Please give me detailed explanation. Thank you

2. A certain queuing system has two types of customers and two types of servers. Type A customers arrive according to a Poisson process with rate 3, and, independently, Type B customers arrive according to a Poisson process with rate 2. If Server A is free, then an arriving Type A customer begins service with Server A. If Server A is busy but Server B is free, then an arriving Type A customer will begin service with Server B. If an arriving Type A customer nds both servers busy, they will leave the system. If Server B is free, then an arriving Type B customer will be served by Server B, and otherwise will leave the system. Server A takes an exponential rate 2 time to nish a service, Server B takes an exponential rate 1 time to nish a service, and all service times are independent and independent of arrivals. (a (b (c Model the system as a four state Markov chain and write down its generator. Find the stationary distribution of the Markov chain. What is the stationary average number of customers in the system? fa D- 5.1545454 Given a customer is not immediately rejected from the system, what is the average time they spend in the system? (e) What is the long-run proportion of time is there a Type A customer being served by Server B