A total of N customers move about among 7 servers in the following manner. When a customer is served by server i, he then goes over to server j.ji, with probability 1/(r - 1). If the server he goes to is free, then the customer enters service; otherwise he joins the queue. The service times are all independent, with the service times at server i being exponential with rate Hi,1,..., . Let the state at any time be the vector (n,..., n,), where n is the number of customers presently at server i, i = 1,...,r. En, N.

(a) Argue that if X(r) is the state at time t, then (X(r), 1 0) is a continuous-time Markov chain.

(b) Give the infinitesimal rates of this chain.

(c) Show that this chain is time reversible, and find the limiting probabilities.