Fan, Xingzhe (Univ. of Miami), Arcak, Murat (Rensselaer Pol. Inst.), Kalyanaraman, Shivkumar (Rensselaer Pol. Inst.), Chan, Yee Sin (Univ. of Miami)

Delay Robustness and AQM in Networks

Scheduled for presentation during the Mini-Symposium "Control and Estimation in Networks" (TuA08), Tuesday, July 25, 2006, 11:15−11:40, Room I

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 19, 2024

Abstract

This paper studies the stability problem of a network fluid model with transmission and queuing delays in the forward and backward channels. We present a novel small gain approach to prove global asymptotic stability for a network with arbitrary time delays and network routing matrix. Specifically, we use a logarithmic state transformation suggested recently in the literature, and establish a linear input-to-state gain for this transformed system. With the new state variables, the gain of the routing matrix is unity and, thus, the stability condition is scalable and independent of routing. Unlike the previously reported results that employ the logarithmic transformation, we give a simple small-gain interpretation for the delay robustness of the networks. We demonstrate that this small-gain technique is generally applicable for the design of a new class of edge-based active queue management (AQM) algorithms where zero steady queuing delay is achieved. We also show that it can be generalized to the study of other networks, such as the uplink power control problem in CDMA systems.