Study On Dynamics Of Congestion Control Mechanism Based On Active Queue Management

Stability of the AQM algorithm plays an important role in congestion control, i.e., the rate of information flow through its links should tend towards an equilibrium, preferably close to link capacity, rather than continually oscillating between the having bandwidth spare and the being completely overloaded. However, in the case of higher bandwidth utility and smaller queueing delay, there are some urgent problems to be solved, which are how to keep the stability of congestion control model, and how to derive some simple and sufficient stability conditions. In addition, how does TCP/AQM system evolve when the congestion control system loses its stability? This field also begins to draw much attention from researchers. These are also just the motivations of this thesis. The main contributions of this thesis are listed as follows:①A novel exponential RED model with heterogeneous delays is introduced, and several stability criteria for the model in frequency domain are derived.By analyzing the essential feature of the AIMD congestion avoidance mechanism and introducing queueing delay and time-varying delay, we develop a novel congestion control model in accordance with the characters of the real network operation. By use of automatic feedback control theory and the Generalized Nyquist theory, we derive and obtain the sufficient stability condition in frequency domain in the case of the round trip delay is dependent and independent of forward delay, respectively. It is shown that the stability condition is mainly dependent on the equilibrium round trip delay and the equilibrium drop probability. Through simulation and comparison with original exponential RED, the present stability criteria are effective to maintain both local stability and good performance, such as high utilization and low queue delay.②Several existence conditions of Hopf bifurcation in a novel exponential RED model with communication delay are estiblished, and several explicit formulae for determining the direction of the Hopf bifurcation and stability of the periodic orbits are presented.We investigate Hopf bifurcation in the exponential RED model with communication delay by analyzing the distributed ranges of eigenvalues of characteristic equation of the corresponding linearized equations. Using communication delay as the bifurcation parameter, linear stability criteria dependent on communication delay are also been derived, and furthermore, we find that the Hopf bifurcation occurs when the communication delay passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Finally, simulation results are verified and demonstrated the correctness of the theoretical results.③A dynamic delayed state feedback controller for Hopf bifurcation in the exponential RED model is developed. Furthermore, it is shown that the controller can delay the onset of Hopf bifurcation.The dynamic delayed state feedback controller is achieved by incorporating filters called"washout filters"into the controller architecture. With this controller, one can increase the critical value of the communication delay, and thus guarantee a stationary data sending rate for larger delay. Furthermore, the explicit formulae determining the stability and the direction of periodic solutions bifurcating from the equilibrium are obtained by applying Hassard et al's approaches. Finally, numerical simulation results are presented to show that the dynamic delayed feedback controller is efficient in controlling Hopf bifurcation.④Several LMI-based novel stability criteria of the primal-dual algorithm with heterogenous communication delays are proposed.An appropriate type of Lyapunov functional is used to investigate the problem of asymptotic stability in the primal-dual algorithm with heterogeneous communication delays. Some LMI-based novel delay-dependent stability criteria are given by use of the free weighting matrices, which can overcome the conservativeness of method involving a fixed model transformation. Simulation results show that the stability criteria proposed in this thesis are less conservative in the sense that the larger range of control gains and communication delays can be accommodated.⑤A second-order primal-dual algorithm with heterogenous interval time-varying communication delays is investigated, and several delay-dependent stability criteria with less conservativeness are proposed.A new approach is proposed to investigate the asymptotic stability of the second-order primal-dual algorithm with heterogeneous interval time-varying delays, where a new classes of Lyapunov-Krasoveskii functionals are constructed by using the free weighting matrix technique and the delay interval division method as well as considering the interactions between the delay ranges. It is shown that the obtained delay-dependent stability criteria are less conservative than the existing results. Finally, numerical examples are given to demonstrate the effectiveness and merits of the proposed method.⑥Several existence conditions of Hopf bifurcation and resonant codimension-two bifurcation in primal-dual algorithm with heterogeneous delays are obtained.The local stability of the equilibrium solution of primal-dual algorithm with heterogeneous delays is investigated by analyzing the corresponding transcendental characteristic equation of its linearized equation. Some general stability criteria involving the delays and the system parameters are derived by generalized Nyquist criteria. Furthermore, by choosing one of the delays as a bifurcation parameter, it is shown that when the delays exceed a critical value a limit cycle emerges via a Hopf bifurcation. Resonant codimension-two bifurcation is also found in this model. Simulation results verify and demonstrate the correctness of the theoretical results.