Mixed lane traffic capacity upper and lower limit calculation and analysis method considering formation scale

Abstract

The invention relates to the technical field of traffic engineering, in particular to a hybrid lane traffic capacity upper and lower limit calculation and analysis method considering formation scale, which comprises the following steps of: acquiring vehicle following modes of a manual driving vehicle and a networked automatic driving vehicle in a hybrid lane to be analyzed and a corresponding safe time headway; the method comprises the following steps: according to a constraint condition and a target function, inputting the constraint condition and the maximum formation scale of the networked autonomous vehicle into a preset first optimization model and a preset second optimization model to obtain the minimum value and the maximum value of the average time headway of a longitudinal lane on a to-be-analyzed hybrid lane, the first optimization model and the second optimization model being constructed according to the constraint condition and the target function; and calculating the upper limit value and the lower limit value of the traffic capacity of the to-be-analyzed mixed traffic lane based on the minimum value and the maximum value of the average time headway of the longitudinal lane, and completing calculation and analysis of the upper limit and the lower limit of the traffic capacity of the to-be-analyzed mixed traffic lane. According to the invention, decision support and technical support can be provided for traffic decision makers to cope with future mixed traffic scenes.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic engineering, and in particular to a method for calculating and analyzing upper and lower limits of mixed traffic lane capacity taking into account the size of a platoon. Background Art

[0002] Compared with human-driven vehicles (HVs), connected and autonomous vehicles (CAVs) have stronger information perception capabilities and faster reaction times, and can theoretically maintain a smaller safe headway distance with the vehicle in front. In addition, through real-time communication and mutual coordination between vehicles, CAVs can travel on the road in the form of a CAV convoy through formation, which is expected to further shorten the safe headway distance between CAV vehicles in the convoy. However, due to limitations such as communication range and signal delay, the size of the CAV convoy is not unlimited, and HVs will not be completely replaced by CAVs in the short term. During a longer transition period, HVs and CAVs will coexist in the traffic network and mix on urban roads.

[0003] The analysis of lane capacity in a mixed HV and CAV scenario is more challenging than that in a pure HV environment. Unlike a fixed value in a pure HV environment, the lane capacity in a mixed HV and CAV scenario is a random variable. Specifically, due to the differences in technical characteristics of different types of vehicles and the limitations on the size of the CAV fleet, the safe headway that a following vehicle can maintain is related to the types of vehicles in front and behind and whether the following vehicle is in the same CAV formation as the leading vehicle. Five vehicle following modes can be divided based on the above two factors. Since the average safe headway directly determines the traffic density and maximum traffic flow, the lane capacity in a mixed HV and CAV traffic scenario is a variable related to the spatial distribution of the two types of vehicles on the longitudinal lane. Since the spatial distribution of the two types of vehicles on the longitudinal lane is uncertain, the mixed lane capacity is a random variable.

[0004] Since lane capacity is an important parameter for traffic planning and management strategy decision-making, it is a scientific problem that needs to be solved urgently to study the upper and lower limits of this random variable and analyze the spatial distribution of the two types of vehicles on the longitudinal lane when the upper and lower limits are reached.

[0005] In the prior art, Li Tongfei et al. proposed a method and system for calculating and analyzing the upper and lower limits of lane capacity in mixed traffic scenarios. Without considering the CAV platooning, the mixed traffic vehicle following modes are simply divided into four categories by assuming that the safe headway of the vehicle during driving is only related to the type of vehicles traveling in front and behind. On this basis, a mathematical programming model is established to calculate and analyze the upper and lower limits of mixed traffic lane capacity. Without considering that CAVs can form a platoon and that platooning can reduce the safe headway, only four types of vehicle following modes and safe headway types are considered, simplifying the classification of vehicle following modes and the corresponding safe headway values. However, in practice, CAVs are generally recognized to be able to travel in platoons and reduce the safe headway of vehicles in the CAV fleet, resulting in the technology not being able to be applied to the calculation and analysis of mixed traffic lane capacity considering the size of the platoon, and being unable to accurately calculate and analyze the upper and lower limits of capacity in mixed traffic scenarios, which has huge limitations.

