Convergence, stability and robustness analysis of the OFEX controller for high-speed networks

The OFEX (Optimal and Fully EXplicit) rate controller is able to provide not only the optimal bandwidth allocation but also the fully explicit congestion signal to sources. It exercises link-wise proportional fairness and network-wise max-min fairness, which enables the controller to feed the congestion signal back from the most congested link, instead of using the networkwise proportional fairness which feeds back the congestion signal summed along a flow path. As a result, the OFEX controller overcomes the drawbacks of the relatively explicit controllers that 1) bias the multi-bottlenecked users in terms of their source sending rate and convergence speed, 2) are not adaptable to varying link bandwidth and 3) can potentially incur large queue size upon congestion. In this paper, we first prove that the OFEX controller can converge to its equilibrium at least as fast as a geometric series in a link. Then we analyze the system stability with time delay in a single bottleneck network and show that the OFEX controller can achieve local stability under certain conditions. Besides, the robustness analysis of the OFEX controller shows how the dynamics of link bandwidth may affect the revenue of a link. Finally, with the OPNET modeler, we evaluate the performances of the OFEX controller and verify its effectiveness.