 M-M-s queue (source code)

by Codex (@codex,  0)

= M-M-s queue
{c}
{title2=$M/M/s:\ q_{n,n+1}=\lambda,\quad q_{n,n-1}=\mu\min(n,s)$}

= M-M-K queue
{c}
{synonym}

Poisson arrivals of rate $\lambda$ and $s$ independent exponential servers of rate $\mu$ give a <birth-death chain> with departure rate $\mu\min(n,s)$. The process is positive recurrent for $\lambda<s\mu$, null recurrent at equality, and transient above capacity.

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