Bounds estimation and practical stability of AIMD/RED systems with time delays
Congestion control for wireless networks is much more challenging than that for wired networks, due to the limited wireless spectrum and severe impairments of wireless medium which suffer from time-varying fading, shadowing, interference, etc. Although the stability of the Internet using TCP congestion control and active queue management (AQM) schemes has been extensively investigated, effective congestion control for wireless networks is a pressing, open issue. Considering the dynamics of wireless links, in this paper, we investigate the stability of TCP/AQM wireless networks with feedback delays, which is formulated as a delay Markov jump linear system (DMJLS). First, a dynamic model based on the DMJLS for TCP/AQM wireless networks is established. Second, a novel stochastic stability analysis for autonomous time-delay systems with a cost function is presented. Delay-dependent linear matrix inequalities (LMIs) criteria for the stochastic stability conditions are obtained. It is noteworthy that this is the first time conditions for the stochastic stability have been derived subject to the linear quadratic (LQ) control strategy, and packet drop probability as the control input under the DMJLS is calculated. In addition, for practical systems where real-time tracking of states is infeasible or costly, the mode-independent congestion control is also investigated. The robustness of random early detection (RED) in wireless environment is proved. Numerical results are given to validate the analytical results which provide important insights for wireless network congestion control and resource management.