For an $M/M/1$ queuing system, a probability distribution of the waiting time in the queue can be written as $$\mathbb{P}(W_{q}> t)= \rho e^{-\mu t(1-\rho)}$$ where $t$ is some time and $\rho$, as usual, is equal to $\frac{\lambda }{\mu }$.
For an $M/M/2$ queuing system, I know that $$W_{q} = \frac{\rho ^{2}}{\mu (1-\rho ^{2})}.$$ Does anyone know how to derive an expression for the probability distribution of $W_{q}$ for an $M/M/2$ system? I know it exists, because I have seen it before, but I can't seem to derive or remember it.
Thanks in advance!