A service station has one gasoline pump. Cars wanting gasoline arrive according to a Poisson process at a rate of 15 per hour. There is only room for at most 5 vehicles at the service station (including the one at the pump). However, if the pump already is being used, these potential customers may balak (drive to another service station). In particular, if there are n cars already at the service station, the probability that an arriving customer potential customer will black is n/3 for n 1, 2, 3. The time required to service a car has an exponential distribution with a mean of 4 minutes. (a) Construct the rate diagram for this queueing system.
(b) Develop the balance equations.
(c) Solve these equations to find the steady-state probability distribution of the number of cars at the station. Verify that this solution is the same as that given by the general solution for the birth-and-death process.
(d) Find the expected waiting time (including service) for those cars that stay