I have 2 dimensional markov chain and I want to calculate steady state probabilities and then basic performance measurements such as expected number of customers, expected waiting time, etc. You can check the transition rate diagram link below:
http://tinypic.com/view.php?pic=2n063dd&s=8
As I search for solution methods, matrix geometric and spectral expansion methods appear. I tried matrix geometric method, however since my Markov chain is not repetitive, it did not work.
I read some paper (e.g. Spectral expansion solution for a class of Markov models: application and comparison with the matrix-geometric method), but I could not figure out how to create matrices and what is the steady state probabilities.
- Does spectral expansion method require "repetitive process" as matrix geometric method does? If no, how to apply to my problem?
- Are there any other methods to compute?
Thanks for all your help!
Ali