Calculation and analysis method of lane capacity in mixed traffic scenarios of connected autonomous driving

Abstract

The present invention discloses a method for calculating and analyzing lane capacity in a mixed traffic scenario of connected autonomous driving. In order to deal with the relationship between the capacity of mixed traffic lanes and the spatial distribution of heterogeneous vehicles, a computable index (i.e., CAV clustering intensity) with clear physical meaning and expression is proposed. The longitudinal distribution of two types of vehicles, HV and CAV, is quantitatively characterized under the assumption that the upper limit of the length of the CAV fleet is considered and the two types of vehicles are not completely randomly distributed on the lane. In view of the problem of calculating the random capacity of lanes in a mixed driving environment of HVs and CAVs, the setting of a proposed circular single lane ensures that the number of headways in the mixed traffic flow is equal to the number of vehicles, thereby establishing a relationship between the vehicle penetration rate and the proportion of different vehicle pairs. Based on the proposed CAV formation intensity index, a Markov chain model is established, and an explicit expression for the capacity of mixed traffic lanes is theoretically derived, and it is expressed as a multivariate function of CAV penetration rate, CAV clustering intensity, and the upper limit of the length of the CAV fleet.

Description

Technical Field

[0001] The present invention belongs to the technical field of networked autonomous driving, and specifically relates to a method for calculating and analyzing lane capacity in a networked autonomous driving mixed traffic scenario. Background Art

[0002] Compared with human-driven vehicles (HVs), connected and autonomous vehicles (CAVs) have shown great potential in improving road capacity by being equipped with advanced autonomous driving and vehicle networking technologies. AI-based autonomous driving technology gives CAVs a shorter reaction time than HVs, and they can maintain a shorter headway with the vehicle in front during driving. In addition, through real-time communication and cooperation between each other, CAVs can achieve platoon driving on the road, and a more compact and safe headway can be maintained within the CAV fleet, but the CAV fleet is also limited by the length of the formation. At the same time, due to factors such as the level of CAV technology development, transportation infrastructure conditions, and personal preferences, HVs cannot be completely replaced by CAVs in the short term. Therefore, in a longer transition period, HVs and CAVs will coexist in the transportation system and share urban road resources.

[0003] The mixed traffic scenario of connected autonomous driving, which consists of HVs and CAVs, will make the calculation and analysis of lane capacity extremely complicated. Unlike the fixed value of lane capacity in a full HV environment, the lane capacity in the mixed traffic scenario of connected autonomous driving is a random variable affected by multiple factors. Specifically, due to the differences in technical characteristics of different types of vehicles and the limitation of the length of the CAV fleet, the safe headway between adjacent vehicles is related to their following mode, and the following mode of adjacent vehicles can be classified according to the type of front and rear vehicles and the driving mode of the rear vehicle (single driving mode or driving in the form of a CAV fleet). Since the average safe headway on the road directly determines the traffic density and traffic flow, the lane capacity in the mixed traffic scenario of connected autonomous driving is a variable, which is related to the proportion of CAVs in all vehicles (i.e., CAV penetration rate), the longitudinal spatial distribution of the two types of vehicles on the lane, and the upper limit of the length of the CAV fleet. The spatial distribution of the two types of vehicles on the longitudinal lane is uncertain, so the lane capacity in the mixed traffic scenario of connected autonomous driving is random.

[0004] Since lane capacity is an important parameter for formulating traffic planning and management strategies, the present invention proposes a method for calculating and analyzing lane capacity in a mixed traffic scenario of networked autonomous driving. Summary of the invention

[0005] In order to solve the technical problems existing in the background technology, the present invention aims to provide a method for calculating and analyzing lane capacity in a connected autonomous driving mixed traffic scenario. For the connected autonomous driving mixed traffic scenario composed of HVs and CAVs, this paper first proposes a computable metric indicator, CAV aggregation intensity, to characterize the longitudinal spatial distribution of HVs and CAVs on the lane, and derives a lane capacity calculation expression in the connected autonomous driving mixed traffic scenario based on this, which is expressed as an explicit expression of CAV penetration rate, CAV aggregation intensity, and the upper limit of CAV fleet length, so as to effectively calculate the lane capacity in the connected autonomous driving mixed traffic scenario, and use it to analyze the influence of the above-mentioned multiple factors on the lane capacity.

