Deterministic fluid models of congestion control in high-speed networks

Congestion control algorithms, such as TCP or the closely-related additive increase-multiplicative decrease algorithms, are extremely difficult to simulate on a large scale. The reasons for this include the complexity of the actual implementation of the algorithm and the randomness introduced in the packet arrival and service processes due to many factors such as arrivals and departures of sources and uncontrollable short flows in the network. To make the simulation tractable, often deterministic fluid approximations of these algorithms are used. These fluid approximations are in the form of deterministic delay differential equations. In this paper, we ignore the complexity introduced by the window-based implementation of such algorithms and focus on the randomness in the network. We justify the use of deterministic models for proportionally-fair congestion controllers under a limiting regime where the number of sources in a network is large.