Question

175-5.* A service station has one gasoline pump. Cars wanting gasoline arrive according to a Poisson process at a mean rate of 15 per hour. However, if the pump already is heing used, these po- tential customers may balk (drive on to another service station). In particular, if there are n cars already at the service station, the prob- ability that an arriving potential customer will balk is n/3 for n 1. 2, 3. The time required to service a car has an exponential dis- tribution with a mean of 4 minutes. (a) Construct the rate diagram for this queueing system. (b) Develop the halance equations. (c) Solve these equations to find the steady-state probability dis- tribution 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.

Answer 1