1. (30 points) Consider the two-server system discussed during the review session (see Ques- tion 1 in the Final Study Guide). Suppose now that on completion of service at the second facility, a customer is satisfied with probability p, and dissatisfied with probability 1 - p, for some p (0,1), independent of whether that customer had been dissatisfied (one or more times) before. A dissatisfied customer will try to reenter service at the first facility: 1 if the first facility is empty the customer will enter service immediately; otherwise s/he will leave the system (albeit very unhappy). All other model elements are assumed to remain the same. (a) (10 points) Construct a CTMC model of this system by specifying the state space and the transition rate matrix. Let = M1 = 42 = 1 and p=0.8. (b) (10 points) Calculate the steady-state probability vector of this CTMC. (c) (10 points) Use the result of part (b) to find the probability that both facilities are occupied. 1. (30 points) Consider the two-server system discussed during the review session (see Ques- tion 1 in the Final Study Guide). Suppose now that on completion of service at the second facility, a customer is satisfied with probability p, and dissatisfied with probability 1 - p, for some p (0,1), independent of whether that customer had been dissatisfied (one or more times) before. A dissatisfied customer will try to reenter service at the first facility: 1 if the first facility is empty the customer will enter service immediately; otherwise s/he will leave the system (albeit very unhappy). All other model elements are assumed to remain the same. (a) (10 points) Construct a CTMC model of this system by specifying the state space and the transition rate matrix. Let = M1 = 42 = 1 and p=0.8. (b) (10 points) Calculate the steady-state probability vector of this CTMC. (c) (10 points) Use the result of part (b) to find the probability that both facilities are occupied