A simulation method of mixed traffic lattice car-following system considering slope factor

Abstract

The present application relates to the technical field of intelligent transportation, in particular to a simulation method of mixed traffic lattice car-following system considering slope factor, which introduces mixed traffic penetration rate, slope and friction coefficient of road, and introduces the number of communication vehicles and flow difference effect to optimize the car-following behavior of connected commercial vehicles. In the V2X environment, the linearization processing of the lattice car-following system is carried out to obtain the evolution equation of density, and the stability analysis of the evolution equation of density is carried out to obtain the stability condition of the lattice car-following system. The nonlinear analysis of the lattice car-following system is carried out, and the partial differential equation describing the perturbation near the stable critical point is derived by using the set stability condition, so as to obtain the coexistence curve of the lattice car-following system, which can accurately depict the car-following behavior of mixed traffic under the slope environment. Finally, the simulation results of the lattice car-following system are analyzed, which proves that the traffic congestion can be effectively relieved and the traffic flow stability can be improved.

Description

Technical Field

[0001] This invention relates to the field of intelligent transportation technology, and specifically to a simulation method for a hybrid traffic flow grid-based car-following system that considers slope factors. Background Technology

[0002] Current grid-based car-following systems primarily model traffic flow using non-connected passenger vehicles, rarely considering the impact of mixed traffic flow characteristics. With the rapid development of passenger and freight transport and the deep integration of intelligent and connected transportation systems, the scale and load capacity of connected commercial vehicles are continuously increasing. New mixed traffic flows, involving connected commercial vehicles, connected passenger vehicles, non-connected commercial vehicles, and non-connected passenger vehicles, will impact the dynamic evolution of traffic, making the interactions between vehicles more complex.

[0003] Most existing traffic flow models characterize the car-following behavior of connected commercial vehicles at the micro level, lacking a macro-level consideration of the impact of these characteristics on traffic flow. While connected commercial vehicles can utilize V2X technology to acquire real-time road traffic information and improve their driving status accordingly, thus benefiting traffic operations to some extent, significant differences in traffic flow patterns occur between the areas in front of and behind them due to their lower speeds, poorer performance, and larger size. This has a significant impact on traffic operations.

[0004] Most existing grid-based car-following systems consider straight-line conditions, rarely taking into account the impact of slopes on the stability of mixed traffic flow. Compared to straight roads, mixed traffic flow on slopes is affected by gravitational acceleration, which puts greater demands on vehicles' climbing and braking capabilities. Summary of the Invention

[0005] The purpose of this invention is to provide a simulation method for a mixed traffic flow grid-based car-following system that considers slope factors. By introducing mixed traffic flow penetration rate, this method changes the situation where existing grid-based car-following systems based on straight road scenarios cannot accurately depict the mixed traffic flow car-following behavior under slope conditions.

[0006] To achieve the above objectives, this invention provides a simulation method for a hybrid traffic flow grid-based car-following system that considers slope factors, comprising the following steps:

[0007] Step 1: Establish a hybrid traffic flow grid-based car-following system considering slope factors in a V2X environment;

[0008] Step 2: Linearize the mixed traffic flow grid car-following system to obtain the density equation;

[0009] Step 3: Use the density equation to perform linear analysis to obtain the stability conditions of the car-following system;

[0010] Step 4: Using the density equation, through nonlinear analysis and by applying the reduction perturbation method, derive the mKdV equation near the critical point describing the evolution characteristics of traffic density waves.

[0011] Optionally, in the process of establishing the hybrid traffic flow grid following system in step 1, the penetration rates of connected passenger vehicles, connected commercial vehicles, non-connected passenger vehicles, and non-connected commercial vehicles are introduced to construct a hybrid traffic flow.

[0012] Optionally, in a V2X environment, the slope factor can be considered by introducing the slope, friction coefficient, vehicle mass, and gravitational acceleration into the basic optimized velocity function, and by introducing the flow difference effect into the control equation of the connected commercial vehicle.

