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We study the parametric perturbation of Markov chains with denumerable state spaces. We consider both regular and singular perturbations. By the latter we mean that transition probabilities of a Markov chain, with several ergodic classes, are perturbed such that (rare) transitions among the different ergodic classes of the unperturbed chain are allowed. Singularly perturbed Markov chains have been studied in the literature under more restrictive assumptions such as strong recurrence ergodicity or Doeblin conditions. We relax these conditions so that our results can be applied to queueing models (where the conditions mentioned above typically fail to hold). Assuming v-geometric ergodicity, we are able to explicitly express the steady-state distribution of the perturbed Markov chain as a Taylor series in the perturbation parameter. We apply our results to quasi-birth-and- death processes and queueing models. [ABSTRACT FROM AUTHOR]

Examines the assignment of packets to M parallel heterogenous servers with no buffers. Problem formulation; Structural results; Examples of arrival processes.

Investigates the stability of non-stationary stochastic processes, arising typically in applications of control, using Borovkov's renovation theory. Stochastic recursive sequences; Construction of probability space stochastic processes; Types of coupling; Presence of renovating events.