On strong ergodicity for nonhomogeneous continuous-time Markov chains

Let X(t) be a nonhomogeneous continuous-time Markov chain. Suppose that the intensity matrices of X(t) and some weakly or strongly ergodic Markov chain (t) are close. Some sufficient conditions for weak and strong ergodicity of X(t) are given and estimates of the rate of convergence are proved. Queue-length for a birth and death process in the case of asymptotically proportional intensities is considered as an example.