Steady state analysis of level dependent quasi-birth-and-death processes with catastrophes

Publication year: 2012
Source: Computers & Operations Research, Volume 39, Issue 2, February 2012, Pages 413-423

Hendrik, Baumann , Werner, Sandmann

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…