| Article ID: | iaor20112504 |
| Volume: | 23 |
| Issue: | 1 |
| Start Page Number: | 165 |
| End Page Number: | 171 |
| Publication Date: | Dec 2011 |
| Journal: | INFORMS Journal on Computing |
| Authors: | Van Houdt Benny, van Leeuwaarden Johan S H |
| Keywords: | queues: theory |
In applying matrix‐analytic methods to M/G/1‐type and tree‐like quasi‐birth‐death (QBD) Markov chains, it is crucial to determine the solution to a (set of) nonlinear matrix equation(s). This is usually done via iterative methods. We consider the highly structured subclass of triangular M/G/1‐type and tree‐like QBD Markov chains that allows for an efficient direct solution of the matrix equation.