Cars arrive at an oil change center following a Poisson process, at the rate of four per hour. There is a single available mechanic, and the time taken to perform an oil change is exponentially distributed, with an average of 12 minutes. Approximate an unlimited car space.
Steady-state distribution for the system:
Distribution for the number of cars in the system:
Probability that there are more than three cars at the oil change center:
Mean and variance for the number of cars in the system: