Mean busy period of an M-M-1 queue
= Mean busy period of an M-M-1 queue
Starting with one customer, the mean busy period of an $M/M/1$ queue is
$$
\mathbb EB=\frac1{\mu-\lambda}
$$
when $\lambda<\mu$. It is infinite when $\lambda\geq\mu$.
= Mean busy period of an M-M-1 queue
Starting with one customer, the mean busy period of an $M/M/1$ queue is
$$
\mathbb EB=\frac1{\mu-\lambda}
$$
when $\lambda<\mu$. It is infinite when $\lambda\geq\mu$.