[0006] In order to solve the technical problem, the technical solution of the present invention is:

[0007] A method for calculating and analyzing lane capacity in a mixed traffic scenario of a connected autonomous driving system, the method comprising:

[0008] S1: Classification of vehicle pairs and vehicle following modes: vehicle pairs are divided according to different vehicle types, and then further divided into different types of vehicle following modes according to whether the front and rear adjacent vehicles belong to the same CAV fleet. Each mode corresponds to a different safe headway time.

[0009] S2: Definition of CAV aggregation intensity: The concept of CAV aggregation intensity E is introduced, which is defined as the ratio of the proportion of CAV-CAV vehicle pairs in mixed traffic flow to the total number of CAVs, to quantify the distribution characteristics of CAVs on the longitudinal lanes;

[0010] S3: Establishment of Markov chain model: Use Markov chain to model the spatial distribution of mixed vehicle types, define the state space and state transition probability matrix to describe the changes of vehicle types at different positions, and calculate the probability of CAVs being at different positions in the CAV fleet in mixed traffic flow;

[0011] S4: Calculate the probability of various safe headway distances: By constructing the probability of following modes for different types of vehicles, the probability distribution of headway distances in mixed traffic scenarios is derived;

[0012] S5: Calculation of lane capacity: Based on the proportion of different vehicle following modes, the relationship between lane capacity and CAV penetration rate, CAV aggregation intensity, and CAV fleet length is derived to provide calculation support for practical applications.

[0013] Further, the step S1 comprises:

[0014] For the mixed traffic flow composed of HVs and CAVs, five different vehicle following modes are divided according to the types of front and rear vehicles during driving and whether the front and rear vehicles belong to the same CAV fleet. Specifically, four types of vehicle pairs are divided according to the types of front and rear vehicles, including HV-HV vehicle pairs, that is, one HV follows another HV; HV-CAV vehicle pairs, that is, one HV follows a CAV; CAV-HV vehicle pairs, that is, one CAV follows an HV; CAV-CAV vehicle pairs, that is, one CAV follows another CAV; The first three types of vehicle pairs correspond to three types of vehicle following modes respectively; According to whether the front and rear vehicles belong to the same CAV fleet, the CAV-CAV vehicle pairs are further divided into two types of vehicle following modes: a CAV follows a CAV fleet that has reached the maximum formation size, and a CAV follows another CAV in the same CAV fleet; In the mixed driving scenario of HV and CAV connected autonomous driving, there are five types of vehicle following modes, each corresponding to a safe headway;

[0015] Let L represent the upper limit of the length of a CAV convoy. When the size of a CAV convoy reaches L, the subsequent CAVs can no longer join the convoy and can only travel alone or form a new CAV convoy with other subsequent CAVs. In the classification of vehicle pairs, in order to distinguish the two types of vehicles, "1" and "2" represent HV and CAV respectively. The proportions of the four types of vehicle pairs in the mixed traffic flow can be represented by τ with different subscripts, where the combination and sequence of "1" and "2" represent different types of vehicle pairs. Therefore, τ 11 , τ 12 , τ 21 and τ 22 They represent the proportions of HV-HV vehicle pairs, HV-CAV vehicle pairs, CAV-HV vehicle pairs, and CAV-CAV vehicle pairs in mixed traffic flows;

[0016] When classifying vehicle following modes, "H" and "C" are used to represent HV and CAV respectively, "P" is used to represent a CAV convoy that has reached the maximum platoon size, and the combination of "H", "C", and "P" represents different types of vehicle following modes as superscripts; specifically, "HH" refers to an HV following another HV, "HC" refers to an HV following a CAV, "CP" refers to a CAV following a CAV convoy that has reached the maximum size, and "CC" refers to a CAV in the same CAV convoy following another CAV. Therefore, the variables and parameters related to the five vehicle following modes are distinguished by these superscripts, and different subscripts of h represent the safe headway time under different vehicle following modes, that is, h HH 、h HC 、h CH 、h CP 、h CC; Different subscripts p represent the proportions of different vehicle following modes in mixed traffic flow, that is, p HH 、p HC 、p CH 、p CP 、p CC .

