Consider the continuous time Markov process that represents the number of users in the system. So state i means that there are i users in the system. It has transition rates q01 = , q10 = , q12 = and q20 = .

(a) Write the transition diagram (This is the graph or net with the transition rates on it).

(b) Write down the transition rate matrix Q. (Hint: Use the provided values and complete what is missing).

(c) Find the equilibrium distribution (i.e., the limiting probabilities P0, P1 and P2).

(d) Find the average number of users in the system (Hint: Note that it is the expected value of a discrete r.v. with values 0, 1 and 2 and probabilities P0, P1 and P2 respectively).