Fluid-Based Modeling of TCP BBR Congestion Control Mechanism

TCP BBR (Bottleneck Bandwidth and Round-trip Propagation Time) has been proposed as an efficient congestion control mechanism that manages network congestion based on end-to-end measurements of bottleneck link bandwidth and round-trip time (RTT), rather than relying on the detection of packet loss events, as used by loss-based TCPs such as TCP CUBIC. Unlike loss-based congestion control mechanisms, TCP BBR estimates the available bandwidth of the bottleneck router and the network's round-trip propagation delay to adjust its congestion window, aiming to achieve the optimal operating point of the network. Numerous studies have examined the performance of TCP BBR through experiments and simulations, but analytical studies primarily focused on modeling its characteristics and behaviors during startup or steady-state phases, falling short in analyzing its dynamic behavior under changing network conditions. This paper presents a discrete-time fluid model to mathematically describe the dynamic interaction between TCP BBR flows and intermediate routers in an arbitrary network topology. The model captures the relationship among the time evolution of TCP BBR congestion window, bottleneck link bandwidth and RTT measurements, and packet queuing in routers, at the granularity of round-trip times. Through numerical examples, we demonstrate the effectiveness of our fluid model for TCP BBR and reveal optimal pacing gain settings analytically.