Article ID: | iaor20116260 |
Volume: | 39 |
Issue: | 2 |
Start Page Number: | 413 |
End Page Number: | 423 |
Publication Date: | Feb 2012 |
Journal: | Computers and Operations Research |
Authors: | Baumann Hendrik, Sandmann Werner |
Keywords: | matrices, queues: theory, simulation: applications |
Quasi‐birth‐and‐death processes, that is multi‐dimensional Markov chains with block tridiagonal transition probability or generator matrices, are appropriate models for various types of queueing systems, amongst many other population dynamics. We consider continuous‐time level dependent quasi‐birth‐and‐death processes (LDQBDs) extended by catastrophes, which means that the transition rates are allowed to depend on the process level and additionally in each state the level component may drop to zero such that the generator matrix deviates from the block tridiagonal form in that the first block column is allowed to be completely occupied. A matrix analytic algorithm (MAA) for computing the stationary distribution of such processes is introduced that extends and generalizes similar algorithms for LDQBDs without catastrophes. The algorithm is applied in order to analyze M/M/