[0013] Optionally, the execution process of step 2 specifically involves performing a Taylor expansion on the control equations of the hybrid traffic flow grid car-following system, ignoring nonlinear terms, and obtaining linearized control equations. Then, a difference operation is performed on the control equations, and the conservation equations are solved simultaneously to eliminate the velocity of the control equations and obtain the density equations.

[0014] Optionally, during the linear analysis in step 3, a linearized perturbation equation is obtained by introducing the steady-state solutions of density and velocity into the density equation and adding a small perturbation, and higher-order terms are omitted during the linear analysis.

[0015] Optionally, in step 4, a small quantity 0 < ε ≤ 1 is introduced into the density equation, and the effects of slow variables X and Y are considered near the critical point.

[0016] This invention provides a simulation method for a mixed vehicle flow grid car-following system considering slope factors. It introduces mixed vehicle flow penetration rate, slope, and road friction coefficient, while also incorporating the number of communicating vehicles and the flow difference effect to optimize the car-following behavior of connected commercial vehicles. In a V2X environment, the grid car-following system is linearized to obtain the density evolution equation. Stability analysis is then performed on this equation to derive the stability conditions of the grid car-following system. Nonlinear analysis is further performed, and using the established stability conditions, partial differential equations describing micro-perturbations near the stability critical point are derived, resulting in the coexistence curve of the grid car-following system. This method accurately characterizes the mixed vehicle flow car-following behavior under slope conditions. Finally, analysis of the simulation results shows that the method can effectively alleviate traffic congestion and improve traffic flow stability. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the execution steps of a simulation method for a hybrid traffic flow grid-based car-following system that considers slope factors, according to the present invention.

[0019] Figure 2 This is a combination of neutral stability curves and coexistence curves showing the increase in connected vehicle penetration rate in this embodiment of the invention.

[0020] Figure 3 This is a combination of neutral stability curves and coexistence curves for increasing the number of communicating vehicles in an embodiment of the present invention;

[0021] Figure 4 This is a combination of neutral stability curves and coexistence curves showing the increasing penetration rates of connected and non-connected commercial vehicles in embodiments of the present invention.

[0022] Figure 5 This is a combined graph of the neutral stability curve and the coexistence curve showing the increase in the flow difference response coefficient in an embodiment of the present invention;

[0023] Figure 6 This is a neutral and stable curve diagram of slope change in an embodiment of the present invention. Detailed Implementation

[0024] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0025] The following explains the English abbreviations and terms used in this invention:

[0026] V2X: vehicle to everything;

[0027] mKdV: modified Korteweg de Vries.

[0028] This invention provides a simulation method for a hybrid traffic flow grid-based car-following system that considers slope factors, comprising the following steps:

[0029] S1: Establish a hybrid vehicle flow grid-based car-following system that considers slope factors in a V2X environment;

[0030] S2: Linearize the mixed traffic flow grid car-following system to obtain the density equation;

[0031] S3: Use the density equation to perform linear analysis to obtain the stability conditions of the car-following system;

[0032] S4: Using the density equation, through nonlinear analysis and by applying the reduction perturbation method, the mKdV equation describing the evolution characteristics of traffic density waves near the critical point is derived.

[0033] The following provides further explanation with specific implementation steps, and a detailed execution process diagram is shown below. Figure 1 As shown, the flowchart in the figure corresponds to steps S1 to S4 respectively:

[0034] In step S1, a hybrid vehicle flow grid-based car-following system considering slope factors is established in a V2X environment, specifically represented as follows:

[0035]

[0036]

[0037] Equation (1) represents the conservation equation for traffic flow at the macro level, and Equation (2) represents the control equation for traffic flow at the macro level. Where ρ j and v j Let ρj represent the local density and velocity at the j-th position on the one-dimensional lattice at time t, respectively. Let ρ0 be the average density and a represent the driver's sensitivity. c,c p represents the penetration rate of connected passenger vehicles. c,h p represents the penetration rate of connected commercial vehicles. n,c p represents the penetration rate of non-connected passenger vehicles. n,h This represents the penetration rate of non-connected commercial vehicles. Clearly, the sum of the penetration rates for the four vehicle types is 1, i.e., p. c,c +p c,h +p n,c +p n,h =1, λ is the flow difference sensitivity coefficient. V(·) is the optimal velocity function, which is a monotonically decreasing function with an upper bound and an inflection point at the critical density, V(ρ j+1 ,ρ j+2 ,···,ρ j+m The optimal speed function expression considering multiple vehicles ahead is as follows:

