(a) Prove that a stationary Markov process is reversible if, and only if, its transition rates satisfy 9(1)(2) (-1) (j) = q(in)9 (in n-1) 9(i,j)9(i,j) ,jn for any finite sequence of states j, j,

(b) Argue that it suffices to verify that the equality in

(a) holds for sequences of distinct states

(c) Suppose that the stream of customers arriving at a queue forms a Poisson process of rate and that there are two servers who possibly differ in efficiency Specifically, suppose that a customer's service time at server i is exponentially distributed with rate ,, for i = 1, 2, where > v. If a customer arrives to find both servers free, he is equally likely to be allocated to either server. Define an appropriate continuous-time Markov chain for this model, show that it is time reversible, and determine the limiting probabilities