M-G-1 queue
= M/G/1 queue
{c}
{wiki}
An $M/G/1$ queue has Poisson arrivals, <independent and identically distributed random variables>[independent identically distributed] service times, and one server. If service has mean $m$ and $\lambda m<1$, its mean busy period is
$$
\frac{m}{1-\lambda m}.
$$
This follows by decomposing the busy period into the first service and the busy-period descendants of arrivals during that service.