Stability Analyses Of Microscopic Traffic Flow Dynamics

With the rapid development of social economy,traffic problems such as traffic pollution,traffic congestion and traffic accident are increasingly serious due to the growth of vehicle population,so it has drawn great attention.However,how to use scientific theory as a guide to accurately recognize and gradually ease the various traffic problems currently facing has become a hot topic in the field of intelligent transportation.Because the congestion phenomena can be regarded as the instability and the phase transition of a dynamical system,the stability analysis of traffic flow helps explain the cause of traffic congestion,therefore has become the focus of traffic flow theory.In addition,the driver’s response time represents the driver’s sensitivity to external traffic environment incentives,which is regarded as a non-negligible factor in the modeling of traffic flow and stability analysis,and can be used to describe the diffierence of the individual vehicle.Consequently,it is of theoretical and practical significance for congestion mitigation based on the modeling of traffic flow and stability analysis considering the effects of time delays.This thesis first researchs traditional traffic flow.Further,an extended traffic flow model is proposed by taking into account the effects of time delays.Finally,stability analysis of the proposed model is performed.The main work and contributions of this thesis are summarized as follows:1.In this thesis,the Full Velocity Difference(FVD)and Throttle-based Full Velocity Difference(T-FVD)models are introduced,Based on the perturbation method and the root locus method,the linear stability conditions of the model are analyzed.And the kink wave of the model is also obtained using the reductive perturbation method,in order to study the stability of the model from multiple perspectives.2.According to the current traffic system,the influence of driver’s reaction time factor was introduced into the vehicles behavior,and a Throttle-based Full Velocity Difference with Delays(T-FVD-D)model was proposed by considering the effects of time delays.The numerical simulation of dynamic performance of the proposed T-FVD-D model is performed.Results from numerical experiments demonstrate that compared with the previous model,the proposed model can better reflect the difference between the driver’s sensitivity to the distance between vehicles and the sensitivity of the speed difference between vehicles.This is of great significance for further investigation into the evolution of the traffic flow when the driver’s behavioral characteristics are influenced by the leading vehicle.3.In this thesis,the proposed T-FVD-D model is firstly analyzed from the perspective of nonlinearity using the reductive perturbation method,and the linear stability analysis of the proposed T-FVD-D model is performed using the perturbation method,the stability conditions of the model are obtained.Finally,the linear stability analysis of the T-FVD/TFVD-D model is performed from the perspective of system control using the root locus method.The stability conditions of the model are obtained and numerical simulations are performed.The simulation results verify the validity of the root locus method.