[0038] V(ρ j+1 ,ρ j+2 ,···,ρ j+m )=β1V(ρ j+1 )+β2V(ρ j+2 )+···+β m V(ρj+m (3)

[0039] The farther the distance between the vehicle in front and the current vehicle, the smaller the impact; the impact weight is β. l The expression is as follows:

[0040]

[0041] m represents the total number of vehicles ahead, l represents the l-th vehicle ahead, and β is a weighting coefficient with a value of 2.

[0042] Considering the relationship between vehicle type penetration rates, it is clear that the penetration rate p of non-connected commercial vehicles... n,h =(p n,h +p c,h (p) n,c +p n,h ), penetration rate of connected commercial vehicles c,h =(p n,h +p c,h (p) c,c +p c,h Non-connected passenger vehicle penetration rate p n,c =(p n,c +p c,c (p) n,c +p n,h ), penetration rate of connected passenger vehicles p c,c =(p n,c +p c,c (p) c,c +p c,h ).

[0043] The V(·) is an optimized speed function based on the characteristics of mixed traffic flow. Considering the slope factor, the optimized speed function is divided into an uphill optimized speed function and a downhill optimized speed function.

[0044] The formula for calculating the uphill optimal velocity function is:

[0045]

[0046] The formula for calculating the downhill optimal velocity function is:

[0047]

[0048] In the formula: θ represents the slope, θ > 0 represents uphill, θ < 0 represents downhill, v f,max ρ represents the maximum speed on a flat road section. c,u,θ and ρ c,d,θ Indicates the safe density when going uphill and downhill, v g,u,max and v g,d,max The maximum speed deviation between uphill and downhill sections is expressed as follows:

[0049]

[0050] In the formula: μ is the coefficient of friction, m is the mass of the car, and g is the acceleration due to gravity. For ease of calculation, let μ be the coefficient of friction, m be the mass of the car, and g be the acceleration due to gravity. Therefore, the optimal velocity function can be rewritten as follows:

[0051]

[0052] In the formula: v g,max v is the maximum speed deviation on a sloping road. g,max =v g,u,max =v g,d,max , This makes

[0053] The established V2X environment hybrid traffic flow grid-based car-following system considering slope factors provides a grid-based car-following system that can be linearized for deriving the density equation in step S2.

[0054] In step S2, in order to characterize the evolution of traffic flow density in the mixed vehicle flow grid car-following system considering the slope factor in the V2X environment, the grid car-following system is linearized.

[0055] Furthermore, the linearization of the governing equations yields the density equation. The specific steps are as follows: Taylor expands equation (2) and ignores the nonlinear terms. After processing, we can obtain:

[0056]

[0057] By eliminating the velocity v in the system j The evolution equation for density can be obtained as follows:

[0058]

[0059] Linearization is performed on the mixed traffic flow grid following system considering the slope factor in the V2X environment to provide easily tractable density equations for the linear and nonlinear analyses in steps S3 and S4.

[0060] In step S3, in order to study the resistance of the lattice following system to small disturbances, the conditions for its stability are obtained based on the density equation and using the linear stability theory method.

[0061] The specific steps for obtaining the stability conditions of the car-following system using the density equation and linear analysis are as follows:

[0062] The solution state is set as follows:

[0063] ρ j (t)=ρ0,v j (t)=V(ρ0) (11)

[0064] Add a small perturbation y j (t), then we have:

[0065] ρ j (t)=ρ0+y j (t) (12)

[0066] After introducing the density equation (10) into equations (11) and (12), and then linearizing the equation, we get...

[0067]

[0068] in, By expanding y j Substituting (t) = exp(ijk + zt) into equation (13), we obtain the following equation about z:

[0069]

[0070] Where i is the virtual unit, j is the spatial variable, k is the deviation value of the spatial variable, t is the time variable, and z is the deviation value of the time variable.

