A method for calculating the capacity of complex heterogeneous traffic flow

Abstract

The application is a kind of complex heterogeneous traffic flow capacity calculation method, first based on homogeneous traffic flow stability discriminant, the stability discriminant of complex heterogeneous traffic flow is established, and the stability of complex heterogeneous traffic flow is discriminated;Then, under the stable state of complex heterogeneous traffic flow, considering the proportion and reaction time of traditional vehicles, ACC vehicles and CACC vehicles, the complex heterogeneous traffic flow flow-density basic graph model is established, and the complex heterogeneous traffic flow capacity expression is obtained according to the complex heterogeneous traffic flow flow-density basic graph model. The complex heterogeneous traffic flow capacity reflects the maximum number of vehicles that the road section can accommodate, when the number of vehicles exceeds the maximum number of vehicles that the road section can accommodate, the intelligent traffic network system can real-time control the number of vehicles entering the road section, and also can control the proportion and reaction time of traditional vehicles, ACC vehicles and CACC vehicles, control the complex heterogeneous traffic flow capacity, and improve the traffic efficiency.

Description

Technical Field

[0001] This invention relates to the field of traffic capacity calculation technology, specifically a method for calculating the traffic capacity of complex heterogeneous traffic. Background Technology

[0002] With the development of vehicle-to-everything (V2X) technology, autonomous vehicles are gradually integrating into traffic flow. Autonomous vehicles are broadly classified into two categories: Adaptive Cruise Control (ACC) and Cooperative Adaptive Cruise Control (CACC). ACC vehicles obtain information such as the speed and distance of vehicles ahead through onboard equipment; the reaction time of ACC vehicles is mainly due to the time delay of the onboard equipment. CACC vehicles, on the other hand, learn about the motion status of vehicles ahead (such as speed, distance, and acceleration) through vehicle-to-vehicle communication technology and automatically adjust their vehicle accordingly; the reaction time is mainly due to communication and control delays. Traditional vehicles are manually driven, relying primarily on the driver to obtain information about vehicles ahead. The driver needs a certain reaction time to adjust their strategy. Therefore, the reaction times of ACC, CACC, and traditional vehicles differ, resulting in different impacts on traffic flow capacity.

[0003] The existing research system on heterogeneous traffic flow capacity is relatively mature. Some scholars have considered the difference in reaction time between autonomous vehicles and traditional vehicles and studied the stability and capacity of heterogeneous traffic flow under different proportions of autonomous vehicles. However, the following problems still exist: (1) In terms of capacity, existing studies have focused on the heterogeneous traffic flow capacity under different proportions of autonomous vehicles. Unlike traditional vehicles, the impact of autonomous vehicles on traffic flow is essentially due to factors such as reaction time and expected inter-vehicle time interval. Different proportions of autonomous vehicles will affect the stability and capacity of heterogeneous traffic flow. (2) In terms of reaction time, existing studies have considered the difference in reaction time between autonomous vehicles and traditional vehicles and studied the stability and capacity of heterogeneous traffic flow under different proportions of autonomous vehicles. However, there are still significant differences in the reaction time of different types of autonomous vehicles (ACC / CACC vehicles). Therefore, it is necessary to consider the impact of the difference in reaction time of different vehicle types on the capacity of heterogeneous traffic flow. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the technical problem this invention aims to solve is to provide a method for calculating the traffic capacity of complex and heterogeneous traffic.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for calculating the capacity of complex heterogeneous traffic flows, wherein the complex heterogeneous traffic flows consist of conventional vehicles, ACC vehicles, and CACC vehicles; characterized in that the method includes the following:

[0007] 1. Based on the homogeneous traffic flow stability criterion, design the complex heterogeneous traffic flow stability criterion as shown in equation (10) to determine the stability of the complex heterogeneous traffic flow; if the inequality of equation (10) holds, it indicates that the complex heterogeneous traffic flow is stable; otherwise, the complex heterogeneous traffic flow is unstable.

