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Consider a gas station with two pumps and three car-spaces as shown in the gure below. Potential customers come to the gas station according to a...

Consider a gas station with two pumps and three car-spaces as shown in the
figure below. Potential customers come to the gas station according to a Poisson
process with parameter λ . An incoming customer behaves as follows: if both
pumps are free, he goes to pump 1. If pump 1 is occupied and pump 2 is free,
he goes to pump 2. If pump 2 is occupied, he waits in the waiting space. If
the waiting space is occupied, the customer goes away. Note that because of
the one-way rules, when the customer at pump 2 finishes he has to wait for
the customer at pump1 (if any) to finish, before he can leave. Assume that
service time at each pump is exponentially distributed with rate µ . Model this
situation as a CTMC.

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