[0006] Therefore, in view of the above technical defects, the present invention proposes a method for calculating and analyzing the upper and lower limits of the mixed lane capacity taking into account the size of the formation. Summary of the invention

[0007] The purpose of the present invention is to provide a method for calculating and analyzing the upper and lower limits of the mixed lane capacity taking into account the size of the formation, which can calculate the lane capacity value under the mixed conditions of HV and CAV, and obtain the corresponding spatial distribution of HV and CAV on the longitudinal lane when the lane capacity reaches the upper and lower limits, so as to provide decision support and technical guarantee for traffic decision makers to deal with future mixed traffic scenarios.

[0008] To achieve the above object, the present invention provides the following solutions:

[0009] The calculation and analysis methods of the upper and lower limits of mixed lane capacity considering the size of the platoon include:

[0010] Obtain the vehicle following modes and corresponding safe headway distances of manually driven vehicles and connected autonomous vehicles in the mixed lane to be analyzed, as well as the maximum platoon size of connected autonomous vehicles;

[0011] Input the vehicle following mode and the corresponding safe headway time, as well as the maximum formation size of the networked autonomous driving vehicles into the preset first optimization model and the second optimization model, to obtain the minimum and maximum average headway time of the longitudinal lane on the mixed traffic lane to be analyzed, wherein the first optimization model and the second optimization model are constructed according to the constraint conditions and the objective function;

[0012] The upper and lower limits of the capacity of the mixed traffic lane to be analyzed are calculated based on the minimum and maximum average headway time of the longitudinal lane, and the calculation and analysis of the upper and lower limits of the capacity of the mixed traffic lane to be analyzed are completed.

[0013] Optionally, constructing the first optimization model and the second optimization model according to the constraint conditions and the objective function includes:

[0014] Define vehicle following modes and corresponding safe headway and following probability in mixed traffic scenarios, wherein the vehicle following modes include HV following HV, HV following CAV, CAV following HV, CAV following a CAV fleet that has reached the largest scale, and CAV following another CAV in the same CAV fleet, wherein HV represents a manually driven vehicle and CAV represents a connected autonomous vehicle;

[0015] Determining decision variables according to the following probability of the vehicle following mode and the formation probability of CAV fleets of different sizes, and constructing constraint conditions based on the decision variables;

[0016] Constructing an objective function based on the safe headway and following probability of the vehicle following mode;

[0017] The first optimization model and the second optimization model are constructed based on the constraint conditions and the objective function.

[0018] Optionally, the decision variable is Among them, p HH is the probability of HV following HV, p HC is the probability of HV following CAV, p CH is the probability of CAV following HV, p CP is the probability of a CAV following a CAV fleet that has reached its maximum size, p CC is the probability of an AV following another CAV in the same CAV convoy, y1 is the ratio of the number of CAVs that do not form a convoy with the front and rear vehicles to the total number of vehicles, and y L is the ratio of the number of CAV fleets that have reached their maximum size to the total number of vehicles, The probability of a CAV fleet that has reached its maximum size being followed by an HV is The probability of a CAV being followed by a CAV fleet that has reached its maximum size.

[0019] Optionally,

[0020] The constraints are:

[0021] All CAV fleets that have reached maximum size are followed by HVs or CAVs:

[0022]

[0023] The proportion of CAVs following the largest CAV fleet is equal to the probability of CAVs following the largest CAV fleet:

[0024]

[0025] The sum of the product of the ratio of CAV fleets of different sizes and the number of CAVs following CAVs in a CAV fleet is equal to the probability of a CAV following another CAV in the same CAV fleet:

[0026]

[0027] The sum of the proportion of CAV fleets that have not reached the maximum scale and the proportion of HVs that are closely behind the CAV fleets that have reached the maximum scale is equal to the probability of HVs following CAVs:

