Customers arrive at a two-server station according to a Poisson process with rate . Upon arriving they join a single queue to wait for the next available server.

Suppose that the service times of the two servers are exponential with rates a and

b and that a customer who arrives to find the system empty will go to each of the servers with probability 1/2. Formulate a Markov chain model for this system with state space f0; a; b; 2; 3; : : :g where the states give the number of customers in the system, with a or b indicating there is one customer at a or b respectively.

Show that this system is time reversible. Set .2/ D c and solve to find the limiting probabilities in terms of c.