Sizing Internet Router Buffers, Active Queue Management, and the Lur'e Problem

In this paper we consider the design of control strategies for implementation in a recently proposed active queue management (AQM) scheme, active drop-tail (ADT) (Stanojevic et al., 2006), The basic idea underlying ADT is to adjust the queue length of a drop-tail buffer to regulate the utilization of a link carrying Internet traffic in order to reduce queuing delays in the network. A basic problem in the design of ADT is to design appropriate strategies to regulate the target utilization using the buffer queue as a control input. This problem is challenging due to the stochastic and time-varying nature of communication networks. Our contribution in this paper is to relate the design of control strategies for this AQM to the classical Lur'e problem. Our formulation naturally accounts for the time-variations and randomness inherent in communication networks, and enables us to design AQMs with guaranteed convergence (under mild and realistic assumptions). Packet level simulations are given to demonstrate the efficacy of our design methodology