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In a queue of type M/M/1 when making the following modification: when there are 3 customers in the system (2 in the queue and 1 being served) if another one arrives he will leave and never come back. How do I obtain the stationary distribution of the chain? How would you interpret it?

Thanks in advance for any suggestions!

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This is a "blocked customers cleared" queue rather than "blocked customers delayed". Interpret it thus:

$$ i \Rightarrow i+1, 0\leq i\leq2$$ $$ i \Rightarrow i-1, 1\leq i\leq3$$

Then just find and solve the balance equations in the normal way.

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