[0017] Further, the step S2 comprises:

[0018] Given the CAV penetration rate, the CAV aggregation intensity is introduced to quantitatively characterize the spatial distribution of heterogeneous vehicles on the longitudinal lanes. It is defined as the degree of CAV aggregation on the longitudinal lanes in the mixed traffic scenario of connected autonomous driving.

[0019] Let E denote the aggregation intensity of CAVs, measured by the ratio of the number of vehicle pairs whose leading and trailing vehicles are both CAVs to the total number of CAVs in the mixed traffic flow; therefore, it is mathematically expressed as follows:

[0020]

[0021] where τ 22 is the ratio of CAV-CAV vehicle pairs in mixed traffic flow.

[0022] Further, the step S3 comprises:

[0023] Considering the uncertainty of the spatial distribution of HVs and CAVs on the longitudinal lanes, the vehicle types at each position in the mixed traffic flow are regarded as a set of random variables, that is, a discrete random process, and a Markov chain model is constructed for this purpose; for a mixed traffic flow composed of a column of HVs and CAVs, all vehicles are numbered in order from front to back, and the index n∈{1,2,…} is used to represent the nth vehicle in the mixed traffic flow; A n Represents the type of the nth vehicle, which is regarded as the state variable of the nth step, A n =1 indicates that the nth vehicle is a HV, A n = 2 indicates that the nth vehicle is a CAV, so a discrete random variable sequence corresponds to the vehicle type at each position on the longitudinal lane {A n ,n∈1,2,…} is regarded as a Markov chain;

[0024] All possible vehicle types at each position constitute the state space of the Markov chain model, and its state space is expressed as:

[0025] S=[1,2] (2)

[0026] The initial state of the Markov chain model is the type of the first vehicle in the longitudinal lane. In mixed traffic flow, the probability that a vehicle is a CAV is P C , the probability of being HV is 1-PC ; Therefore, the initial state is:

[0027]

[0028] The one-step transition probability matrix of the Markov chain model is defined as the probability of the current vehicle type transitioning to the subsequent vehicle type, and its expression is:

[0029]

[0030] Among them, t sr represents the probability that a type r vehicle is followed by a type s vehicle, so,

[0031] To calculate the one-step transition probability between different states, it is assumed that all vehicles travel on a single-lane circular road and form a sequence from the beginning to the end, and the number of headways is equal to the number of vehicles;

[0032] Because only in the "11" and "12" vehicle pairs, the following vehicle is a HV, so the sum of the proportions of these two vehicle pairs on the road should be equal to the HV penetration rate in the mixed traffic flow, that is, 1-P C , so the following equation:

[0033] τ 11 +τ 12 =1-P C (5)

[0034] Similarly, only in the “21” and “22” vehicle pairs is the following vehicle a CAV, so the sum of the proportions of these two vehicle pairs should be equal to the penetration rate of CAVs in the mixed traffic flow:

[0035] τ 21 +τ 22 =P C (6)

[0036] Since only the leading vehicles in vehicle pairs “11” and “21” are HVs among all vehicle pairs, the sum of the proportions of these two vehicle pairs on the road should be equal to the HV penetration rate in the mixed traffic flow, which can be expressed as:

[0037] τ 11 +τ 21 =1-P C (7)

[0038] Similarly, among all vehicle pairs, only the leading vehicles in the “12” and “22” vehicle pairs are CAVs, and the sum of the proportions of these two vehicle pairs on the road should be equal to the penetration rate of CAVs in the mixed traffic flow:

[0039] τ 12 +τ22 =P C (8)

[0040] According to the above established formulas (5)-(8), the ratio of vehicle pairs of different types can be expressed as τ 22 and P C Function:

[0041] τ 11 =1-2P C +τ 22 (9)

[0042] τ 21 =P C -τ 22 (10)

