Problem 2: Consider a single server queue with Poisson arrivals and exponential service times having the following variation: Whenever a service is completed a departure occurs only with probability p. With probability 1-p the customer, instead of leaving, joins the end of the queue. Note that a customer may be serviced more than once. Let {Q(t), t > 0} be the number of customers in system at time t. (i) Set up the generator and find the steady-state distribution, stating conditions for it to exist. (ii) Find the expected waiting time of a customer from the time he arrives until he enters service for the first time