On the Asymptotic Queueing Behavior of General AQM Routers

In this paper, we study the asymptotic behavior of an AQM router serving many AIMD flows. Our model for the AQM router is general and covers most AQM schemes in the current literature. We use a window-based model for the AIMD flows. When the number of AIMD flows is large, we show that the system converges point wise to a limit model. Further, under certain technical conditions, we prove that the system converges uniformly in time and that a steady state exists. We then study the steady state of the system. We show that using appropriate feedback control, the backward accumulation process of net input to the router can be bounded. Under this condition and Gaussian assumption, the queue length distribution can be shown to decay very fast in terms of the buffer size (squared exponential decay). We also provide numerical results to study and support our analytical results.