Nesterov

pp. 250-261

pp. 206-216

This article deals with the method to determine average residence time, average waiting time and utilization in nodes of multiclass closed queuing system with non-preemptive priorities and general distribution function of service time Mr|GIr|1||N. The method uses the embedded Markov’s chain-based design, which is linked to the regenerations points i.e. moments when the service time is over. The formula for unknown elements of transition matrix for this chain is proved. The solution for probability distribution of this chain is proved. The next step is to define the states probability of closed queuing system in a stationary mode on the basis of system of equations of global balance for such system. The formula to determine an average residence time, average waiting time and utilization of server facility is proved. Generally, the proposed method is very efficient.

This article deals with the method to estimate the average residence time in nodes of closed queuing networks with priorities and a wide range of conservative disciplines to be served. The method is based on a decomposition of entire closed queuing network into a set of simple basic queuing systems such as M|GI|m|N for each node. The unknown average residence times in the network nodes are interrelated through a system of nonlinear equations. The fact that there is a solution of this system has been proved. An iterative procedure based on Newton-Kantorovich method is proposed for finding the solution of such system. This procedure provides fast convergence to solution. Today possibilities of proposed method are limited by known analytical solutions for simple basic queuing systems of M|GI|m|N type.