M-M-s-K queue
= M-M-s-K queue
{c}
{title2=$M/M/s/K$}
An $M/M/s/K$ queue has arrivals forming a <Poisson process> of rate $\lambda$, $s$ servers with independent service times having an <exponential distribution> of rate $\mu$, and total system capacity $K\geq s$. Its occupancy is the finite <birth-death process> on $\{0,\ldots,K\}$ with
$$
b_n=\lambda\mathbf1_{\{n<K\}},
\qquad
d_n=\mu\min(n,s).
$$