Consider a simple automatic car wash. Only one car can be in the wash tunnel at any one time. This car wash is in a crowded part of town, and waiting cars cannot spill onto the street, and there is space for only 4 cars waiting to be washed. Due to the various services provided, we will assume the service (actual wash) time is exponential, and cars are washed at the rate of 15 per hour. Customers arrive according to a Poisson process, at the rate of 12 per hour. a. What is the average arrival rate to the system? b. What is the probability that the car wash is empty? c. What is the expected time to get your car washed? That is, time in the system (waiting and washing)? d. What is the probability that an arriving car cannot enter the car wash because the spots are all taken