English summary
We consider an open network with $M$ nodes and $K$ customer types. The service discipline used is the absolute priority discipline. We study how stability and performance depend on the parameters of the system. In addition, we will give a qualitative analysis of extremal situations. A situation is called extremal if for some reason there are long queues of customers at some of the nodes. We are interested in the time necessary for the network to stabilise from an extremal situation. We discuss possible settings of optimisation problems. For the analysis of a network with a large number of customers we use a new method of scalingand reduction to a dynamical system. This method is based on the ideology of induced chains and the second vector field.
Abstracts in Russian and French are also available.