[0008] P R F R +P A F A +P C F C ≥0 (10)

[0009] In the formula, P R P A and P C The proportions of traditional vehicles, ACC vehicles, and CACC vehicles are respectively, P R +P A +P C =1, P R P A P C ∈[0,1];F R F A and F C These are the stability terms for conventional vehicles, ACC vehicles, and CACC vehicles, respectively, with the following expressions:

[0010]

[0011]

[0012]

[0013] In the formula, g v g h and g Δv These represent the partial derivatives of the traditional car-following model with respect to vehicle speed, headway, and speed difference, respectively. This indicates the reaction time of a conventional vehicle to changes in its distance from the vehicle in front. This represents the reaction time of a conventional vehicle to a change in the speed of the vehicle in front; y v y h and y Δv Let represent the partial derivatives of the ACC vehicle following model with respect to vehicle speed, headway, and speed difference, respectively. This indicates the reaction time of the ACC vehicle to changes in its distance from the vehicle in front. Indicates the reaction time of the ACC vehicle to changes in the speed of the vehicle in front; and Let represent the partial derivatives of the CACC car-following model with respect to vehicle speed, headway, and speed difference, respectively. This indicates the CACC vehicle's reaction time to changes in its distance from the vehicle in front. This indicates the CACC vehicle's reaction time to changes in the speed of the vehicle in front;

[0014] 2. Under stable traffic flow conditions, establish a basic flow-density diagram model of complex heterogeneous traffic flow as shown in Equation (20);

[0015] q = kv e (20)

[0016] In the formula, q represents the flow rate of complex heterogeneous traffic flow, and v e Let represent the steady-state vehicle speed, and k represent the density of the complex heterogeneous traffic flow;

[0017]

[0018] In the formula, Δx R Δx A and Δx C f represents the steady-state headway of the conventional vehicle, the ACC vehicle, and the CACC vehicle, respectively. R (v e ), f A (v e ) and f C (v e Let ) represent the steady-state speed-headway function of conventional vehicles, ACC vehicles, and CACC vehicles under steady-state conditions of homogeneous traffic flow, respectively. The expressions are:

[0019]

[0020] f A (v e )=Δx A =(t a +τ a )v e +L+s0 (15)

[0021] f C (v e )=Δx C =(t c +τ c )v e +L+s0 (16)

[0022] In the formula, s0 represents the minimum headway, v0 represents the free-flow vehicle speed, and τ r τa and τ c These represent the reaction times of conventional vehicles, ACC vehicles, and CACC vehicles, respectively; L represents the vehicle length; α represents the sensitivity coefficient; and t represents the reaction time of the vehicle. a t c These represent the expected inter-vehicle time intervals for ACC vehicles and CACC vehicles, respectively.

[0023] Substituting equations (14) to (16) into equation (19), and then into equation (20), we obtain equation (21):

[0024]

[0025] In equation (21), let:

[0026]

[0027] According to equation (21), the function relating complex heterogeneous traffic flow volume and steady-state vehicle speed is:

[0028] q(v e ) = v e / u(v e )(twenty three)

[0029] According to equation (23), for the steady-state vehicle speed v e Taking the first derivative, we get:

[0030]

[0031] In the formula, Represents u(v) e For steady-state vehicle speed v e The first derivative of is expressed as:

[0032]

[0033] From equation (24), let Then there is right Solve the problem to obtain the possible extreme points.

[0034] Then, according to equation (24), the steady-state vehicle speed v e Taking the first derivative, we get:

[0035]

[0036] In the formula, Represents u(v) e For steady-state vehicle speed v e The second derivative of is expressed as:

[0037]

[0038] From equations (22) and (25), we can obtain:

[0039]

[0040] Since the speed of a vehicle in free flow is greater than the speed of a vehicle in steady state, therefore v e <v0, will v e Substituting <v0 into equations (22), (25), (28), and (28) respectively, we get: u(v e ) > 0, but:

[0041]

[0042] From equation (29), we can obtain that Heng was established, making but For q(v) e The maximum point of ) then The maximum value of the function relating complex heterogeneous traffic flow volume to steady-state vehicle speed, i.e., within the speed range of 0 to v0. The expression representing the flow capacity of complex heterogeneous traffic is:

[0043]

[0044] The traffic flow capacity of complex heterogeneous traffic is calculated using equation (30).

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0046] This invention considers the differences in reaction time among different types of vehicles, linking reaction time to steady-state headway. Based on the homogeneous traffic flow flow-density fundamental graph model, a complex heterogeneous traffic flow flow-density fundamental graph model is established, consisting of conventional vehicles, ACC vehicles, and CACC vehicles. Based on this model, an expression for the capacity of complex heterogeneous traffic flow is derived. With the development of autonomous driving technology, autonomous vehicles are integrated into traffic flow, increasing not only the complexity of traffic flow but also the difficulty of traffic flow control. Traffic capacity refers to the maximum number of vehicles passing through a specific section of a road per unit time under certain road and traffic conditions. Therefore, the expression for the capacity of complex heterogeneous traffic flow can calculate the maximum number of vehicles that a road section can accommodate. When the number of vehicles exceeds the maximum capacity of the road section, the intelligent traffic network system can control the number of vehicles entering the road section in real time. This is achieved by sending control commands to CACC vehicles about to enter the road section via communication technology, preventing them from entering temporarily and maintaining the optimal density of traffic flow to avoid traffic congestion. In addition, the traffic network system can also regulate the flow capacity of complex and heterogeneous traffic by controlling the proportion and reaction time of traditional vehicles, ACC vehicles and CACC vehicles, thereby improving traffic efficiency. Attached Figure Description

[0047] Figure 1(a) is a flow-density curve of complex heterogeneous traffic flow under different CACC vehicle ratios;

[0048] Figure 1(b) shows the velocity-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios;

[0049] Figure 1(c) shows the flow-speed curves of complex heterogeneous traffic flows under different CACC vehicle ratios.

