Analysis of a Fluid Approximation to Flow Control Dynamics

We consider a ow control mechanism that dynamically regulates the rate of data ow into a network based on feedback information about the network state. Such mechanisms have been introduced recently in a variety of networks including the Internet, and have been advocated for future high-speed networks. We rst model the ow control mechanism by a discrete-space stochastic process and deene appropriate performance measures for transient and steady-state regimes. However, the model does not appear to be analytically tractable and we study it through simulation. We then simplify it to a continuous-space de-terministic (or uid) model for which we can easily derive closed-form solutions. We nd the analytical results for the uid model to agree well with the simulation results obtained using the discrete-space model. Both models explicitly consider delay of the feedback information, thus making them relevant for high-speed networks.