Research On Improved Coupled Map Car-following Model Considering Multi-car Effect

Car-following model describes the dynamic process of following cars moving withleading car in a motorcade which driving in single lane without overtaking. It analyzesthe evolution of traffic flow in single lane, and is of great theoretical value and practicalsignificance in modern traffic simulation, evaluation and management control. Coupledmap (CM) car-following model, which is a corresponding discrete version of thecar-following model, is suitable for describing complex traffic control problems andcomputer simulation as its concise algorithm. However, traditional CM model isrelatively simple to describe the real traffic due to less driving factors considered.With the increasing of vehicle density in traffic system, the relationship betweenvehicles becomes more and more important, so the running state of the vehicle is notonly influenced by its nearest-neighbour preceding vehicle, but also by its multiplepreceding vehicles and its rear vehicle. However, traditional CM car-following modelhardly considered the effect of the multiple preceding vehicles and the rear vehicle. Inmodern intelligent transportation system (ITS), drivers can get information of morevehicles around his or her vehicle. So in this paper, we improved the traditional CMcar-following model based on front and rear multi-car effect in order to describe themodern traffic flow more better, and then we study the control method to suppresstraffic jam based on the new model to provide a reference to explain the traffic jammechanism and how to suppress it. The concrete work of the paper is as follows:Firstly, a Multiple Preceding Vehicles Coupled Map (MPVCM) car-followingmodel is presented based on the modified optimal velocity (OV) function according tothe headway of multiple preceding vehicles. The linear stability condition of thepresented model was obtained by employing the linear stability theory. Numericalsimulation in the open boundary condition shows that MPVCM car-following modelimproved the stability of traffic flow under small disturbance, and the best number ofpreceding vehicles we should consider is three.Secondly, since drivers will check the rear vehicle’s information through rearviewmirror or ITS to control his or her vehicle in real traffic, a backward looking optimalvelocity function is designed and a Comprehensive Effect Couple Map(CECM)car-following model is presented based on MPVCM model. And then weanalyzed its linear stability condition. Numerical simulation shows that the new model effectively improves the stability of traffic flow by selecting proper weight ratio ofpreceding and rear vehicles, and velocity fluctuation of the following cars decreases incontrast with the MPVCM model as the steady headway of the vehicles increases inCECM model.Lastly, we studied the traffic jam suppression scheme based on CECMcar-following model. We added a control signal related to the velocity difference andsafe headway between the vehicle and its nearest-neighbor preceding vehicle to CECMmodel. Then, the condition which there is no traffic jam in the system was obtained, anda system process to design the feedback control gain was provided. Theory andnumerical simulation show that our model has better temporal behavior and larger rangeof feedback gain than traditional CM model when we employ the same control signalthough both can suppress the traffic jam. And we find that there is a linear relationshipbetween the feedback gain range and the sensitivity coefficient of drivers andthe maxvelocity of the vehicles which consistent with the real traffic situation.