[0050] Figure 2 This is a graph showing the relationship between the CACC vehicle ratio and the maximum flow rate of complex heterogeneous traffic flow.

[0051] Figure 3(a) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the CACC vehicle reaction time is 0.1s.

[0052] Figure 3(b) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the CACC vehicle reaction time is 0.2s.

[0053] Figure 3(c) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the CACC vehicle reaction time is 0.3s.

[0054] Figure 3(d) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the CACC vehicle reaction time is 0.4s.

[0055] Figure 4(a) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the ACC vehicle reaction time is 0s.

[0056] Figure 4(b) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the ACC vehicle reaction time is 0.1s.

[0057] Figure 4(c) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the ACC vehicle reaction time is 0.2s.

[0058] Figure 4(d) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the ACC vehicle reaction time is 0.3s.

[0059] Figure 4(e) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the ACC vehicle reaction time is 0.4s.

[0060] Figure 5(a) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the expected inter-vehicle time interval of CACC vehicles is 0.6s.

[0061] Figure 5(b) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the expected inter-vehicle time interval of CACC vehicles is 0.7s.

[0062] Figure 5(c) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the expected inter-vehicle time interval of CACC vehicles is 0.9s.

[0063] Figure 5(d) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the expected inter-vehicle time interval of CACC vehicles is 1.3s.

[0064] Figure 5(e) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the expected inter-vehicle time interval of CACC vehicles is 1.3s.

[0065] Figure 5(f) is a magnified view of the boxed portion of Figure 5(e);

[0066] Figure 6(a) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the expected inter-vehicle time interval of ACC vehicles is 1.6s.

[0067] Figure 6(b) shows the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle ratios when the expected inter-vehicle time interval of ACC vehicles is 2.2s.

[0068] Figure 7 It is a flow-density curve diagram of complex heterogeneous traffic flow under different proportions of traditional vehicles;

[0069] Figure 8 It is a graph showing the change in the proportion of traditional vehicles and the maximum flow rate of complex heterogeneous traffic flow. Detailed Implementation

[0070] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments, but this does not limit the scope of protection of this application.

[0071] This invention relates to a method for calculating the traffic capacity of complex heterogeneous traffic (hereinafter referred to as the method, see Figures 1-8), which includes the following:

[0072] 1. Design a stability criterion for complex heterogeneous traffic flows to determine the stability of complex heterogeneous traffic flows;

[0073] If the traditional car-following model uses the FVD model, then the traditional car-following model is:

[0074]

[0075] In the formula, a n (t), v n (t) represent the acceleration and velocity of the nth vehicle at time t, respectively. V represents the driver's sensitivity coefficient to the vehicle in front, V represents the optimal speed function, and Δx represents the speed coefficient. n (t), Δv n (t) represents the headway and speed difference between the nth vehicle and the vehicle in front, respectively, and λ * The model coefficients are represented by L, which represents the vehicle length.

[0076] The expression for the ACC (Adaptive Cruise Control) vehicle following model is:

[0077] a n (t)=k1[Δx n (t)-s0-Lt a v n (t)]+k2Δv n (t) (2)

[0078] In the formula, k1 represents the vehicle spacing control coefficient, s0 represents the minimum frontage distance, and t a k1 represents the expected inter-vehicle time distance for ACC vehicles, and k2 represents the speed difference control coefficient.

