I went to the DMV for my annual car inspection on Tuesday. I noticed that on ave

Question

I went to the DMV for my annual car inspection on Tuesday. I noticed that on average every 4 minutes another car was joining the line (lambda = 15 cars/hr). I guessed that the service time on average is 3 minutes per car (Mu = 20 cars/hour). How long will I be waiting on the average before the inspection? How many cars are in the inspection station on average? What is the utilization of the inspection station? The manager opened a second lane for inspection. What is the average waiting time now?

Explanation / Answer

a) My Waiting Time in line = Wq = /(-) = 0.15 hours = 9 minutes.

b) Average number of cars in the system = L = /(-) = 3 cars

c) Utilistion = / = 75%

d) New Average waiting time = 0.0082 hours = 30 seconds

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