【題組】

(b) Consider a two-server system in which customer inter-arrival times are exponentiallydistributed with rate λ at server 1. After being served by server 1, customers then join thequeue for server 2. We assume that there is infinite waiting space at both servers. Eachserver serves one customer at a time with server i taking an exponential time with rate μifor a service, i = 1,2. To analyze this system, we need to keep track of the number ofcustomers at server 1 and the number of customers at server 2. Let define the state by pair(n,m)- meaning that there are n customers at server 1 and m customers at server 2 and

denote the probability of being in that state.
(b-1) (10 points) What are the balance equations for this system?
(b-2) (S points) If the number of customers at server 1 and server 2 were independentrandom variables, what would be the expression for 

 ?
 (b-3) (S points) Verify that your solution satisfies the balance equations from (b-1).