[0071] z1 is the first-order coefficient of z, and z2 is the second-order coefficient of z. Both z1 and z2 are stability parameters used to solve for the stability range. Expanding z = ikz1 + (ik) 2 Substituting z2+··· into equation (14), we get:

[0072]

[0073] Further simplification yields:

[0074]

[0075] Because p c,c +p c,h +p n,c +p n,h =1, therefore we can conclude:

[0076]

[0077]

[0078] According to stability theory, if z2 < 0, the initially uniform traffic flow exhibits instability in the long-wavelength mode; if z2 > 0, the system maintains its original stable state. Therefore, z2 = 0 corresponds to the critical stability condition of the new car-following system:

[0079]

[0080] The corresponding stability condition is:

[0081]

[0082] Clearly, when the penetration rates of connected commercial vehicles, non-connected commercial vehicles, and connected passenger vehicles are all 0, the stability condition is consistent with the lattice fluid dynamics model characterizing traditional transportation.

[0083]

[0084] In linear analysis, higher-order terms are considered to have minimal effects and are therefore omitted. However, near the critical stability condition, higher-order terms may have unexpected effects. Therefore, nonlinear analysis of the car-following system is required in step S4 to reveal the role of higher-order terms.

[0085] In step S4, using the density equation and through nonlinear analysis, the reduced perturbation method is applied to derive the mKdV (modified Korteweg de Vries) equation describing the evolution characteristics of traffic density waves near the critical point. The specific steps are as follows:

[0086] Introducing a small quantity 0 < ε ≤ 1, at the critical point (ρ c ,a c Considering the slow variables X and Y in the vicinity, they are defined as follows:

[0087] X = ε(j + bt), Y = ε 3 t (22)

[0088] Where b is a parameter to be determined, let the density of the j-th cell be:

[0089] ρ j (t)=ρ c +εG(X,Y) (23)

[0090] Substituting the slow variable and the density of lattice point j into the density equation (10), Taylor expands it to the fifth power of ε to obtain the nonlinear partial differential equation (24), where

[0091]

[0092] Pick Eliminable ε in the formula 2 and ε 3 The final result is:

[0093]

[0094] The coefficients for each item are:

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] To obtain the standard mKdV equation with higher-order small quantities, the following transformation is performed:

[0101]

[0102] The equation for mKdV containing the correction term o(ε) is obtained:

[0103]

[0104] In the formula, If we ignore the correction term o(ε) in equation (32), we obtain the standard form of the mKdV equation, and its solution is:

[0105]

[0106] In order to determine the propagation wave velocity c in equation (33), the following condition must be met:

[0107]

[0108] Here, M[G0′]=M[G0], and by integrating equation (34), the propagation speed of the knot-anti-knot wave can be obtained:

[0109]

[0110] Finally, the knot-anti-knot wave solution of the mKdV equation is derived as follows:

[0111]

[0112] Furthermore, the amplitude A of the density wave is:

[0113]

[0114] The solution of the density wave reflects the existence of a coexisting phase of traffic, and this coexistence curve can be represented by ρ=ρc±A.

[0115] Furthermore, such as Figures 2 to 6 As shown, the present invention is further illustrated through simulation examples:

[0116] Appendix Figure 2The horizontal axis represents the average traffic flow density p0, and the vertical axis represents the driver sensitivity coefficient a. The area above the curve is the stable region, and the area below the curve is the unstable region. The dashed line shown is the coexistence curve, and the solid line is the neutral stability curve. When p c,c =p c,h =p n,h When θ = 0, λ = 0.2, and m = 3, the new model reverts to the original Nagatani model, which aligns with the conclusions of the preceding linear analysis. Figure 2 As the penetration rate of connected vehicles increases, the curve shows a significant decline, the stability region becomes larger, and the stability of the transportation system becomes stronger.

[0117] Appendix Figure 3 When p c,h =p n,h =0,θ=0,λ=0.2,p c,c When = 0.5, from Figure 3 It can be clearly seen that as the number of communication vehicles m increases, the neutral stability curve and coexistence curve decrease, and the stable region becomes larger, indicating that the number of communication vehicles has a positive impact on system stability.

