The Nonlinear Density Wave Equations On City Traffic Flow

With the rapid development of urbanization process, public transport facilities have beenunder stress. Traffic accident and pedestrian jam occur frequently in actual public facilities.Thereflore, traffic flow study has catched great attention of scholars due to the increasing needto reduce hidden trouble and public safety risk. In this thesis, the efect of complex factors ontraffic flow is studied. In order to provide theoretical advice about traffic programme、publicsecurity and road construction, the nonlinear density wave equations on modifed traffic flowmodels are investigated by theoretical analysis and numerical simulation.The thesis is arranged as follows:1. The TDGL equation flor car-following model with consideration of traffic interruptionprobabilityBased on the optimal velocity car-following model, Tang tieqiao investigated the efect oftraffic interruption probability on traffic flow. The reductive perturbation method is taken toderive the time-dependent Ginzburg Landau (TDGL) equation to describe the traffic flow nearthe critical point based on the model proposed by Tang. Moreover, the coexisting curve and thespinodal line are obtained by the frst and second derivatives of the thermodynamic potential,respectively. The connection between reaction coefficients、traffic interruption probability andcritical sensitivity is studied. We also discussed the reasonable range of reaction coefficients.2. A bidirectional pedestrian flow model with the efect of friction parameterThe two dimensional traffic lattice hydromechanics model is extended to pedestrian flow.By introducing the friction parameter, the movement of pedestrian flow is studied when theaverage friction on bidirectional pedestrian is in unequilibrium. Linear stability analysis is usedto obtain the stability condition. The modifed Korteweg-de Vries (mKdV) equation and TDGLequation are deduced by means of the reductive perturbation method respectively. The connec-tion between the two equations is discussed. Further, the infuence of the friction parametersupon pedestrian flow has been discussed by simulation.3. A lattice model flor bidirectional pedestrian flow on gradient roadA new lattice model flor bidirectional pedestrian flow on gradient road is introduced basedon the modifed optimal velocity. We discussed the stability condition by using linear stabilitytheory. The nonlinear analysis method is employed to derive the mKdV equation, and thespace of pedestrian flow is divided into three regions: the stable region, the metastable regionand the unstable region respectively. Furthermore, the TDGL equation is deduced and solved through the reductive perturbation method. Finally, we presented measures to improve crowdssafe evacuation process from assembly occupancies with lots of stairs.