[0079] The CACC vehicle following model is:

[0080]

[0081] In the formula, v p Let k represent the speed of the nth car at the previous moment. p k d All are control coefficients, e n (t) represents the deviation between the actual front-end spacing and the desired front-end spacing. For e n The first derivative of (t), t c This indicates the expected inter-vehicle time interval for CACC vehicles;

[0082] Performing a first-order Taylor expansion on the velocity term in equation (3), we obtain:

[0083]

[0084] In the formula, Δt represents the time interval;

[0085] Existing research indicates that when traffic flow is in a steady state, all vehicle speeds are steady-state speeds, vehicle spacing is steady-state spacing, the speed difference between adjacent vehicles is zero, and the acceleration of all vehicles is zero, i.e., v0. n =v e , Δv n =0 and a n (t)=0, v n Let v represent the steady-state velocity of the nth vehicle. e h represents the steady-state vehicle speed. n This represents the distance between the nth car and the car in front. Denotes the steady-state vehicle spacing, Δv n Let represent the speed difference between the nth vehicle and the vehicle in front in a steady state. Then the steady-state vehicle following state equation is:

[0086]

[0087] In a stable traffic flow, applying a disturbance to a vehicle in the flow can change its driving state; assuming that the deviations in vehicle speed, headway, and speed difference in a stable traffic flow are δv n δh n and δ.Δv n The partial derivatives of the steady-state vehicle car-following state equation with respect to vehicle speed, headway, and speed difference are respectively... and Then we have the following formula:

[0088]

[0089] From equation (5), we can obtain that and The expressions are as follows:

[0090]

[0091] According to existing literature, and The constraint condition of equation (8) must be satisfied;

[0092]

[0093] In summary, the stability criterion for homogeneous traffic flow is shown in equation (9). If the inequality in equation (9) holds, it indicates that the homogeneous traffic flow is stable; otherwise, the homogeneous traffic flow is unstable.

[0094]

[0095] In the formula, N represents the total number of vehicles in the traffic flow. This represents the reaction time of the nth vehicle to changes in its distance from the vehicle in front. This represents the reaction time of the nth vehicle to the speed change of the vehicle in front;

[0096] Complex heterogeneous traffic flow consists of conventional vehicles, ACC vehicles, and CACC vehicles. Assume the proportions of conventional vehicles, ACC vehicles, and CACC vehicles are P, respectively. R P A and P C P R +P A +P C =1, P R P A P C ∈[0,1];

[0097] According to equation (9), the stability criterion for complex heterogeneous traffic flow is shown in equation (10). If the inequality in equation (10) holds, it indicates that the complex heterogeneous traffic flow is stable; otherwise, the complex heterogeneous traffic flow is unstable.

[0098] P R F R +P A F A +P C F C ≥0 (10)

[0099] In the formula, F R F A and F C These are the stability terms for conventional vehicles, ACC vehicles, and CACC vehicles, respectively, with the following expressions:

[0100]

[0101]

[0102]

[0103] In the formula, g v g h and g Δv Let represent the partial derivatives of the traditional car-following model with respect to vehicle speed, headway, and speed difference, respectively, calculated according to the traditional car-following model in equation (1). This indicates the reaction time of a conventional vehicle to changes in its distance from the vehicle in front. This represents the reaction time of a conventional vehicle to a change in the speed of the vehicle in front; y v y h and y Δv Let represent the partial derivatives of the ACC vehicle following model with respect to vehicle speed, headway, and speed difference, respectively, calculated according to the ACC vehicle following model in equation (2). This indicates the reaction time of the ACC vehicle to changes in its distance from the vehicle in front. Indicates the reaction time of the ACC vehicle to changes in the speed of the vehicle in front; and Let represent the partial derivatives of the CACC vehicle following model with respect to vehicle speed, headway, and speed difference, respectively, calculated according to the CACC vehicle following model in equation (4). This indicates the CACC vehicle's reaction time to changes in its distance from the vehicle in front. This indicates the CACC vehicle's reaction time to changes in the speed of the vehicle in front;

[0104] 2. Under the stable state of complex heterogeneous traffic flow, establish a basic flow-density diagram model of complex heterogeneous traffic flow, and obtain the expression of the traffic capacity of complex heterogeneous traffic flow based on the basic flow-density diagram model of complex heterogeneous traffic flow.

[0105] Under the steady-state conditions of homogeneous traffic flow, the steady-state "speed-frontage distance" functions for conventional vehicles, ACC vehicles, and CACC vehicles are as follows:

[0106]

[0107] f A (v e )=Δx A =(t a +τ a )v e +L+s0 (15)

[0108] f C (v e)=Δx C =(t c +τ c )v e +L+s0 (16)

[0109] In the formula, Δx R Δx A and Δx C The steady-state headway of the conventional vehicle, the ACC vehicle, and the CACC vehicle are respectively represented, v0 represents the free-flow vehicle speed, and τ represents the vehicle speed. r τ a and τ c These represent the reaction times of conventional vehicles, ACC vehicles, and CACC vehicles, respectively, and α represents the sensitivity coefficient.

