Poisson () arrivals join a queue in front of two parallel servers A and B, having exponential service rates A and B. When the system is empty, arrivals go into server A with probability and into B with probability 1 . Otherwise, the head of the queue takes the first free server. (a) Model this problem as a continuous-time Markov chain problem. Defining the states of the process and and set up the balance equations. (Do not solve the equations). (b) In terms of the probabilities in part (a), what is the average number in the system? Average number of servers idle? (c) In terms of the probabilities in part (a), what is the probability that an arbitrary arrival will get serviced in A?