Study On The Traffic Flow Modeling And Its Characteristics Based On The Comprehensive Effect Of Ahead-Backward Vehicles

With the increasing of traffic flow, the interaction of the individuals becomes moreobvious especially vehicles in the traffic system. This shows the state of the followingcar will be impacted by driving state of the ahead-backward vehicles, the followingtheory which researchs the interaction of the individuals has obtained manyachievements from the micro level, however the following theory which considersmultisource information under the interaction of ahead-backward vehicles is less.Therefore, there can more in-depth analyze the evolution characteristics of traffic flowunder the interaction of multisource information from ahead and backward vehicles,provide a important method to reveal the evolution microscopic nature properties ofactual traffic flow.Since the existing following theory don’t study the joint action of ahead-backwardvehicles. The paper considers the effect of the ahead car, the backward car and theircoaction respectively, to present the corresponding new model, and makes use oftheoretical analysis and numerical simulation analysis to research nonlinearcharacteristics, the stability, and the evolution rule of traffic flow. The concrete work ofthe paper is as follows:①Based on the full velocity difference model, considering the effect ofinformation about the optimal velocity difference of the two non-neighboring leadingcars to the following car, the optimal velocity difference of the two non-neighboringleading cars model is presented.When the ahead cars’ velocity achieves the optimal velocity, the driver shouldconsider the variation of the optimal velocity difference of the two non-neighboring cars,and takes corresponding measures of speeding up or slowing down to achieve theoptimal velocity in the operation process. Based on this analysis, the paper considers theeffect of the optimal velocity difference information, the optimal velocity differencemodel is presented. The linear stability condition of the presented model is obtained byemploying the linear stability theory, and it analyzes the nonlinear dynamic behavior ofthe model. Numerical simulation shows the new model can avoid the appearance ofnegative velocity, and the stability of traffic flow is enhanced, and it is identical withtheoretical analysis.②Based on the full velocity difference model, considering the effect of backward looking and the velocity difference to the current vehicle, backward looking and thevelocity difference model is presented.On the basis of①, in addition, the driver will observe information of the followingcar by the rearview mirror in order to travel safely. So considering the effect ofbackward looking and the velocity difference information, the new model is presented.The linear stability condition of the model is obtained by employing the linear stabilitytheory. The density wave of traffic flow near the critical point is investigated with thenonlinear analysis method. The occurrence of traffic jamming transitions can bedescribed by the kink-antikink solution of the modified Kortewege-de Vries (mKdV)equation. The simulation results show that the model can suppress traffic jameffectively.③Based on FVD model, considering the comprehensive effect of the optimalvelocity difference of the two non-neighboring leading cars and backward looking, andthe optimal velocity difference information and backward looking model is presented.On the basis of①and②, considering the comprehensive effect of theahead-backward cars, the comprehensive effect of the car following model is presented.Numerical simulation shows that the stability of traffic flow is enhanced obviously, thecritical value of the sensitivity is decreased. The fluctuation of all the cars’ velocitiesbecomes further small comparing with FVD model, the mKdV equation analyzes thenonlinear dynamic behavior of the model at the same time.