Bounds estimation and practical stability of AIMD/RED systems with time delays

The Additive Increase and Multiplicative Decrease (AIMD) congestion control algorithm of TCP deployed in the end systems and the Random Early Detection (RED) queue management scheme deployed in the intermediate systems contribute to Internet stability and integrity. Previous research based on the fluid-flow model analysis indicated that, with feedback delays, the TCP/RED system may not be asymptotically stable when the time delays or the bottleneck link capacity becomes large [3]. However, as long as the system operates near its desired equilibrium, small oscillations around the equilibrium are acceptable, and the network performance (in terms of efficiency, loss rate, and delay) is still satisfactory. In this paper, we study the practical stability of AIMD/RED system with feedback delays and with both homogeneous and heterogeneous flows. We obtain theoretical bounds of the flow window size and the RED queue length, as functions of the number of flows, link capacity, RED queue parameters, and AIMD parameters. Numerical results with Matlab and simulation results with NS-2 are given to validate the correctness and demonstrate the tightness of the derived bounds. The analytical and simulation results provide important insights on which system parameters contribute to higher system oscillations and how to set parameters (such as buffer size and queue management parameters) to ensure system efficiency with bounded delay and loss. Our results can also help to predict and control the system performance for Internet with higher data rate links multiplexed with heterogeneous flows with different parameters.