Occupation measures of singularly perturbed Markov chains with absorbing states
The authors continue their study of the asymptotic properties of occupation measures for singularly perturbed Markov chains with inclusion of absorbing states which has applications in production planning, queueing networks and system reliability [see \textit{G. G. Yin} and \textit{Q. Zhang}, Continuous-time Markov chains and applications: A singular perturbation approach (1998; Zbl 0896.60039)]. They separate the states in accordance with their rates of changes, regroup them with like or similar transition rates, and introduce a small parameter \(\varepsilon >0\) resulting in a singularly perturbed system. Such an approach leads to insights of the probabilistic structure of the underlying system, which are important to the further study and design of control policies for operating these systems. They study unscaled occupation measures, and derive a mean-square estimate on a sequence of occupation measures centered around their limit distribution and obtain the convergence of the aggregate process. Although the aggregated process itself may be non-Markovian, its weak limit is a Markov chain with much smaller state space. Moreover, a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.
scientific article; zbMATH DE number 1471204
scientific article