[0028]

[0029] The sum of the probability of HV following HV and CAV following HV is equal to the HV penetration rate:

[0030] p HH +p CH =1-P C

[0031] The sum of the following probabilities of an HV following a CAV, a CAV following a CAV fleet that has reached its maximum size, and a CAV following another CAV in the same CAV fleet is equal to the CAV penetration rate:

[0032] p CP +p CC +p HC =P C

[0033] The sum of the probability of HV following HV and HV following CAV is equal to the HV penetration rate:

[0034] p HH +p HC =1-P C

[0035] The sum of the following probabilities of a CAV following an HV, a CAV following a CAV fleet that has reached its maximum size, and a CAV following another CAV in the same CAV fleet is equal to the CAV penetration rate:

[0036] p CH +p CP +p CC =P C

[0037] The ratios of different car-following modes and different sizes of CAV fleets are non-negative:

[0038]

[0039] Among them, y i is the ratio of the number of CAV fleets of size i to the total number of vehicles, P C is the CAV penetration rate.

[0040] Optionally, the objective function is:

[0041] h=h HH p HH +h HC p HC +h CH p CH +h CP p CP +h CC p CC

[0042] Where h is the average headway time of the longitudinal lane, h HH is the safe headway time between HV and HV, h HC is the safe headway time between HV and CAV, h CH is the safe headway distance between CAV and HV, h CP is the safe headway time for a CAV to follow a CAV convoy that has reached its maximum size, h CC It is the safe headway time for an AV to follow another CAV in the same CAV convoy.

[0043] Optionally, the first optimization model is:

[0044]

[0045] The second optimization model is:

[0046]

[0047] Where h is the minimum average headway time of the longitudinal lane, It is the maximum average headway time of the longitudinal lane.

[0048] Optionally, the method for calculating the upper limit value of the traffic capacity of the mixed traffic lane to be analyzed is:

[0049]

[0050] The method for calculating the lower limit value of the traffic capacity of the mixed traffic lane to be analyzed is:

[0051]

[0052] in, is the upper limit of the mixed lane capacity, and c is the lower limit of the mixed lane capacity.

[0053] Optionally, the method further comprises:

[0054] Based on the decision variable values ​​corresponding to the upper and lower limits of the traffic capacity, the spatial distribution of manually driven vehicles and networked autonomous driving vehicles on the longitudinal lane of the mixed lane to be analyzed is analyzed.

[0055] The beneficial effects of the present invention are:

[0056] The present invention innovatively transforms the problem of calculating the upper and lower limits of the mixed lane capacity considering the formation into the problem of the longitudinal arrangement of two types of vehicles on a single-lane circular road, designs and defines variables representing CAV fleets of different sizes, and successfully constructs the relationship between the proportion of CAV fleets of different sizes in mixed traffic flow and the proportion of five types of vehicle following modes in mixed traffic flow based on the setting of a single-lane circular road. Based on this, the method of establishing a linear programming model is used to solve the problem of calculating the upper and lower limits of the mixed lane capacity, and the spatial distribution of the two types of vehicles on the longitudinal lane and the formation of CAV vehicles can be analyzed. The method proposed by the present invention can be used for solving and analyzing the upper and lower limits of the mixed lane capacity under any parameter conditions, and the model in the form of a linear programming problem is easy to solve efficiently using very mature commercial solvers such as CPLEX, Matlab, and Gurobi, and can quickly calculate the lane capacity value under the mixed conditions of HV and CAV, and obtain the corresponding spatial distribution of HV and CAV on the longitudinal lane when the lane capacity obtains the upper and lower limits, which can provide decision support and technical guarantee for traffic decision makers to deal with future mixed traffic scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0058] Figure 1 This is a flow chart of a method for calculating and analyzing upper and lower limits of mixed lane capacity considering platoon size according to an embodiment of the present invention;

