How would you answer each part to this question? Please draw a rate diagram in part a.

NAME: A Suppose that eatoners arrive to a service facility with respect to a Poison process with tale A. There are two servers, Server A and Server B. Service times are independent of each other and exponentially distributed. The man service time at Server A is 1/p, and the mean service time at Server Il is 1/us. When the system is empty, arriving customers go into Server A with probability a and into Server I with probability Lea. Otherwise, customers pick the first available server Toul system capacity is s so that there are at moet & three entonces wiling without meiving service Comers who find the system full are bost a Noded this system as a CTMC Clearly define your states and give the transition rate matrix (15 points) For the following thece questions, do not solve the balance equations Just give your answers using your notation, is in terms of say " where pe is the limiting probability of being in state i. b What is the average number of customers in the system? (5 points) What is the average number of servers idle? (5 points) d What is the probability that an arriving customer will be served by Server A? (5 points)