Modeling And Density Wave Analysis Of The Car-Following Model Considering The Time Effect

The rapid development of social economy has accelerated the process of urbanization.The increasing travel demand and the current basic transportation construction are greatly different,and the contradiction between transportation supply and demand is increasing intensified.The harm caused by traffic congestion to economic and social development and human health is inestimable.Traffic congestion has become an inevitable and difficult problem in urban development.At the same time,it has also brought harm to people’s travel and urban development,and has severely restricted the development of cities.Therefore,the traffic problem has aroused global attention.The research and practice of traffic flow theory y domestic and foreign scholars have brought a new dawn to solve the actual traffic congestion problem.Based on the optimal velocity model(OVM)and full velocity difference model(FVDM)proposed by Bando,this paper considers the actual traffic factors and proposes the corresponding improved model.The stability condition of the new model is derived by linear analysis,and the influence of these factors on the stability of traffic flow is studied.TDGL equation and m Kd V equation are derived by nonlinear analysis to explore the characteristics of density wave propagation.Finally,matlab is used for numerical simulation to verify the correctness of the theoretical results.The main work of this paper is as follows:Firstly,in the actual driving process,the driver often observes the information of the following car and adjusts according to the current information,changing the driving state to achieve a steady state of traffic flow;in actual traffic,the driving behavior of the driver will be affected by the past information.Summarizing the above two points,a car-following model considering backward looking effect and driver memory effect is proposed.The theoretical analysis and numerical simulation results show that the combination of the two factors of backward looking effect and memory effect is helpful to improve the stability of traffic flow and achieve the purpose of alleviating traffic congestion.Secondly,in the intelligent transportation system,the driver uses the current traffic information to adjust the driving behavior at the next moment.Based on the optimized speed difference model,the expected effect is considered,and the influence of the speed difference and the optimized speed difference on the traffic flow within the expected time is studied.Mainly by adjusting the driving speed of the vehicle,the traffic flow reaches a stable state.Theoretical analysis and numerical simulation results show that the expected effect has a positive effect on the stability of traffic flow and effectively relieves traffic congestion.Thirdly,in the actual traffic environment,drivers always need some time to react to the current traffic situation;However,slope is rarely taken into account in the existing traffic models.By combining these two factors,a car following model that considers the driver’s memory effect on the slope is presented.The results show that when in uphill,an increase of slope is conducive to the stability of the traffic flow;when in downhill,an increase of slope is not conducive to the stability of the traffic flow.The driver’s memory effect has a good effect on alleviating traffic congestion within a certain period of time.