Periodic Solutions Of Two State-dependent Delayed Network Congestion Control Models Based On HB-AFT Method

State-dependent delayed system is a more practical research object in nature and human society.Its dynamic behavior is a hot issue and difficult problem in current research.In the network congestion control model,the round trip delay depends on the state and the periodic oscillation will lead to the decrease of link utilization and the synchronization service of TCP flow,which will lead to the decline of the end to end service quality.Wireless networks are widely used at present.FAST TCP networks are suitable for large broadband and long distance networks and have the excellent delayed dynamic performance.Therefore,it is of great practical significance to study these two network congestion control models.In order to grasp the dynamic rules of network congestion control models and improve network performances,under the support of the National Natural Science Foundation(NO.11372282)of China,the approximate analytical expressions of periodic oscillations of the more practical state-dependent round trip delayed wireless congestion control model and the state-dependent round trip delayed FAST TCP network congestion control model are investigated in this thesis.Because of the complexity of the models,it is very difficult to investigate the problem by the traditional analytical method.The approximate solutions are obtained by the semi analytic and semi numerical harmonic balance and altering frequency/time domain(HB-AFT)method in this thesis,in which the AFT method can avoid complicated calculations of the series expansion and the truncations,integrations of the complex nonlinear term in the differential equation.It is very simple and effective to solve steady harmonic response of nonlinear system.The main processes of HB-AFT method is as follows.Firstly,process of harmonic balance is carried out.Then,according to the harmonic balance,the algebraic equations that determining the relationships of each order harmonic coefficients are obtained.The unknown variables are established by AFT process.Finally,Newton-Raphson iteration is employed to solve the equations,the each order harmonic coefficients of periodic solutions,that is,the approximate solutions of periodic solutions are obtained.The numerical comparisons by Winpp display that the method is effective and correct for the state dependent round trip delayed network congestion control model.The innovation in this thesis is that the HB-AFT method is employed to obtain the approximate expressions of the periodic solutions of two state-dependent delayed differential equations for the first time.By adjusting the parameters,the periodic oscillations in the network can be avoided and the stability and performance of the networks can be improved.