I've a question i can't solve.

1) Consider a M/G/infinity queue where customers arrive according to a Poisson process with rate \lambda and let the service times of the customers be iid r.v. with finite mean \mu. Then the limiting distribution is Po(\lambda \mu). Now, let the r.v. L be the length of a busy period. A busy period begins when an arrival finds the system empty and ends when there are no longer any customers in the system. Use the renewal-reward theorem to show that E[L]=\frac{e^{\lambda \mu}-1}{\lambda}.