) There are two types of customers. Type 1 and 2 customers arrive in accordance with independent Poisson processes with respective rate λ1 and λ2. There are two servers. A type 1 arrival will enter service with server 1 if that server is free; if server 1 is busy and server 2 is free, then the type 1 arrival will enter service with server 2. If both servers are busy, then the type 1 arrival will go away. A type 2 customer can only be served by server 2; if server 2 is free when a type 2 customer arrives, then the customer enters service with that server. If server 2 is busy when a type 2 arrives, then that customer goes away. Once a customer is served by either server, he departs the system. Service times at server i are exponential with rate µi , i = 1, 2. Suppose we want to find the average number of customers in the system. (a) Formulate the problem as a continuous-time Markov chain. Define the states of the 1 process, and set up the balance equations (Do not attempt to solve them) In terms of the long-run probabilities, what is (b) the average number of customers in the system? (c) the average time a customer spends in the system?