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 availab

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 ratesandand that a customer who arrives to find the system empty will go to each server with probability 1/2. Formulate a markov chain modelfor this system with state space {0,,, 2, 3,……} where the states give the number of customers in the system, withorindicating there is one customer atorrespectively. Show that the stationary distribution exists and satisfies the detailed balance condition. Setand solve to find the limiting probabilities in terms of.