Design of AQM in supporting TCP based on the well-known AIMD model

In this paper, we investigate how to design AQM with a low-pass filter (average queuing) in supporting TCP based on the well-known AIMD dynamic model sharing a common bottleneck router. Since we formulate the AQM design problem for the given TCP as a state-space model, we get two interesting and important results: (1) we derive PD-type (proportional-derivative) AQM structure is derive in terms of queue length which supports the conjecture in the literature that the AQM RED is not enough to control TCP dynamic behavior, where RED can be classified as P-type AQM structure; (2) we propose a delay-dependent AQM structure to compensate for delays in congestion measure explicitly from the knowledge of RTT, capacity and number of sources, where the previous AQMs RED, REM/PI and AVQ are delay-independent controls. As one trial to obtain stabilizing gains of the proposed structures, we minimize a LQ (linear quadratic) cost of the transients on average-queue length, average-queue length rate, jitter in the rate and the loss probability. Finally, we illustrate the above theoretical results through ns simulations for TCP Reno.