Constant Estimation for Convergence Rate of Queueing Network With Changing Structure

This paper is a continuation of the previous author’s research on the ergodicity of some models for queuing networks. The set of random graphs and the sequence of matrices describing the changing network structure has been used instead of the fixed graph here. The main results about ergodicity and bounds for rate of convergence to stationary distribution are formulated under more general assumptions on intensity rates. The standard queueing network model [1] has been modified by an assumption about changing structure: each node may be blocked and restored with intensities αi, βi, i= 1,..., m, where m (m < ∞) - the number of nodes. This assumption results in adding some components to standard state space of the network process. The standard approach implies the network matrix to be fixed, the network model considered here is quite different. We denote the state space of the graph transformation process as the set G. Via geometry approach the constant in the convergence inequality is derived explicitly