[0118] Appendix Figure 4 When p c,h +p c,c When = 0.5, m = 3, λ = 0.2, θ = 0, from Figure 4 It is evident from the data that the penetration rate of connected commercial vehicles is higher than that of non-connected commercial vehicles. c,h +p n,h As the value increases, the neutral stability curve and coexistence curve rise, and the stable region shrinks, indicating that connected and non-connected commercial vehicles have a negative impact on system stability.

[0119] Appendix Figure 5 When p c,h +p c,c =0.5,p c,h +p n,h When m = 0.5, θ = 3, and θ = 0, from Figure 5 It can be clearly seen that when the flow difference coefficient λ increases, the neutral stability curve and the coexistence curve decrease, and the stable region becomes larger, indicating that the flow difference effect has a positive impact on the system stability.

[0120] Appendix Figure 6 When p c,h +p c,c =0.5,p c,h +p n,h When = 0.5, m = 3, λ = 0.2, from Figure 6As can be seen from the data, when going downhill, the neutral stability curve rises as the slope θ increases, and the stable region becomes smaller. Going downhill has a negative impact on system stability. When going uphill, the neutral stability curve decreases as the slope θ increases, and the stable region becomes larger. Going uphill has a positive impact on system stability.

[0121] In summary, the present invention has the following advantages:

[0122] 1. Based on the traffic characteristics of mixed traffic flow, and considering vehicle perception, communication capabilities, and vehicle type differences, a novel mixed traffic flow grid-based car-following system is established using mixed traffic flow penetration rate as a parameter.

[0123] Traditional grid-based car-following systems often overlook vehicle perception, communication capabilities, and model differences, resulting in an inability to accurately describe the car-following behavior of connected commercial vehicles, connected passenger vehicles, and non-connected commercial vehicles. In contrast, this invention incorporates the penetration rates of connected passenger vehicles, connected commercial vehicles, non-connected passenger vehicles, and non-connected commercial vehicles.

[0124] This invention, by considering the perception and communication capabilities of vehicles and the differences in vehicle models, introduces the penetration rates of connected passenger vehicles, connected commercial vehicles, non-connected passenger vehicles, and non-connected commercial vehicles to construct a novel hybrid vehicle flow grid-based car-following system. This system can describe the car-following behavior of different types of vehicles and reflect the proportion of different types of vehicles in the traffic flow, thereby characterizing the impact of hybrid vehicle flow on traffic flow and solving the difficulty of macro-traffic flow models in characterizing the micro-car-following behavior of different types of vehicles.

[0125] 2. Based on the car-following characteristics of connected commercial vehicles, and considering the real-time information of vehicles ahead obtained by connected commercial vehicles using V2X technology, the car-following behavior of connected commercial vehicles is optimized by introducing the effect of communication vehicle number and traffic difference.

[0126] Most existing traffic flow models are based on micro-level traffic flow models to characterize the car-following behavior of connected commercial vehicles. Few scholars have used macro-level traffic flow models to characterize the car-following characteristics of connected commercial vehicles from a macro-level perspective. Connected commercial vehicles can utilize V2X technology to obtain real-time information about vehicles ahead. However, the amount of vehicle information obtained is affected by the number of communicating vehicles. Furthermore, due to the differences in climbing and braking capabilities between connected commercial vehicles and passenger cars, mobile congestion bottlenecks often occur around connected commercial vehicles, resulting in significant differences in traffic flow before and after them. Therefore, this invention considers the car-following characteristics of connected commercial vehicles in the control equations, introducing the effects of the number of communicating vehicles and traffic flow differences to optimize their car-following behavior.

[0127] The flow difference effect and the number of communicating vehicles are introduced into the control equation to describe the influence weight of the optimized speed function of different vehicles ahead on the optimized speed function of the current vehicle. The weight coefficients are calculated using an inverse function of communication distance. The weight coefficients are smaller as the distance is greater, and the sum of the weight coefficients is 1. This yields the optimized speed function of connected commercial vehicles, which can characterize the impact of the communication capability of connected commercial vehicles on traffic flow and indirectly characterize the mobile congestion bottleneck phenomenon caused by connected commercial vehicles, thereby optimizing the car-following behavior of connected commercial vehicles.

