A degenerate central limit theorem for single resource loss systems
This paper deals with a loss network at which \(R\) types of calls arrive and require only one link. The sojourn times in the network are exponentially distributed. Due to the intrinsic complexity of this type of networks, the authors assume a scaling parameter (introduced by Kelly) to get the asymptotic loss probabilities and limiting results. It is known that the scaled number of customers of type \(r\) in the network converges to a fluid limit. The aim of the paper is to investigate the case when the fluid limit is on the boundary of the domain. In this case, the perturbation around the fluid limit is shown to be a degenerate \((R-1)\)-dimensional diffusion.
scientific article; zbMATH DE number 2005168