[0110] The road length covered by traffic flow can be considered as the sum of the headway distances of all vehicles under steady-state traffic flow. Therefore, the road length B0 covered by complex heterogeneous traffic flow is:

[0111] B0 = NP R Δx R +NP A Δx A +NP C Δx C (17)

[0112] According to equation (17), the average headway in the steady state of complex heterogeneous traffic flow is:

[0113]

[0114] Under steady-state traffic flow conditions, density and headway are reciprocals. Therefore, the density k of complex heterogeneous traffic flow is:

[0115]

[0116] The basic flow-density graph model for complex heterogeneous traffic flows is as follows:

[0117] q = kv e (20)

[0118] In the formula, q represents the flow rate of complex heterogeneous traffic flow;

[0119] Substituting equations (14) to (16) into equation (19), and then into equation (20), we obtain equation (21):

[0120]

[0121] In equation (21), let:

[0122]

[0123] According to equation (21), the function relating complex heterogeneous traffic flow volume and steady-state vehicle speed is:

[0124] q(v e ) = v e / u(v e ) (twenty three)

[0125] According to equation (23), for the steady-state vehicle speed v e Taking the first derivative, we get:

[0126]

[0127] In the formula, Represents u(v) e For steady-state vehicle speed v e The first derivative of is expressed as:

[0128]

[0129] From equation (24), let Then there is right Solve the problem to obtain the possible extreme points.

[0130] Then, according to equation (24), the steady-state vehicle speed v e Taking the first derivative, we get:

[0131]

[0132] In the formula, Represents u(v) e For steady-state vehicle speed v e The second derivative of is expressed as:

[0133]

[0134] From equations (22) and (25), we can obtain:

[0135]

[0136] Since the speed of a vehicle in free flow is generally greater than the speed of a vehicle in steady state, therefore v e <v0, will v e Substituting <v0 into equations (22), (25), (28), and (28) respectively, we get: u(v e ) > 0, but:

[0137]

[0138] From equation (29), we can obtain that Heng was established, making but For q(v) e The maximum point of ) then The maximum value of the function relating complex heterogeneous traffic flow volume to steady-state vehicle speed, i.e., within the speed range of 0 to v0. The expression representing the traffic capacity of complex heterogeneous traffic is as follows:

[0139]

[0140] The traffic flow capacity of complex heterogeneous traffic is calculated using equation (30).

[0141] Simulation verification:

[0142] Numerical simulations of capacity were performed using MATLAB software to simulate complex heterogeneous traffic flows. The simulation method is described in (Qin Yanyan. Research on the Analysis Method of Heterogeneous Traffic Flow Characteristics under Intelligent Connected Environment [D]. Southeast University, 2019). In the experimental scenario, the road segment was assumed to be a single-lane highway segment with a road length of 1200m, an average vehicle length of 5m, and an average vehicle width of 2m. There were no restrictions on traffic demand upstream and downstream of the road segment, with the aim of statistically determining the maximum flow rate. ACC vehicles, CACC vehicles, and conventional vehicles were randomly distributed on the road segment, with the proportion of conventional vehicles, P, set to... R =0.1, the ratio of CACC vehicles to ACC vehicles is P C (0≤P C ≤0.9) and P A =0.9-P C The free-flow velocity was set to 33.0 m / s, the simulation time was 10 h, and the simulation step size was 0.1 s. Traffic capacity simulation was carried out under different CACC vehicle ratios.

[0143] The traffic capacity of complex heterogeneous traffic is calculated according to equation (30), and the theoretical analysis result of the traffic capacity is obtained. The numerical simulation result of the traffic capacity is obtained by MATLAB software. The comparison of the two results is shown in Table 1.

[0144] Table 1 Comparison of theoretical analysis and numerical simulation results of traffic capacity.

[0145]

[0146] As shown in Table 1, the maximum flow rate gradually increases with the increase of the CACC vehicle ratio. When the CACC vehicle ratio is 0.9, the maximum flow rate is about 1.6 times that when the CACC vehicle ratio is 0. In addition, due to the limitations of free flow speed, the capacity of complex heterogeneous traffic flow will not increase indefinitely with the increase of the CACC vehicle ratio. Furthermore, the theoretical analysis results of the capacity are basically consistent with the numerical simulation results, with the deviation percentages ranging from 0.5% to 3.5%. This shows that the reliability of calculating the capacity of complex heterogeneous traffic flow according to Equation (30) is relatively high. Figures 1(a) to (c) are the flow-density, speed-density, and flow-speed curves of complex heterogeneous traffic flow, respectively. When the traditional vehicle ratio is constant, the capacity of complex heterogeneous traffic flow gradually increases with the gradual increase of the CACC vehicle ratio and the gradual decrease of the ACC vehicle ratio. Therefore, increasing the CACC vehicle ratio can significantly improve the capacity of complex heterogeneous traffic flow. Based on the numerical simulation results of the capacity, the following graphs are plotted: Figure 2 The graph showing the relationship between the CACC vehicle ratio and maximum flow rate is shown below; Figure 2 It can be seen that, under the condition that the reaction time of the three types of vehicles remains unchanged, as the proportion of CACC vehicles increases, the maximum flow of complex heterogeneous traffic flow gradually increases, that is, the capacity gradually improves, and the slope of the curve gradually increases, that is, the capacity increase gradually increases, and the capacity improvement effect is more significant.

