Annals of Operations Research
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.
Alfa, Attahiru Sule and Margolius, Barbara Haas, "Two Classes of Time-Inhomogeneous Markov Chains: Analysis of The Periodic Case" (2008). Mathematics Faculty Publications. 245.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10479-007-0300-3