[0059] Figure 2 Schematic diagram of different types of vehicle following modes in a mixed traffic scenario according to an embodiment of the present invention;

[0060] Figure 3 A schematic diagram of all possible combinations of a CAV fleet of any size and adjacent vehicles on a longitudinal lane according to an embodiment of the present invention;

[0061] Figure 41 is a curve showing the change in the upper and lower limits of the mixed lane capacity under different CAV penetration rates according to an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0063] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0064] This embodiment provides a method for calculating and analyzing the upper and lower limits of mixed lane capacity considering the size of the platoon, such as Figure 1 As shown, including:

[0065] Obtain the vehicle following modes and corresponding safe headway distances of manually driven vehicles and connected autonomous vehicles in the mixed lane to be analyzed, as well as the maximum platoon size of connected autonomous vehicles;

[0066] Input the vehicle following mode and the corresponding safe headway time, as well as the maximum formation size of the networked autonomous driving vehicles into the preset first optimization model and the second optimization model, and obtain the minimum and maximum average headway time of the longitudinal lane on the mixed lane to be analyzed, wherein the first optimization model and the second optimization model are constructed according to the constraint conditions and the objective function;

[0067] The upper and lower limits of the capacity of the mixed traffic lane to be analyzed are calculated based on the minimum and maximum values ​​of the average headway time of the longitudinal lane, and the calculation and analysis of the upper and lower limits of the capacity of the mixed traffic lane to be analyzed are completed.

[0068] Specifically, the first optimization model is used to obtain the minimum value of the average headway time on the longitudinal lane, and the second optimization model is used to obtain the maximum value of the average headway time on the longitudinal lane. This embodiment can calculate the lane capacity value under the mixed traffic condition of HV and CAV through the first optimization model and the second optimization model, and obtain the corresponding spatial distribution of HV and CAV on the longitudinal lane when the lane capacity has the upper and lower bounds, which can provide decision support and technical guarantee for traffic decision makers to deal with future mixed traffic scenarios.

[0069] Further, constructing the first optimization model and the second optimization model according to the constraint conditions and the objective function includes:

[0070] Define vehicle following modes and corresponding safe headway and following probability in mixed traffic scenarios, where the vehicle following modes include HV following HV, HV following CAV, CAV following HV, CAV following the largest CAV fleet, and CAV following another CAV in the same CAV fleet, where HV represents a manually driven vehicle and CAV represents a connected autonomous vehicle;

[0071] Determine decision variables based on the following probability of the vehicle following mode and the formation probability of CAV fleets of different sizes, and construct constraint conditions based on the decision variables;

[0072] The objective function is constructed based on the safe headway and following probability of the vehicle following mode;

[0073] A first optimization model and a second optimization model are constructed based on the constraint conditions and the objective function.

[0074] This embodiment constructs the first optimization model and the second optimization model according to the constraint conditions and the objective function, and specifically includes the following steps:

[0075] Step 1: Classify vehicle following mode and safe headway time type, and define related symbols;

[0076] like Figure 2 As shown in the figure, in a mixed traffic flow composed of HVs and CAVs, the two vehicles following each other can be divided into five following modes according to the types of the vehicles and whether they belong to the same CAV fleet, namely: one HV follows another HV, one HV follows a CAV, one CAV follows an HV, one CAV follows a CAV fleet that has reached the maximum size (i.e., the front and rear CAVs are not in the same fleet), and one CAV follows another CAV in the same CAV fleet (i.e., the front and rear CAVs are in the same fleet). During driving, vehicles maintain different safe headway times in different following modes. Therefore, there are five following modes in the mixed traffic flow of HVs and CAVs, corresponding to the five safe headway times.

