
Help with renewal theory
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 $\displaystyle \lambda$ and let the service times of the customers be iid r.v. with finite mean $\displaystyle \mu$. Then the limiting distribution is $\displaystyle Po(\lambda \mu)$. 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 renewalreward theorem to show that $\displaystyle E[L]=\frac{e^{\lambda \mu}1}{\lambda}$.