Modeling And Simulation Of Lattice Traffic Flow Dynamics Based On Dynamic Sensitivity Coefficients

As the lifeblood of the national economy,transportation plays a significant role in the development of civilization.Only proper management and control strategies can improve the traffic capacity of roads and advance the pace of human civilization.Although governments of various countries continue to invest in transportation infrastructure,traffic congestion still occurs from time to time,and the impact on society cannot be ignored.In response to this problem,researchers in various fields have proposed different coping strategies to alleviate traffic congestion,but they have not fundamentally solved this worldwide problem.The reason is that the existing research fails to fully reveal the inherent evolution mechanism of the transportation system.Therefore,it is necessary to start with the actual vehicle driving information to deeply analyze the internal evolution mechanism of traffic flow.Based on the driver’s response to the traffic conditions at different driving speeds,this paper proposes a dynamic sensitivity coefficient function that can reflect the actual traffic driving behavior,constructs single-lane and two-lane lattice models,and conducts stability analysis on them.and numerical simulations to discuss the influence of disturbance on traffic state.Furthermore,the parameters of the model are identified and verified through actual data,and an analytical model that can accurately describe the dynamic evolution characteristics of the actual traffic flow is obtained.The general work includes:（1）The dynamic sensitivity coefficient function is constructed,and a single-lane grid traffic flow model is proposed.During driving,when the speed is different,the sensitivity of the driver is also different,,but in previous models,researchers mostly set the sensitivity coefficient as a constant.This paper proposes a dynamic sensitivity coefficient function based on the sigmoid function,which can dynamically describe the change of the sensitivity coefficient with the change of vehicle speed.Then this function is integrated into the original Nagatani model,and a single-lane grid traffic flow model considering dynamic sensitivity coefficients is constructed.And the stability condition is obtained by analyzing the model in the form of Fourier series;and based on the initial condition that the vehicles are evenly distributed on the circular road,the model is numerically simulated,and the density fluctuation diagram is obtained,which shows that the improvement of the driver’s safety is achieved.Dynamic sensitivity coefficients can reduce traffic congestion.（2）Based on the current situation of the road,a two-lane lattice model considering the dynamic sensitivity coefficient is constructed.In actual traffic,single-lane roads account for a small proportion,and public roads are mostly two-lane or multi-lane.In order to better simulate the dynamic evolution process of the actual traffic flow,this paper proposes a lanechanging rule that some vehicles seek to change the driving lane when the density of the current lane is too large,thus constructing a two-lane lattice model considering the dynamic sensitivity coefficient.A small perturbation is added to the model equation,and then the equation containing the perturbation is Z-transformed,and the stability conditions that can make the model in a uniform and stable state are derived.Finally,the two-lane model is simulated,and the spatiotemporal state diagrams of density waves under different conditions are drawn,revealing how the dynamic sensitivity coefficient and lane change rate will affect the stability of the traffic system.（3）The optimal parameters are determined by calibrating the model with measured traffic data.It is difficult for an uncalibrated model to fully describe the real traffic conditions.In order to make the model describe various phenomena in real traffic more perfectly,it is necessary to verify the parameters of the model.This paper uses the NGSIM data set to calculate the traffic density according to the vehicle information recorded by the detector,and then calibrates the parameters of the model proposed above through the threestage calibration method,and also calibrates the original Nagatani model.Finally,comparing the image obtained by the model simulation with the actual data waveform,it can be concluded that the calibrated dynamic sensitivity coefficient model can more accurately restore various traffic phenomena than the Nagatani model.