Customers arrive at a full-service gas station, with two pumps, at rate of 30cars per hour. However, customers will go to another station if there are at least fourcars in the station: i. e., two being served and two waiting. Suppose that the servicetime for customers is exponential with mean 5 minutes. Denote by Xt the number ofcars at the gas station at timet(both waiting and being served). Requried:
a. In the long-run, how many cars per hour are served at the station?
b. If the gas station is currently empty, what is the expected time until it becomes full?