Question: A car wash is open 6 days a week, bit its busiest day is always Saturday.  From historical data, it is estimated that dirty cars arrive at the rate of 20 per hour all day Saturday.  With a full crew working the hand-wash line, it is figured that cars can be cleaned at the rate of one every 2 minutes.  One car at a time is cleaned.  Assuming Poisson arrivals and exponential service times, what is the average number of cars in line?  What is the average time that a car waits before it is washed?  What is the average time that a car spends in the service system.  What is the utilization rate of the car wash?  What is the probability that no cars are in the system?

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