Problem #2 (30 points) Consider a birth/death process with H, = 2 customers per time unit, n = 1, 2, ..., 20 = 3 arrivals per time unit, 2y = 2, 22 = 1, and 2n = 0), n = 3, 4, ... (note that, when there are 3 customers in the systems, the arrival rate is zero). (a) (5 points) Display the transition rate diagram, including the transition rates. (b) (10 points) Calculate the steady state probabilities. (C) (10 points) Calculate L, L, W, W. (d) (5 points) Uso Kendall notation to define this qucucing model and its parameter values. (Ilint: note that the arrival rate decreases with the number of customers in the queueing system; the number of customers in the input source depends on the number of customers inside the queueing systems; note also that, if the arrival rate eventually becomes zero, it is because there are no more customers in the input source)