Modeling And Simulation Of Lattice Traffic Flow Dynamics At Sag Section

The macroscopic traffic flow model is a key to understanding the dynamic characteristics of macroscopic traffic flow.Its main idea is to regard vehicles on the road as fluids,and to describe the collective behavior of traffic flow by establishing continuous hydrodynamic equations.The research results are applied to practical traffic management and control,providing solutions to alleviate traffic congestion.The lattice model is a discrete form of the macroscopic traffic flow model,which has both microscopic characteristics and macroscopic features.It can describe actual traffic flow phenomena more intuitively.In order to study the evolution mechanism of traffic flow jamming at sag section,this paper constructs single-lane and two-lane lattice traffic flow models based on the traffic conditions at sag section.The linear and nonlinear analytical analysis and numerical simulation are carried out.Then,the model parameters are calibrated using the actual traffic data to explore the dynamic evolution characteristics of traffic flow at the sag section.The lattice traffic flow model that can describe the actual traffic flow evolution is obtained.The specific research content is as follows:(1)Based on the road environment of the sag section,a single-lane traffic flow model at sag section is constructed.The stability condition and neutral stability curves are obtained by the linear stability analysis method.On the basis of the linear analysis,the analytical result of the model is obtained by nonlinear analysis of the model using the reduced perturbation method.Thus,the evolution of density wave in the unstable region and near the critical point is studied.Then,numerical simulations are used to study the influence of local small disturbances on the fluctuations of the traffic system under different slope values.Based on the obtained density wave evolution diagram to analyze the stability of the traffic flow.The evolution mechanism of traffic congestion at the sag section is revealed.In addition,this paper explores the evolution laws of different perturbations in the metastable region under low and high density conditions.(2)Based on actual lane-changing experience,a two-lane lattice traffic flow model at sag section considering dynamic lane-changing rate is proposed.This paper overcomes the shortcomings of traditional lattice models by setting the lane-changing rate as a constant value.Based on the actual lane-changing experience,the dynamic lanechanging rate function is proposed.It is introduced into research content(1)to construct a two-lane lattice model at sag section with dynamic lane-changing rate.The linear analytical analysis of the model is carried out by Fourier transform to obtain the influence of the lane-changing rate parameter on the stability of traffic flow.The solution of the kink-antikink density wave that can describe traffic congestion near the critical point is obtained by using nonlinear analysis.Both theoretical analysis and numerical simulation show that the introduction of dynamic lane-changing rate can realistically portray the actual traffic flow evolution process and improve the traffic flow stability.(3)The model parameters are calibrated and verified based on the measured data.In order to test whether the proposed model can truly reflect the actual traffic conditions,this paper uses the NGSIM dataset to calibrate and verify the parameters of the model in the research content(1)and related model.The parameter calibration process adopts the three-stage calibration method.The minimum error of the model and the corresponding optimal parameter value is obtained by using the actual data calibration.The calibration results show that the calibration error of the model in this paper is much smaller.The parameter validation results illustrate that the calibrated sag section lattice traffic flow model can describe the actual traffic phenomena.