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.

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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