[0147] For traditional vehicles, the driver relies entirely on the vehicle itself to obtain information about surrounding vehicles. The driver needs to constantly monitor the speed changes of the vehicle in front. After obtaining information about the speed difference and distance between the vehicle and the vehicle in front, the driver still needs a certain reaction time to take appropriate measures. According to relevant literature, the reaction time of traditional vehicles is usually 0.2 to 1 second. For CACC vehicles, CACC vehicles can obtain information about the vehicles in front and the surrounding environment in advance through vehicle-to-vehicle communication technology. Therefore, the reaction time of CACC vehicles is mainly due to communication and control delays, and the reaction time of CACC vehicles is usually 0 to 0.4 seconds. Unlike CACC vehicles, ACC vehicles cannot communicate with surrounding vehicles and mainly obtain information about the vehicle in front through onboard detection equipment. The reaction time is the time delay of the onboard detection equipment, and the reaction time of ACC vehicles is usually 0 to 0.4 seconds.

[0148] a) To investigate the impact of different reaction times of conventional vehicles, ACC vehicles, and CACC vehicles on the flow capacity of complex heterogeneous traffic, the proportion of conventional vehicles was set to 0.1, the reaction times of conventional vehicles and ACC vehicles were 0.4s and 0.2s, respectively, and the reaction times of CACC vehicles were set to 0.1, 0.2, 0.3, and 0.4s, respectively, with other parameters remaining constant. Figures 3(a) to (d) show the flow-density curves of complex heterogeneous traffic under different CACC vehicle proportions. Comparative analysis shows that, under the condition of the same CACC vehicle reaction time, the flow of complex heterogeneous traffic gradually increases with the increase of the CACC vehicle proportion. Under the condition of the same CACC vehicle proportion, the flow gradually increases with the shortening of the CACC vehicle reaction time, and the flow capacity of complex heterogeneous traffic is significantly improved. When the CACC vehicle reaction time is 0.4s, increasing the CACC vehicle proportion does not significantly improve the flow capacity of complex heterogeneous traffic.

[0149] Similarly, with the proportion of conventional vehicles set to 0.1, and the reaction times of conventional vehicles and CACC vehicles to be 0.4s and 0s respectively, and the reaction times of ACC vehicles to be 0, 0.1, 0.2, 0.3 and 0.4s respectively, while keeping the other parameters unchanged, the flow-density curves of complex heterogeneous traffic flow under different CACC vehicle proportions are shown in Figures 4(a) to (e). As the reaction time of ACC vehicles shortens, the traffic capacity of complex heterogeneous traffic flow shows an upward trend, but the increase is small. When the proportion of CACC vehicles is 0.9, the complex heterogeneous traffic flow consists of 10% conventional vehicles and 90% CACC vehicles, so the density and flow rate change curves of complex heterogeneous traffic flow under different ACC vehicle reaction times are the same. When the proportion of CACC vehicles is 0.7, the optimal density of complex heterogeneous traffic flow hardly changes under different ACC vehicle reaction times, and the maximum flow rate is between 3000 and 3500 veh / h, with a small change.

[0150] In summary, shortening the reaction time of ACC and CACC vehicles, as well as increasing the proportion of CACC vehicles, can improve the flow capacity of complex heterogeneous traffic. If the reaction time of CACC vehicles is too long, increasing the proportion of CACC vehicles will not significantly increase the flow rate of complex heterogeneous traffic. Compared with ACC vehicles, reducing the reaction time of CACC vehicles has a more significant effect on improving the flow capacity of complex heterogeneous traffic.

