A gas station only has one pump for refueling the Pertamax type. The arrival of Pertamax-fueled cars to the gas station follows the process Poisson with an arrival rate of 15 cars / hour. However, when this pump is being used (there is cars that are filling Pertamax), potential customers who come can move to another gas station. In particular, if there are n cars at the gas station, chances are potential customers who come, will move to another gas station is n / 3, for n = 1, 2, 3. The time needed to serve a car is exponentially distributed with an average of 4 minutes.
a. Draw the transition diagram and write the balance equations for the system this queue.
b. Complete equilibrium equations to obtain the proportion of time long term number of cars at the gas station.
c. Determine the expected waiting time of a car in this queue system.