[0077] Let L represent the maximum size of a CAV convoy, that is, the maximum number of vehicles allowed in a CAV convoy. When the size of a CAV convoy reaches L, the subsequent CAVs can no longer form a convoy with the preceding vehicle and can only travel alone or form a new CAV convoy with the subsequent CAVs. For this reason, the symbols "H" and "C" are used to represent the two types of vehicles, HV and CAV, respectively, and the symbol "P" is used to represent the CAV convoy that has reached the maximum size. The combination of "H", "C", and "P" as subscripts represents different vehicle following modes, that is, "HH" represents an HV following another HV, "HC" represents an HV following a CAV, "CH" represents a CAV following an HV, "CP" represents a CAV following a CAV convoy that has reached the maximum size, and "CC" represents a CAV following another CAV in the same CAV convoy. The variables and parameters related to the five vehicle following modes are distinguished by these subscripts, and let h with different subscripts represent the safe headway time in different vehicle following modes, that is, h HH 、h HC 、h CH 、h CP 、h CC , different subscripts p represent the proportion of different vehicle following modes in mixed traffic flow, that is, p HH 、p HC 、p CH 、p CP 、p CC .

[0078] Step 2: Establish a calculation model for the upper and lower limits of mixed traffic lane capacity;

[0079] Step 2.1: The problem of calculating the upper and lower limits of the mixed lane capacity is transformed into the problem of arranging two types of vehicles on the circular road;

[0080] like Figure 3 As shown, it is assumed that HVs and CAVs travel on a single-lane circular road, thereby ensuring that the number of headways is equal to the number of vehicles. This embodiment can equate the problem of calculating the upper and lower limits of the mixed lane capacity to the following mathematical programming problem: given the known CAV penetration rate and the maximum size of the CAV fleet, how to arrange the two types of vehicles on the circular single-lane road to achieve the maximum or minimum mixed lane capacity. Based on this, a mathematical programming model is established to solve the upper and lower limits of the mixed lane capacity.

[0081] Step 2.2: Determine the decision variables;

[0082] The CAV fleet in mixed traffic flow includes both CAV fleets that have reached the maximum size and CAV fleets that have not reached the maximum size. Figure 2All possible combinations of CAV convoys of any size and adjacent vehicles on the longitudinal lane are shown, where the dashed vehicle outline represents an HV or a CAV convoy that has reached the maximum size. It can be seen that all CAV convoys that have not reached the maximum size will be followed by an HV, while all CAV convoys that have reached the maximum size will be followed by an HV or a CAV. At the same time, the leading vehicle of a CAV convoy of any size can be an HV or a CAV convoy that has reached the maximum size.

[0083] In order to distinguish CAV fleets of different sizes, let y i represents the ratio of the number of CAV fleets of size i to the total number of vehicles in the mixed traffic flow, i∈{1,2,...L}. Among them, y1 represents the ratio of the number of CAVs that do not form a formation with the front and rear vehicles in the mixed traffic flow to the total number of vehicles, y L It represents the ratio of the number of CAV convoys that have reached the maximum scale to the total number of vehicles in the mixed traffic flow. Because the CAV convoy that has reached the maximum scale can be further divided into two categories according to the type of the following vehicle: the CAV convoy that has reached the maximum scale is followed by an HV, and the CAV convoy that has reached the maximum scale is followed by a CAV. In mixed traffic flow, the proportion of the former is defined as The latter ratio is defined as Therefore, the decision variables of the above mathematical programming problem can be regarded as the proportion of the five vehicle following modes in the mixed traffic flow and the proportion of different-sized fleets in the mixed traffic flow, that is,

[0084] Step 2.3: Construct constraints;

[0085] Since all CAV fleets that have reached their maximum size can be followed by one HV or one CAV, the following relationship exists:

[0086]

[0087] There is a relationship between the proportions of different types of CAV convoys and different following modes. In mixed traffic flow, the proportion of a CAV convoy that has reached its maximum size and is followed by a CAV is equal to p CP :

[0088]

[0089] The sum of the product of the proportion of CAV fleets of different sizes and the number of corresponding “CC” vehicles in the CAV fleet is equal to p CC :

[0090]

