>I'm still confused about the Markov graph you gave us for the question #1 in HW2. For the "1,2,0" state to "1,1,0" state, you said that the service time should be 2 * mu_slow, but intuitively, since both the two slow servers are occupied, how can the speed of service be doubled? 

The reason is that in state "1,2,0", each of two slow servers is able to service customers at the rate of mu_s, so the "aggregate" customer service rate is therefore 2*mu_s. 

>I am currently stack in the HW1 (problem 1), question 5, about the throughput of the server. On my note, I write down X = sum of Pn * something and I don't have the following. I think I forgot to write it down. Could you please give me a hint?

Do you mean HW#2, problem 1, part 5 about the system throughput? The easiest way is to get the rejection probability, say P_rej, from part 1. Then the system throughput is simply equal to (1-P_rej)*lambda. Another way is to do a probability-weighted sum calculation, i.e., X = sum {P_i * X_i) where P_i is the probability of state i and X_i is the throughput of state i. For example if state i is (1,2,0) then X_i = mu_f + 2 *mu_s because in this state, the fast server and the two slow servers are busy serving their customers so the throughput in this state is simply the sum of their service rates, i.e.,  mu_f + 2 *mu_s. These above two ways of computing X should give you the same answer.


>I have some new trouble when I implement the mm310 server. After I have all the nodes setted, it returns an error message like:"error: unknown keyword: 000 (mm310.sh: line   41)". 


Remove the following two lines:

000 1.0
end

This is because the Markov model is irreducible with no absorbing states so there is no need to specify the initial condition at t=0.

>Do I also need to add "readprobs" in the beginning?

For a steady state analysis on an irreducible Markov model, there is no need to add "readprobs".

Note that if you add readprobs at the beginning of the code, then your original code would work just fine because it expects you to specify the initial condition for performing a transient analysis on an irreducible Markov model.