We study the behavior of large loss networks in which the offered traffic is subject to acceptance controls. Hunt and Kurtz proved a functional law of large numbers for the dynamics of such networks, as capacity and offered traffic are allowed to increase in proportion. However, limiting dynamics were not in general uniquely identified. We establish further results identifying these dynamics under given conditions. We also investigate the existence of fixed points for these dynamics and relate them to limiting equilibrium behavior, permitting the investigation of common modelling assumptions. We study in detail single- and two-resource networks and we give an example of bistability for the former.
"Dynamic and equilibrium behavior of controlled loss networks." Ann. Appl. Probab. 7 (4) 873 - 885, November 1997. https://doi.org/10.1214/aoap/1043862415