[0091] Since the vehicles following a CAV convoy that has not reached the maximum size must be HVs, in mixed traffic flow, the sum of the proportion of CAV convoys that have not reached the maximum size and the proportion of CAV convoys that have reached the maximum size followed by a HV is equal to p HC :

[0092]

[0093] In addition, since only in the “HH” and “CH” vehicle-following modes the leading vehicle is an HV, the sum of the proportions of these two vehicle-following modes in the mixed traffic flow is equal to the HV penetration rate (i.e., 1-P C ):

[0094] p HH +p CH =1-P C (5)

[0095] Only in the three car-following modes of “CP”, “CC” and “HC”, the leading vehicle is a CAV. Therefore, the sum of the proportions of these three car-following modes in the mixed traffic flow is equal to the CAV penetration rate:

[0096] p CP +p CC +p HC =P C (6)

[0097] Only in the two vehicle following modes "HH" and "HC" the following vehicle is an HV, so the sum of the proportions of these two vehicle following modes in the mixed traffic flow is equal to the HV penetration rate:

[0098] p HH +p HC =1-P C (7)

[0099] Only in the three car-following modes of “CH”, “CP” and “CC”, the following vehicle is a CAV, so the sum of the proportions of these three car-following modes in the mixed traffic flow is equal to the CAV penetration rate:

[0100] p CH +p CP +p CC =P C (8)

[0101] In addition, the ratios of different car-following modes and different fleet sizes should be non-negative:

[0102]

[0103] Step 2.4: Construct the objective function;

[0104] Due to the inverse relationship between the average safe headway and the lane capacity, the objective function of the mixed lane capacity upper and lower limit calculation model can be defined as minimizing or maximizing the average safe headway, and the average safe headway can be expressed as a functional relationship of the proportion of the five vehicle following modes in the mixed traffic flow. Let h represent the average headway on the longitudinal lane, so there is the following relationship:

[0105] h=h HH p HH +h HC p HC +h CH p CH +h CP p CP +h CC p CC (10)

[0106] Step 2.5: Establish upper and lower limit calculation models for mixed traffic lane capacity, namely, the first optimization model and the second optimization model;

[0107] Let h represent the minimum value of the average headway time on the longitudinal lane, which can be obtained by solving the following optimization model [HMIN], which is the first optimization model, specifically:

[0108]

[0109] The constraints are equations (1)-(9).

[0110] Similarly, suppose The maximum value of the average headway time on the longitudinal lane can be obtained by solving the following optimization model [HMAX], which is the second optimization model, specifically:

[0111]

[0112] The constraints are equations (1)-(9).

[0113] Furthermore, the calculation of the upper and lower limits of the traffic capacity of the mixed traffic lane to be analyzed based on the minimum and maximum average headway times of the longitudinal lanes includes:

[0114] Calculate the capacity upper limit:

[0115] set up It represents the upper limit of the mixed lane capacity. Due to the inverse relationship between the average safe headway and the lane capacity, h can be obtained by solving the optimization model [HMIN] and then directly calculated according to the following formula:

[0116]

[0117] Calculate the lower capacity limit:

[0118] Assume that c represents the lower limit of the mixed lane capacity. Due to the inverse relationship between the average safe headway and the lane capacity, the solution to the optimization model [HMAX] can be obtained as It can be directly calculated according to the following formula:

[0119]

[0120] Since the objective function and the constraints are both linear expressions of the decision variables, the mathematical programming models [HMIN] and [HMAX] are both linear programming models, which can be solved using commercial solvers such as CPLEX, Matlab, and Gurobi. In this embodiment, Matlab is used for solving.

[0121] Furthermore, the method proposed in this embodiment also includes: based on the decision variable values ​​corresponding to the upper and lower limits of the capacity, analyzing the spatial distribution of manually driven vehicles and networked autonomous driving vehicles on the longitudinal lane of the mixed lane to be analyzed.

