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.