Arrivals occur at rate $\lambda$ according to a Poisson process the
service time have an exponential distribution with parameter $1/\mu$ in an [M/M/1](https://en.wikipedia.org/wiki/M/M/1_queue) queue, where $\mu$ is the mean service rate where $\mu\geq \lambda$ (stability condition). 

According to [Burke's theorem](https://en.wikipedia.org/wiki/Burke%27s_theorem) the departure process of an M/M/1 queue is a Poisson process with rate parameter $\lambda$ if the arrival follows a Poisson process with rate parameter $\lambda$.

Now, lets assume arrival rate is 2 jobs/sec ($\lambda=2$) and service rate is 3 jobs/sec ($\mu=3$). Then the departure rate should be 3 jobs/sec under the condition that all jobs leave the server after getting service. But according to the Burke's theorem 2 jobs/sec should be leaving the server. What I'm missing here?