5. Customers arrive at a queue according to a Poisson process with rate A. Most of the time there is no server but every now and then there appears a superserver serving all the customers instantaneously and emptying the queue. The time intervals between the appearances of the superserver are independent and follow an exponential distribution with parameter. Initially the queue is empty. Let p (t) denote the probability that there are n customers in the queue at time t. a) Prove that po(t) satisfies the equation dpo(t) dt = -(+)po(t) +. Moreover, derive the rest of the forward Kolmogorov equations for all pi(t). [8 marks]