10.11 A gas station has only one pump. The time to fill the tank is distributed as...

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10.11 A gas station has only one pump. The time to fill the tank is distributed as Exp(λ). However, after filling the tank, the customers pay by walking inside the gas station while leaving the car at the pump thus blocking all other cars from filling their tank. The service time at the counter is distributed as Exp(μ). The customer leaves immediately after paying in the gas station. When I arrive at the station, there is a customer there filling the tank of his car. What is my expected time until I leave the station?

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