“…In the present work, we use the concepts of Lyapunov functions and ν-geometric ergodicity ( [9], [16], [21], [27], [28]) that allow us to treat the cases that satisfy neither Doeblin conditions nor the strong ergodicity condition. Works on the application of singularly perturbed Markov chains to quasibirth-and-death models, queueing models and reliability theory include [1], [2], [7], [11], [20], [24]. The singular perturbation techniques allow us to solve models with significantly larger state space than in the case of direct application of standard tools.…”