[0122] verify:

[0123] By solving the above two linear programming models [HMIN] and [HMAX], the upper and lower limits of the mixed lane capacity and the corresponding spatial distribution of the two types of vehicles under any parameter conditions (safe headway, CAV penetration rate, and maximum size of the CAV fleet) can be obtained. In order to illustrate the effect of the method proposed in this embodiment, a set of parameters is selected for illustration, and the values ​​of different types of safe headway are set as: h HH =2s,h HC =2.4s,h CH =2.8s,h CC =2.2s,h CP = 2.5s, the maximum size of the CAV fleet is set to 5, that is, L = 5. The CAV penetration rate changes from 0 to 1 with a step size of 0.01. By solving the linear programming model [HMIN] and [HMAX] by Matlab, the upper and lower limits of the mixed lane capacity can be obtained as the CAV penetration rate increases, as shown in Figure 4 For ease of presentation, the results under some CAV penetration rates are shown in Table 1.

[0124] Table 1

[0125]

[0126] At the same time, the spatial distribution of the two types of vehicles on the longitudinal lane can be obtained when the mixed lane capacity reaches the upper and lower limits. C =0.5), when the mixed lane capacity reaches the upper limit, the proportions of the five vehicle following modes in the mixed traffic flow are: HH =0.5, p HC =0, p CH =0, p CP =0.1, p CC =0.4, which means that HVs and CAVs gather together on the longitudinal lanes, and the proportions of CAV fleets of different sizes in the mixed traffic flow are: y1=y2=y3=y4=0, y5=0.1, That is, all CAVs form a CAV convoy with a maximum size of 5 on the longitudinal lane.

[0127] In addition, when the mixed lane capacity reaches the lower limit, the proportions of the five vehicle following modes in the mixed traffic flow are: HH =0, p HC =0.5, p CH =0.5, p CP =0, p CC =0, which means that HVs and CAVs are distributed in the longitudinal lanes in an alternating order, and there is no situation where the front and rear vehicles are of the same type. The proportions of CAV fleets of different sizes in the mixed traffic flow are: y1 = 0.5, y2 = y3 = y4 = y5 = 0, That is, all CAVs travel alone in the longitudinal lanes and do not form a convoy with other CAVs.

[0128] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. The upper and lower limits of mixed lane capacity calculation and analysis method considering the size of the platoon is characterized by: include: Obtain the vehicle following modes and corresponding safe headway distances of manually driven vehicles and connected autonomous vehicles in the mixed lane to be analyzed, as well as the maximum platoon size of connected autonomous vehicles; Input the vehicle following mode and the corresponding safe headway time, as well as the maximum formation size of the networked autonomous driving vehicles into the preset first optimization model and the second optimization model, to obtain the minimum and maximum average headway time of the longitudinal lane on the mixed traffic lane to be analyzed, wherein the first optimization model and the second optimization model are constructed according to the constraint conditions and the objective function; The upper and lower limits of the capacity of the mixed traffic lane to be analyzed are calculated based on the minimum and maximum average headway time of the longitudinal lane, and the calculation and analysis of the upper and lower limits of the capacity of the mixed traffic lane to be analyzed are completed.

2. The method for calculating and analyzing the upper and lower limits of mixed lane capacity considering platoon size according to claim 1 is characterized in that: Constructing the first optimization model and the second optimization model according to the constraint conditions and the objective function includes: Define vehicle following modes and corresponding safe headway and following probability in mixed traffic scenarios, wherein the vehicle following modes include HV following HV, HV following CAV, CAV following HV, CAV following a CAV fleet that has reached the largest scale, and CAV following another CAV in the same CAV fleet, wherein HV represents a manually driven vehicle and CAV represents a connected autonomous vehicle; Determining decision variables according to the following probability of the vehicle following mode and the formation probability of CAV fleets of different sizes, and constructing constraint conditions based on the decision variables; Constructing an objective function based on the safe headway and following probability of the vehicle following mode; The first optimization model and the second optimization model are constructed based on the constraint conditions and the objective function.

