Cars arrive at a gas station according to a poisson process, Ask an Expert

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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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Operation Management, Management Studies

Category:- Operation Management
Reference No.:- M91881225

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