Application Research Of Lattice Hydrodynamics Model For Traffic Flow

Traffic congestion is an important area of research in the field of transportation,as it relates to people’s daily travel.The operational state of traffic flow directly affects the stability of the entire transportation system.Once the transportation system enters an unstable state,it results in many negative impacts,such as traffic congestion,environmental pollution,and frequent traffic accidents.Therefore,it is necessary to study the operational laws of traffic flow and alleviate transportation problems.Traffic flow models are mainly used to describe the changing patterns of traffic flow over time and space.The lattice hydrodynamic traffic flow model is a typical traffic flow model with macroscopic discrete characteristics and high computational efficiency.Based on the lattice hydrodynamic traffic flow model,this paper conducts research on traffic feedback control,energy dissipation and fuel consumption,and traffic cyber-attacks.The main research contents are as follows:1、Based on the dynamics equation of the lattice hydrodynamics model,the difference between the average optimized traffic flow of the nearest neighboring lattice and the current delayed traffic flow is considered as the delayed feedback control term to establish the control equation.The stability condition is derived according to the traffic control theory and Hurwitz stability criterion.Through nonlinear analysis,the m Kd V equation and kink-antikink wave solution is obtained.The density equation of the model is discretized using the forward difference method for numerical simulation.When traffic flow is in an unstable state and the control term is not considered,significant stop-and-go phenomena occur as the initial perturbation evolves over time.However,when the control term is introduced with increased feedback gain and response time,the fluctuation amplitude of the density wave tends to decrease,indicating that this delayed feedback control has a positive impact on the stability of the traffic system and can improve traffic flow stability and suppress traffic congestion.2、A lattice hydrodynamics model with feedback control of the average optimal flow rate of multiple downstream units is constructed and the new model is subjected to linear stability analysis and nonlinear analysis.The results showed that selecting more downstream units led to more stable traffic flow and better control effects.Energy dissipation and fuel consumption are studied under traffic control.A new energy dissipation formula is defined based on the kinetic energy theorem,and the fuel consumption of each vehicle at time t in the VTMicro model was converted to the fuel consumption of each unit.Short-term and long-term behaviors of density waves,spatiotemporal evolution of density,hysteresis loops,as well as spatiotemporal evolution of energy dissipation and fuel consumption are studied through numerical simulations.The research shows that considering the average optimal flow rate of multiple downstream units can achieve control strategies to suppress traffic congestion,and energy dissipation and fuel consumption are closely related to traffic flow stability.Under traffic control conditions,the more stable the traffic flow,the less energy dissipation and fuel consumption occur.3、Cyber-attacks are considered in the two-lane lattice hydrodynamics model,and the changes in traffic flow stability under different cyber-attack weights are studied.By analyzing the linear and nonlinear stability of the system,a traffic phase diagram was obtained.The results indicate that when the cyberattack weight is greater than 1,the unstable region of the phase diagram increases,posing a threat to traffic flow stability and potentially leading to congestion.Conversely,when the network attack weight is less than 1,the unstable region decreases,and the attack does not have the expected negative impact,resulting in poor attack effectiveness.Numerical simulations were conducted to analyze the behavior of density waves,spatiotemporal evolution,and hysteresis loops.When cyber-attacks were introduced during stable traffic flow,different network attack weights had varying effects on traffic flow stability,which confirms the results of the theoretical analysis.