3. The method for calculating and analyzing the upper and lower limits of mixed lane capacity considering platoon size according to claim 2 is characterized in that: The decision variables are Among them, p HH is the probability of HV following HV, p HC is the probability of HV following CAV, p CH is the probability of CAV following HV, p CP is the probability of a CAV following a CAV fleet that has reached its maximum size, p CC is the probability of a CAV following another CAV in the same CAV convoy, y1 is the ratio of the number of CAVs that do not form a convoy with the front and rear vehicles to the total number of vehicles, and y L is the ratio of the number of CAV fleets that have reached their maximum size to the total number of vehicles, The probability of a CAV fleet that has reached its maximum size being followed by an HV is The probability of a CAV being followed by a CAV fleet that has reached its maximum size.

4. The method for calculating and analyzing the upper and lower limits of mixed lane capacity considering platoon size according to claim 3 is characterized in that: The constraints are: All CAV fleets that have reached maximum size are followed by HVs or CAVs: The proportion of CAVs following the largest CAV fleet is equal to the probability of CAVs following the largest CAV fleet: The sum of the product of the ratio of CAV fleets of different sizes and the number of CAVs following CAVs in a CAV fleet is equal to the probability of a CAV following another CAV in the same CAV fleet: The sum of the proportion of CAV fleets that have not reached the maximum scale and the proportion of HVs that are closely behind the CAV fleets that have reached the maximum scale is equal to the probability of HVs following CAVs: The sum of the probability of HV following HV and CAV following HV is equal to the HV penetration rate: p HH +p CH =1-P C The sum of the following probabilities of an HV following a CAV, a CAV following a CAV fleet that has reached its maximum size, and a CAV following another CAV in the same CAV fleet is equal to the CAV penetration rate: p CP +p CC +p HC =P C The sum of the probability of HV following HV and HV following CAV is equal to the HV penetration rate: p HH +p HC =1-P C The sum of the following probabilities of a CAV following an HV, a CAV following a CAV fleet that has reached its maximum size, and a CAV following another CAV in the same CAV fleet is equal to the CAV penetration rate: p CH +p CP +p CC =P C The ratios of different car-following modes and different sizes of CAV fleets are non-negative: Among them, y i is the ratio of the number of CAV fleets of size i to the total number of vehicles, P C is the CAV penetration rate.

5. The method for calculating and analyzing the upper and lower limits of mixed lane capacity considering platoon size according to claim 4 is characterized in that: The objective function is: h=h HH p HH +h HC p HC +h CH p CH +h CP p CP +h CC p CC Where h is the average headway time of the longitudinal lane, h HH is the safe headway time between HV and HV, h HC is the safe headway time between HV and CAV, h CH is the safe headway distance between CAV and HV, h CP is the safe headway time for a CAV to follow a CAV convoy that has reached its maximum size, h CC It is the safe headway time for an AV to follow another CAV in the same CAV convoy.

6. The method for calculating and analyzing the upper and lower limits of mixed lane capacity considering platoon size according to claim 5 is characterized in that: The first optimization model is: The second optimization model is: Where h is the minimum average headway time of the longitudinal lane, It is the maximum average headway time of the longitudinal lane.

7. The method for calculating and analyzing the upper and lower limits of mixed lane capacity considering platoon size according to claim 6 is characterized in that: The method for calculating the upper limit value of the traffic capacity of the mixed traffic lane to be analyzed is: The method for calculating the lower limit value of the traffic capacity of the mixed traffic lane to be analyzed is: in, is the upper limit of the mixed traffic lane capacity, and c is the lower limit of the mixed traffic lane capacity.

8. The method for calculating and analyzing the upper and lower limits of mixed lane capacity considering platoon size according to any one of claims 1 to 7, characterized in that: The method further comprises: Based on the decision variable values ​​corresponding to the upper and lower limits of the traffic capacity, the spatial distribution of manually driven vehicles and networked autonomous driving vehicles on the longitudinal lane of the mixed lane to be analyzed is analyzed.

Images