I would appreciate some help with this

Consider a queue With a Poisson arrival With rate A and two servers. The service times of customers are independent exponential variables of rate ,u, independent of the arrival process. Whenever there are two or more customers present in the system, two customers are being served in parallel. Let Xt denote the number of customers in the system at time t. (a) (1 points) Describe the transition rates for the Markov chain Xt. (b) (3 points) Find conditions on A and ,u Which ensure that the limit 79- : limt_>00 lP',(Xt = j) exists and is strictly positive for all nonnegative i and j, and evaluate 7Tj. (c) (2 points) Under these conditions, over the long run, What fraction of time are both servers busy? (d) (2 points) Starting from an empty system, busy periods are dened as continuous stretches of time during Which at least one server is busy. Are the lengths of successive busy periods independent? Are they identically distributed? (e) (2 points) Evaluate the expected length of the rst busy period