[0151] b) To study the impact of expected inter-vehicle headway on the flow capacity of complex heterogeneous traffic, the reaction time of CACC vehicles was set to 0 s, the reaction time of ACC vehicles to 0.2 s, the expected inter-vehicle headway of ACC vehicles to 1.1 s, the proportion of conventional vehicles to be 0.1, and the expected inter-vehicle headway of CACC vehicles to be 0.6, 0.7, 0.9, 1.1, and 1.3 s, respectively. The flow-density curves of complex heterogeneous traffic flow are shown in Figures 5(a) to (e). Figure 5(f) is a magnified view of the boxed portion in Figure 5(e). As shown in Figure 5, the flow capacity of complex heterogeneous traffic gradually increases as the expected inter-vehicle headway of CACC vehicles decreases. Therefore, reducing the expected inter-vehicle headway of CACC vehicles is beneficial to significantly improving the flow capacity of complex heterogeneous traffic. When 0 ≤ P c When the CACC vehicle expected inter-vehicle time interval is ≤0.3, reducing the CACC vehicle expected inter-vehicle time interval has no significant effect on improving traffic capacity. In Figure 5(f), when the CACC vehicle expected inter-vehicle time interval is 1.3s, the basic curves under different CACC vehicle ratios intersect. When the fleet density is less than the density at the intersection, the traffic capacity of complex heterogeneous traffic is improved as the CACC vehicle ratio increases. However, when the fleet density is greater than the density at the intersection, the higher the CACC vehicle ratio, the faster the traffic capacity of complex heterogeneous traffic decreases. This is because under the condition of a larger CACC vehicle inter-vehicle time interval, the traffic capacity of traditional vehicles is greater than that of CACC vehicles. Therefore, when the density of complex heterogeneous traffic flow is large and the CACC vehicle expected inter-vehicle time interval is large, the flow rate of complex heterogeneous traffic flow decreases as the CACC vehicle ratio increases. At this time, the CACC vehicle expected inter-vehicle time interval is one of the important parameters for improving traffic capacity. Reducing the CACC vehicle expected inter-vehicle time interval can significantly improve the traffic capacity of complex heterogeneous traffic.

[0152] Similarly, by setting the reaction time of CACC vehicles to 0s, the reaction time of ACC vehicles to 0.2s, the expected inter-vehicle distance of CACC vehicles to 0.6s, the proportion of conventional vehicles to 0.1, and the expected inter-vehicle distances of ACC vehicles to 1.6s and 2.2s respectively, the flow-density curves of complex heterogeneous traffic flow are obtained as shown in Figures 6(a) and (b). The analysis shows that reducing the expected inter-vehicle distance of ACC vehicles helps to improve the traffic capacity of complex heterogeneous traffic. However, compared with the expected inter-vehicle distance of CACC vehicles, reducing the expected inter-vehicle distance of ACC vehicles has no significant effect on improving the traffic capacity of complex heterogeneous traffic.

[0153] To investigate the impact of the proportion of conventional vehicles on the flow capacity of complex heterogeneous traffic, the reaction time of CACC vehicles was set to 0 s, and the reaction time and proportion of ACC vehicles were set to 0.2 s and 0.1 s, respectively. The proportion of conventional vehicles was set to 0, 0.1, 0.3, 0.5, 0.7, and 0.9, respectively. The results are as follows: Figure 7The diagram shows the flow-density curves for complex heterogeneous traffic flow. It demonstrates that reducing the proportion of conventional vehicles helps improve the traffic capacity of complex heterogeneous traffic. Because the maximum flow rate of complex heterogeneous traffic varies with the proportion of conventional vehicles, the diagram is plotted as follows: Figure 8 The curves showing the maximum flow rate variation of complex heterogeneous traffic flows under different proportions of traditional vehicles are shown; for example... Figure 8 It can be seen that as the proportion of traditional vehicles decreases, the absolute value of the curve slope gradually increases, reaching 0.5. <P R When the value is less than 0.9, the maximum flow rate is approximately linearly related to the proportion of traditional vehicles, while when the value is less than 0.9... <P R When the value is less than 0.5, reducing the proportion of conventional vehicles can significantly increase the maximum flow rate, meaning the change in maximum flow rate gradually increases. Therefore, reducing the proportion of conventional vehicles is beneficial for improving the traffic flow capacity in complex and heterogeneous traffic environments under the Internet of Vehicles (IoV) model, and significantly increases the maximum flow rate.

