Consider a small oil change center where there is only one worker. Arriving cars have exponential interarrival times with an arriving rate of 10 cars per hour. Whenever there are three or less cars at the center, the worker works at a rate of 10 cars per hour where the service time is also exponentially distributed. However, when there are more than three cars, the worker provides a faster service with a service rate of 20 cars per hour.
What is the percentage of time that the worker is idle?
On average, how many cars are available in the queuing system?
On average, how long it takes for a car to be served?