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A gas station has a diesel pump. Vehicles arrive as a Poisson process at a rate of 20 per hour. A vehicle gives up on
A gas station has a diesel pump. Vehicles arrive as a Poisson process at a rate of 20 per hour. A vehicle gives up on 1 refuel with a probability qn = n/4, where n is the number of vehicles at the post. The time for a vehicle to be served has an exponential distribution averaging 3 minutes.
A) What is the average number of vehicles at the station?
B) Determine, for vehicles that decide to refuel, the average time to leave the gas station and the average waiting time in the queue until refueling begins.
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