Customers arrive at the average rate of 8 per hour to the Ajax Old Time Car Wash, where each vehicle goes through a single-lane "Gentle Hands" (real people) wash process that averages four minutes.
Vehicles move directly from the car wash to one of several "finishing" lanes where workers wipe, vacuum, clean windows, etc. to finish the vehicle. If all finishing stations are busy the vehicle waits for the next available finishing station. All the finishing stations take on average 11 minutes, exponentially distributed, to finish a vehicle.
What is the minimum number of finishing stations needed to assure that on average, total time in the system (time it takes a customer from arrival at the car wash to completion of service) is no more than 20 minutes?
What portion of the time is the hand wash facility not being used?