this paper---to Phil Hunt for some help with the proof of Theorem 2.2, to Terence Chan, Frank Kelly, Brian Moretta, Gareth Roberts and the referees for helpful conversations and/or suggestions, and to Edward Ionides for assistance with constructing the simulations. References

We study the limit behaviour of controlled loss networks as capacity and offered traffic are allowed to increase in proportion, reviewing and extending recent work based on the functional law of large numbers of Hunt and Kurtz. We consider in detail single and two-resource networks. 1 Introduction In this paper we study large loss networks in which the offered traffic is subject to acceptance controls. We review recent work of Hunt and Kurtz (1994), who established rigorous results for the asymptotic dynamics of such networks as capacity and offered traffic are allowed to increase in proportion, and we relate these results to asymptotic equilibrium behaviour. We further study the detailed behaviour of networks with at most two resources, extending results of Bean et al. (1994b, 1995), and giving some additional results. The asymptotic results considered here have important applications to the control of modern communications networks, which are typically large and which may simultane...