Consider a small self-service car wash that has cars arriving with exponentially distributed inter arrival times at a mean rate of 15 per hour. The car wash has 3 washing bays, each equipped with a pressure spraying hose that the customer uses to wash off the car. Washing time, in either bay, is exponentially distributed with a mean washing time of 4 minutes. The car wash has very little space and can accomodate only 2 washing cars in addition to those being washed. If all 2 spots are occupied arriving cars leave and go elsewhere to be washed.
1. What is the expected number of cars at the car wash?
2. What is the expected number of cars in the queue?
3. What is the actual average arrival rate at the car wash?
4. What is the expected waiting time at the car wash?
5. What is the expected waiting time in the queue?