On the Scalability of Fluid Models of IP Networks Loaded by Long-lived TCP Flows

Fluid models of IP networks have been recently proposed, to break the scalability barrier of traditional performance evaluation approaches, both simulative (e.g., ns-2) and analytical (e.g., queues and Markov chains). Fluid models adopt a deterministic description of the average source and network dynamics through a set of (coupled) ordinary differential equations that are solved numerically, obtaining estimates of the time-dependent behavior of the IP network. The most attractive property of fluid models resides in the fact that they are scalable, i.e., their complexity is independent of the number of TCP flows and of link capacities. In this paper we provide a theoretical investigation of the origins of the scalability of fluid models. We show that the set of differential equations defining the network dynamics under both drop-tail and AQM buffering exhibits a nice invariance property, that allows an equivalence relation to be established among different systems. The validity of the invariance property is verified in realistic network scenarios with ns-2 simulations.