Research On Stability And Nonlinear Dynamic Of Internet Congestion Control System

As the Internet constantly expanding the size and type of business, and an increas-ing demand for networking, network congestion control issues become more impor-tant. To develop Internet, network congestion problems must be addressed. Therefore,it's important to study and resolve the congestion control problem in the Internet.The Internet congestion control mechanism can be regarded as a dynamic nonlin-ear feedback system with time delay, which consists of two parts: the TCP congestioncontrol mechanism at hosts and the queue management mechanism at links. These twoparts interact with each other and act as the main ways of solving the congestion prob-lem of the Internet. The Internet congestion control has become a new research hotspotinvolving several disciplines like computer networks, communication, automatic con-trol etc, and draws much attention of researchers. Though many achievements havebeen made in this field,.more work has to be done in the future.This dissertation focuses on the stability analysis and the nonlinear dynamic anal-ysis of the Internet congestion control strategies. Different from many methods de-riving the stability conditions using conservative and approximate analysis, here theexact stability conditions are derived based on rigid stability analysis. The obtainedresults may benefit greatly the modeling of the Internet congestion control systems,the improvement of the Internet congestion control algorithms and the guidance of theparameter design.The main contents and contributions of this dissertation can be summarized asfollows:(1) Based on the stability theory of time delay systems, the stability of theclassic AVQ algorithm with time delay is investigated. The stability conditions are de- rived without conservation. Further, the optimal parameters of the AVQ algorithm aredrived by computing the rightmost root of the characteristic equation. The obtainedparameters can ensure not only stability but also best convergence. Finally, the simula-tion results using Matlab an NS2are given to validate the correctness of the theoreticalresults.(2) Based on stability switch, time-scale conversion and the D-subdivision method,derive the exact necessary and sufficient stability conditions of the Fast TCP conges-tion control algorithm, which is very popular recently and is regarded to be suitable forhigh bandwidth and high delay networks in the future. Besides, the possible complexnonlinear phenomenon when the stability is just lost is analyzed using nonlinear the-ories. It's shown that the Hopf bifurcation will appear and the stable equilibrium maybecomes a limit cycle when the gain parameter is less than a critical value. Besides,the direction of the Hopf bifurcation and the stability and the calculation formula ofperiodic solutions is also determined by the central manifold theorem.(3)By anlyzing the characteristic equation, the local stability and the robust sta-bility of the recently proposed LRC-REC algorithm are studied. The stability condi-tions without conservation are presented, which can provide better guidance for theparameter setting of the algorithm. The way of stability analysis is not limited to thealgorithm, and can be referenced for the stability analysis of other similar algorithmswith time delay.(4) To enhance the system stability and control the harmful bifurcation, based onthe classic delay dual model of the Internet congestion control algorithm, an improvedTDFC (Time-delayed Feedback Control) strategy are proposed. It's shown that thesystem stability region is improved and the Hopf bifurcation can be suppressed ef-fectively. Meanwhile, based on the normal form theory, the direction of bifurcationand the stability of bifurcation periodic solutions along with the calculation formula isdetermined.(5)Based on systematic and rigid stability analysis, the conditions of local stabil-ity and robust stability of the recently proposed HighSpeedTCP/RED algorithm withtime delay are derived. First, the exact stability region in terms of key tuning parame-ters is derived without approximation. Then, a robust way of parameter configuration is proposed. The obtained results can provide better guidance for parameter setting ofthe algorithm.