Practical Stability and Bounds of Heterogeneous AIMD/RED System with Time Delay

The Additive Increase and Multiplicative Decrease (AIMD) congestion control algorithm of TCP protocol 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 an AIMD/RED system may not be asymptotically stable when the feedback delays or the link capacity becomes large [3]. However, as long as the system operates near its desired equilibrium, small oscillations are acceptable and the network performance is still satisfactory. Deriving the bounds of these oscillations for the heterogeneous AIMD/RED system with time delays is non-trivial. In this paper, we study the practical stability of the AIMD/RED system with heterogeneous flows and feedback delays, and obtain theoretical bounds of the AIMD flow window size and the RED queue length, as functions of 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 of the theorems and demonstrate the tightness of the derived bounds. The analytical and simulation results provide important insights on which system parameters contribute to higher oscillations of the system and how to set system parameters to ensure system efficiency with bounded delay and loss.