Intensity Matrix

Hi, sorry to keep harassing everyone like this, but I'm stuck again. It's the same setup as the last question, but this time it's asking about the intensity matrix.

So again, customers arrive in pairs in a Poisson stream with intensity lambda: There is waiting room for one customer. Service time is exponentially distributed with parameter mu. If the server is busy and the waiting room is empty when a pair arrives, one person stays and the other person leaves. The state space corresponding to the number of customers is {0,1,2}.

What I've figured out for the intensity matrix so far is

|lamda 0 lamda|
|mu ? ? |
|0 mu -mu |

It's the entries on the second row that's got me buggered. Can someone explain how to get those entries please?


TS Contributor
Hi again :)

-\lambda & 0 & \lambda \\
\mu & -(\lambda+\mu) & \lambda \\
0 & \mu & -\mu

The diagonal entries should "match" with the parameters (negative) of the corresponding
sojourn time, and the other entries (i, j) are the parameters of the transition time
from state i to state j