[0128] 3. Based on the mixed traffic flow grid-based car-following system, considering the characteristics of sloping road sections, the gradient and road friction coefficient are introduced to characterize the car-following behavior of mixed traffic flow under sloping conditions.

[0129] Most existing mixed traffic flow models are based on straight road scenarios and do not consider road segment characteristics such as slope gradient and road friction coefficient. This results in the mixed traffic flow models being unable to accurately depict the car-following behavior of mixed traffic flow in sloping environments. Therefore, this invention, based on the construction of a mixed traffic flow grid car-following system, considers road segment characteristics such as slope gradient and road friction coefficient, thereby depicting the car-following behavior of mixed traffic flow in sloping environments.

[0130] To characterize the car-following behavior of mixed traffic flow in a sloping environment, features of sloping road sections such as slope and friction coefficient are introduced into the mixed traffic flow grid car-following system. This extends the mixed traffic flow model in a straight road environment to a mixed traffic flow model in a sloping environment, thereby improving the model's adaptability, enabling traffic flow to pass through the slope more stably, and reducing potential accident risks.

[0131] The above description discloses only one preferred embodiment of the present invention, and should not be construed as limiting the scope of the present invention. Those skilled in the art will understand that all or part of the processes of the above embodiments can be implemented, and equivalent changes made in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A simulation method for a hybrid traffic flow grid-based car-following system considering slope factors, characterized in that, Includes the following steps: Step 1: Establish a hybrid traffic flow grid-based car-following system considering slope factors in a V2X environment; In the process of establishing the hybrid traffic flow grid following system in step 1, the penetration rates of connected passenger vehicles, connected commercial vehicles, non-connected passenger vehicles, and non-connected commercial vehicles are introduced to construct the hybrid traffic flow. The combined penetration rate of the four vehicle types is 1. The optimal speed function expression considering multiple vehicles ahead is as follows: Indicates time The first one-dimensional lattice Local density at each location, It is the optimal speed function; the greater the distance between the vehicle in front and the current vehicle, the smaller the influence, with an influence weight of [value missing]. The expression is as follows: This indicates the total number of vehicles considered ahead. Indicates the preceding number a car, The weighting coefficient is set to 2; Step 2: Linearize the mixed traffic flow grid car-following system to obtain the density equation; Step 3: Use the density equation to perform linear analysis to obtain the stability conditions of the car-following system; Step 4: Using the density equation, through nonlinear analysis and by applying the reduction perturbation method, derive the mKdV equation near the critical point describing the evolution characteristics of traffic density waves.

2. The simulation method for a hybrid traffic flow grid-based car-following system considering slope factors as described in claim 1, characterized in that, In the V2X environment, the slope factor is specifically considered by introducing the slope, friction coefficient, vehicle mass, and gravitational acceleration into the basic optimized velocity function, and by introducing the flow difference effect into the control equation of connected commercial vehicles.

3. The simulation method for a hybrid traffic flow grid-based car-following system considering slope factors as described in claim 2, characterized in that, The specific execution process of step 2 is as follows: Taylor expansion is performed on the control equations of the hybrid traffic flow grid car-following system, and nonlinear terms are ignored. After processing, linearized control equations can be obtained. Then, difference operations are performed on the control equations, and the conservation equations are solved simultaneously to eliminate the velocity of the control equations and obtain the density equations.

4. The simulation method for a hybrid traffic flow grid-based car-following system considering slope factors as described in claim 3, characterized in that, In step 3, during the linear analysis, a linearized perturbation equation is obtained by introducing the steady-state solutions of density and velocity into the density equation and adding a small perturbation. Higher-order terms are omitted during the linear analysis.

5. The simulation method for a hybrid traffic flow grid-based car-following system considering slope factors as described in claim 4, characterized in that, In step 4, a small quantity is introduced into the density equation. And consider slow variables near the critical point. and The impact.

Images