A Carwash is located on a busy street. Due to limited space, at any point of time at most 12 cars can line up, plus one car in the wash bay. Every busy saturday morning, cars arrive at the facility at a rate of one car per minute following a Poisson process. It takes on the average one minute to wash a car with the wash time exponentially distributed.
1) On the average, how many cars will be in the system? In the waiting line?
2) What percentage of business is lost due to limited space? On average, how many cars will be turned away in an hour?
3) If a car can line up to get the wash, on the average, how long will it take to get the car washed (waiting plus washing)?
3) If the owner buys the next door property, this will effectively remove the space limit. If the customer arrival rate and the car wash rate do not change, what will happen to the carwash? in order to avoid this problem, what should the owner do?
$10 to whoever can answer this.