Stability And Solitary Waves Of The Optimal Velocity Model With Intelligent Speed Limit Information And Multiple Delays

Nowadays,with the continuous development and expansion of urban construction,urban population and urban scale,the number of road vehicles increases also day by day,which makes the demand for urban traffic increase rapidly and results in four problems such as traffic congestion,traffic pollution,traffic accidents and energy consumption.Traffic congestion is an overloaded phenomenon of traffic flow,which is essentially the solitary wave problem of traffic flow model.The rapid development of advanced intelligent transportation system(ITS for short)is changing the way of traffic control and management by providing traffic information and has become means to solve the problem of severe traffic congestion.In this dissertation,based on the classical optimal velocity model,considering that the driver is informed of the intelligent speed limit information in advance,and there are multiple response delays affecting the traffic flow due to various factors,three new vehicle following models are presented,and the linear stability and nonlinear isolated modes of the models are analyzed.The specific work is as follows:Firstly,an optimal velocity model is presented,which considers the driver to know the speed limit information of intelligent prompt in advance.The stability conditions of the model are obtained by linear stability analysis.The results show that the stable area of traffic flow is expanded obviously in getting the speed limit information in advance time.Furthermore,under three cases of accurate speed limit information,the accuracy of the stability condition is analyzed.Density wave equations of the stable region,metastable region and unstable region-Burgers equation,KdV equation and mKdV equation are derived by reduction perturbation method.Through their solitary waves or kink and anti-kink solutions,it is suggested that the speed limit information can be obtained in advance to solve the traffic jam problem.Secondly,an optimal velocity model is presented,which considers the driver to know the speed limit information of intelligent prompt in advance,and the time headway and relative speed.The stability condition of the model is obtained and the influence of the different value with double delay on the expansion of the stable region of traffic flow is analyzed.The Burgers equation,KdV equation and mKdV equation are derived in the stable region,metastable region and unstable regionrespectively.The effect of the difference of double time delay on traffic jam is analyzed by them and anti-kink solutions.Finally,an optimal velocity model with three response time delays is presented,which considers the driver to know the speed limit information of intelligent prompt in advance,the time headway,the relative speed and the speed limit information to be known in advance.The stability condition of the model is obtained and the influence of the difference between three time delays on the expansion of the traffic flow stability region is analyzed.The Burgers equation,KdV equation and mKdV equation are derived in the stable region,metastable region and unstable region respectively.The effects of three time-delay differences in traffic jam are analyzed by their solitary waves or kink and anti-kink solutions.