Singularly Perturbed Discrete-Time Markov Chains

Source abstract

Originating from a wide range of applications in optimization and control of large-scale systems (such as telecommunications, queueing networks, and manufacturing systems), this work is devoted to a class of singularly perturbed discrete-time Markov chains. The states of the Markov chain are naturally decomposable into recurrent and transient classes such that within each class the interactions are strong and among different classes the interactions are weak. Our study focuses on the difference equations representing the probabilityvector, and aims at deriving matched asymptotic expansions of the solutions. Justification and error analysis are also provided. Both time-homogeneous and time-inhomogeneous models are examined.