THE SHORTEST QUEUE MODEL AND THE MEAN-FIELD APPROACH TO TIME-SCALE QUEUEING SYSTEMS WITH A SMALL PARAMETER

In this paper we apply the Dobrushin mean-field approach for evolution dynamics analysis of the time-scale queueing systems (TSQS) with the shortest queue policy (SQP). The evolution dynamics TSQS can be demonstrated through the use of the functions that can be found by solving a system of differential equations infinite degree. We consider the singularly perturbed Cauchy problem for such system of differential equations with a small parameter. We apply the the Dobrushin mean-field approach for this singularly perturbed Cauchy problem and investigate the finite order system of differential equations with with a partial differential equation of the first order. We use a high-order non-uniform grid scheme for numerical solving of the singularly perturbed Cauchy problem. Using a numerical scheme show good convergence of solutions of this Cauchy problem when a small parameter tend to zero.