Towards Stability Analysis of Data Transport Mechanisms: A Fluid Model and Its Applications

The Transmission Control Protocol (TCP) utilizes a congestion avoidance and control mechanism as a preventive measure against congestive collapse and as an adaptive measure in the presence of changing network conditions. The set of available congestion control algorithms is diverse, and while many have been studied from empirical and simulation perspectives, there is a notable lack of analytical work for some variants. To gain more insight into the dynamics of these algorithms, we: (1) propose a general modeling scheme consisting of a set of functional differential equations of retarded type (RFDEs) and of the congestion window as a function of time; (2) apply this scheme to TCP Reno and demonstrate its equivalence to a previous, well known model for TCP Reno; (3) show applications of the new framework to the widely-deployed congestion control algorithm TCP CUBIC, for which analytical models are few and limited; as well as to H-TCP, another high-speed congestion control algorithm; and (4) validate the model using simulations. Our modeling framework yields a fluid model for window- or rate-based congestion control variants. From a theoretical analysis of this model with TCP CUBIC, we discover that CUBIC is locally uniformly asymptotically stable - a property of the algorithm previously unknown. Through further analysis, we derive a sufficient condition for H-TCP's stability, but observe via a numerical analysis and simulations that H-TCP rarely converges to an equilibrium and is usually not asymptotically stable in practical high-speed settings.