49) days
To convert this to hours, we multiply by 24:
Wq = (4/49) x 24 = 1.52 hours (approximately)

A Crew of Mechanics at the Department of Transportation Garage