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Cars arrive at a gas station according to a Poisson process with an average of 10 customers per hour. A car enters the station only if four or fewer cars are already at the gas station. The gas station has only one pump. The amount of time required to serve a car has an exponential distribution with a mean of four minutes.
a. Formulate a continuous-time Markov chain to analyze the situation of the gas station. Specify the state diagram.
b. Solve the equilibrium equations (i.e., find the steady-state probabilities).
c. What is the long-run average number of cars in the station?
d. What is the long-run fraction of potential customers that are lost?
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