On monotonicity of some classes of Markov chains

The authors define a relation of partial order for Markov chains and study conditions of monotonicity for some classes of continuous-time Markov processes. The corresponding theorems of monotonicity are formulated. The authors describe in detail the classes of processes which satisfy conditions of monotonicity. There are a lot of applications of Markov chains with interval intensities that is why the authors consider it. The monotonicity conditions obtained in this paper make it possible to advance in some way in the study of Markov processes with interval intensities. Namely, in the present paper, the authors consider as an example a queuing system $M_t/M_t/S/S$ with interval coefficients. The results obtained are confirmed by a computational experiment and illustrated by the corresponding graphs of the limiting characteristics.