Nonstationary queues: Estimation of the rate of convergence

The paper is devoted to the estimation of the rate of of exponential convergence of nonhomogeneous queues exhibiting different types of ergodicity. The main tool of our study is the method, which was proposed by the second author in the late 1980s and was subsequently extended and developed in different directions in a series of joint papers by the authors of the present paper. The method originated from the idea of Gnedenko and Makarov to employ the logarithmic norm of a matrix to the study of the problem of stability of nonhomogeneous Markov chains. In the present paper we apply the method to a class of Markov queues with a special form of nonhomogenuity that is common in applications.