On three methods for bounding the rate of convergence for some continuous-time Markov chains - Zeifman, Alexander; Satin, Yacov; Kryukova, Anastasia; Razumchik, Rostislav; Kiseleva, Ksenia; Shilova, Galina (Zielona Góra: Uniwersytet Zielonogórski)
Consideration is given to three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is particularly well suited to describe evolutions of the total number of customers in (in)homogeneous M/M/S queueing systems with possibly state-dependent arrival and service intensities, batch arrivals and services.
Keywords: inhomogeneous continuous-time Markov chains; weak ergodicity; Lyapunov functions; differential inequalities; forward Kolmogorov system