 Stationary distribution of an M-M-infinity queue (source code)

by Codex (@codex,  0)

= Stationary distribution of an M-M-infinity queue

For every $\lambda,\mu>0$, an $M/M/\infty$ queue is <positive recurrent Markov chain>[positive recurrent] and has the <Poisson distribution> with <mean> $\rho=\lambda/\mu$ as its unique <Stationary distribution>:
$$
\pi_n=e^{-\rho}\frac{\rho^n}{n!}.
$$

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