Derivation of occupancy rate of an M/M/$\infty$ queue https://en.wikipedia.org/wiki/M/M/%E2%88%9E_queue
I am presuming occupancy rate $\rho = \dfrac{E[S]}{E[A]}$ where $S$ is the exponential service random variable(rate $\mu$) and $A$ denotes the exponential inter arrival time random variable (Poisson rate $\lambda$). $E[S] = \dfrac{1}{\mu}$, $E[A] = \dfrac{1}{\lambda}$, then $\rho = \dfrac{\lambda}{\mu}$.
Or if we go with formula of $\rho=\dfrac{\lambda}{K\mu}$ as with M/M/K servers , then $\rho$ should be 0 for M/M/$\infty$.
Kindly state which is right