This paper gives a refinement of the results of Hunt and Kurtz on the dynamical behavior of large loss networks. We introduce a Liapounov function technique which, under the limiting regime of Kelly, enables the unique identification of limiting dynamics in many applications. This technique considerably simplifies much previous work in this area. We further apply it to the study of the dynamical behavior of large single-resource loss systems under virtual partitioning, or dynamic trunk reservation, controls. We identify limiting dynamics under the above regime, describing the behavior of the number of calls of each type in the system. We show that all trajectories of these dynamics converge to a single fixed point, which we identify. We also identify limiting stationary behavior, including call acceptance probabilities.
"A Refinement of the Hunt-Kurtz Theory of Large Loss Networks, with an Application to Virtual Partitioning." Ann. Appl. Probab. 12 (1) 1 - 22, February 2002. https://doi.org/10.1214/aoap/1015961154