On Modeling Feedback Congestion Control Mechanism of TCP using Fluid Flow Approximation and Queueing Theory

The Internet uses a window-based congestion control mechanism in TCP (Transmission Control Protocol). In the literature, there have been a great number of analytical studies on TCP. Most of those studies have focused on the statistical behavior of TCP by assuming a constant packet loss probability in the network. However, the packet loss probability, in reality, changes according to packet transmission rates from TCP connections. In this paper, we explicitly model the interaction between the congestion control mechanism of TCP and the network as a feedback system. Namely, we model the congestion control mechanism of TCP as a dynamic system, where the input to the system is the packet loss probability and the output is the window size. Inversely, we model the network as a dynamic system, where the input is the window size and the output is the packet loss probability. The network is modeled by a M/M/1/m queueing system by assuming an existence of a single bottleneck link. Using our analytic model, the transient behavior of TCP connections is quantitatively evaluated with several numerical examples.