[0154] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for calculating the capacity of complex heterogeneous traffic flow, wherein the complex heterogeneous traffic flow consists of conventional vehicles, ACC vehicles, and CACC vehicles; characterized in that, The method includes the following:

1. Based on the homogeneous traffic flow stability criterion, design the complex heterogeneous traffic flow stability criterion as shown in equation (10) to determine the stability of the complex heterogeneous traffic flow; if the inequality of equation (10) holds, it indicates that the complex heterogeneous traffic flow is stable; otherwise, the complex heterogeneous traffic flow is unstable. P R F R +P A F A +P C F C ≥0 (10) In the formula, P R P A and P C The proportions of traditional vehicles, ACC vehicles, and CACC vehicles are respectively, P R +P A +P C =1, P R P A P C ∈[0,1];F R F A and F C These are the stability terms for conventional vehicles, ACC vehicles, and CACC vehicles, respectively, with the following expressions: In the formula, g v g h and g Δv These represent the partial derivatives of the traditional car-following model with respect to vehicle speed, headway, and speed difference, respectively. This indicates the reaction time of a conventional vehicle to changes in its distance from the vehicle in front. This represents the reaction time of a conventional vehicle to a change in the speed of the vehicle in front; y v y h and y Δv Let represent the partial derivatives of the ACC vehicle following model with respect to vehicle speed, headway, and speed difference, respectively. This indicates the reaction time of the ACC vehicle to changes in its distance from the vehicle in front. Indicates the reaction time of the ACC vehicle to changes in the speed of the vehicle in front; and Let represent the partial derivatives of the CACC car-following model with respect to vehicle speed, headway, and speed difference, respectively. This indicates the CACC vehicle's reaction time to changes in its distance from the vehicle in front. This indicates the CACC vehicle's reaction time to changes in the speed of the vehicle in front; 2. Under stable traffic flow conditions, establish a basic flow-density diagram model of complex heterogeneous traffic flow as shown in Equation (20); q=kv e (20) In the formula, q represents the flow rate of complex heterogeneous traffic flow, and v e Let represent the steady-state vehicle speed, and k represent the density of the complex heterogeneous traffic flow; In the formula, Δx R Δx A and Δx C f represents the steady-state headway of the conventional vehicle, the ACC vehicle, and the CACC vehicle, respectively. R (v e ), f A (v e ) and f C (v e Let ) represent the steady-state speed-headway function of conventional vehicles, ACC vehicles, and CACC vehicles under steady-state conditions of homogeneous traffic flow, respectively. The expressions are: f A (v e )=Δx A =(t a +τ a )v e +L+s0(15) f C (v e )=Δx C =(t c +τ c )v e +L+s0 (16) In the formula, s0 represents the minimum headway, v0 represents the free-flow vehicle speed, and τ r τ a and τ c These represent the reaction times of conventional vehicles, ACC vehicles, and CACC vehicles, respectively; L represents the vehicle length; α represents the sensitivity coefficient; and t represents the reaction time of the vehicle. a t c These represent the expected inter-vehicle time intervals for ACC vehicles and CACC vehicles, respectively. Substituting equations (14) to (16) into equation (19), and then into equation (20), we obtain equation (21): In equation (21), let: According to equation (21), the function relating complex heterogeneous traffic flow volume and steady-state vehicle speed is: q(v e )=v e / u(v e ) (23) According to equation (23), for the steady-state vehicle speed v e Taking the first derivative, we get: In the formula, Represents u(v) e For steady-state vehicle speed v e The first derivative of is expressed as: From equation (24), let Then there is right Solve the problem to obtain the possible extreme points. Then, according to equation (24), the steady-state vehicle speed v e Taking the first derivative, we get: In the formula, Represents u(v) e For steady-state vehicle speed v e The second derivative of is expressed as: From equations (22) and (25), we can obtain: Since the speed of a vehicle in free flow is greater than the speed of a vehicle in steady state, therefore v e <v0, will v e Substituting <v0 into equations (22), (25), (28), and (28) respectively, we get: u(v e ) > 0, but: From equation (29), we can obtain that Heng was established, making but For q(v) e The maximum point of ) then The maximum value of the function relating complex heterogeneous traffic flow volume to steady-state vehicle speed, i.e., within the speed range of 0 to v0. The expression representing the flow capacity of complex heterogeneous traffic is: The flow capacity of complex heterogeneous traffic is calculated using equation (30); The ACC vehicles mentioned above are adaptive cruise control vehicles, while CACC vehicles are cooperative adaptive cruise control vehicles.

2. The method for calculating the traffic capacity of complex heterogeneous traffic according to claim 1, characterized in that, The stability criterion for homogeneous traffic flow is shown in equation (9). If the inequality in equation (9) holds, it indicates that the homogeneous traffic flow is stable; otherwise, the homogeneous traffic flow is unstable. In the formula, N represents the total number of vehicles in the traffic flow. and Let represent the partial derivatives of the steady-state vehicle following state equation with respect to vehicle speed, headway, and speed difference, respectively. This represents the reaction time of the nth vehicle to changes in its distance from the vehicle in front. This represents the reaction time of the nth vehicle to the speed change of the vehicle in front.

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