Article ID: | iaor20091350 |
Country: | Netherlands |
Volume: | 160 |
Issue: | 1 |
Start Page Number: | 121 |
End Page Number: | 137 |
Publication Date: | Apr 2008 |
Journal: | Annals of Operations Research |
Authors: | Alfa Attahiru Sule, Margolius Barbara Haas |
Keywords: | Matrix-analytic methods, M/G/1 queues, GI/M/1 queues |
We consider the M/G/1 and GI/M/1 types of Markov chains for which their one step transitions depend on the times of the transitions. These types of Markov chains are encountered in several stochastic models, including queueing systems, dams, inventory systems, insurance risk models, etc. We show that for the cases when the time parameters are periodic the systems can be analyzed using some extensions of known results in the matrix-analytic methods literature. We have limited our examples to those relating to queueing systems to allow us a focus. An example application of the model to a real life problem is presented.