3.10 Chapter summary

In this chapter, we derived the basic matrix analytic results for the solution of M/G/1-type, GI/M/1-type, and QBD processes. Via simple examples and from first principles, we illustrated why the solution of QBD and GI/M/1-type processes is simpler than the solution of M/G/1-type processes. We presented the classic solution techniques for such processes, the elegant matrix-geometric and the matrix-analytic methods. We gave an overview of the recent advances in matrix-analytic methodology, concentrating on the most efficient algorithms for computation of $G$ and ${\mathbf{R}}$ and the FFT Ramamswami's formula. We direct the interested reader in the two books of Neuts [67,69] for further details, as well as to the book of Latouche and Ramaswami [47].