[0043] τ 12 =P C -τ 22 (11)

[0044] Therefore, the external given P C Under the condition of sr Expressed as a function of CAV aggregation strength:

[0045]

[0046]

[0047] Furthermore, the probability of a CAV being at different positions in a CAV fleet in a mixed traffic flow is calculated, including:

[0048] Let p m represents the probability that a vehicle is the mth vehicle in a CAV convoy, m∈{1,2,…,L}; depending on whether the vehicle is the leading vehicle in the CAV convoy, the value of m is divided into two categories: m∈{2,…L} and m=1;

[0049] (1)m∈{2,3,…,L}

[0050] Indicates that a vehicle is in a CAV convoy, but is not the leading vehicle of the CAV convoy; at this time, the probability that the vehicle is the mth vehicle in the CAV convoy is expressed as:

[0051] p m =Pr{A m =2,A m-1 =2,…,A1=2} (16)

[0052] According to the conditional probability formula and Markov property, the following inferences can be made:

[0053] p m =Pr{Am =2|A m-1 =2,…,A1=2}Pr{A m-1 =2,…,A1=2}=Pr{A m =2|A m-1 =2}Pr{A m-1 =2,…,A1=2}

[0054] =t 22 p m-1 (17)

[0055] Since Equation (17) is applicable to all m∈{2,3,…,L}, according to mathematical induction, the probability that a vehicle is the mth vehicle in a CAV queue is expressed as:

[0056] p m =(t 22 ) 2 p m-2 =(t 22 ) m-1 p1 (18)

[0057] (2) m = 1

[0058] It indicates that a vehicle is the leading vehicle in a CAV convoy; at this time, the vehicle in front of it is an HV or a CAV convoy that has reached its maximum size, so p1 = p CP +p CH ; The proportion of certain types of vehicle pairs in a mixed traffic flow is directly equal to the probability of the corresponding vehicle following mode, such as τ 12 =p HC , τ 21 =p CH Therefore, according to equations (9)-(11), p CH =p HC In addition, according to formula (14), we get p HC =τ 12 =Pr(A n+1 =1,A n =2) = P C t 12 ; Therefore, the following equation is obtained:

[0059] p1=p CP +p CH =p CP +p HC =p CP +P C t 12 (19)

[0060] According to equations (15) and (18), the probability that a CAV follows a CAV fleet that has reached its maximum size is:

[0061] p CP =Pr{A L+1 =2,A L =2,…,A1=2}=(t 22 ) L p1 (20)

[0062] Substituting equation (20) into equation (19), if t 22 ≠1, we can get:

[0063]

[0064] According to formula (15), we know that t 22 = 1 is equivalent to E = 1, which represents the extreme case where all CAVs are clustered together in the longitudinal lane; considering that the maximum number of rows L is relatively small relative to the number of vehicles on the lane, or all CAVs form an integer maximum-scale platoon, when t 22 =1, that is, when E=1, the following formula is obtained:

[0065]

[0066] To sum up, the probability of a vehicle being the leading vehicle in a CAV fleet is:

[0067]

[0068] Substituting formula (23) into formula (20), we can get:

[0069]

[0070] Furthermore, in step S4: according to equations (12)-(15), (18), (23) and (24), the probabilities of different vehicle following modes in the mixed traffic flow are derived.

[0071] Further, in step S4:

[0072] The variable h is used to represent the headway time between any two adjacent vehicles in the mixed traffic flow. Based on the one-to-one mapping relationship between the vehicle following mode and the headway time, the probability distribution of the headway time in the mixed traffic flow is obtained as follows:

[0073] (1) The probability of an HV following an HV in a mixed traffic flow is:

[0074] Pr{h=h HH =p HH =(1-P C )t 11 =1-2P C +τ 22 (25)

[0075] (2) The probability of an HV following a CAV in mixed traffic flow is:

[0076] Pr{h=h HC =p HC =P C t 12 =P C -τ 22 (26)

[0077] (3) The probability of a CAV following an HV in mixed traffic flow is:

[0078] Pr{h=h CH =p CH =(1-P C )t 21 =P C -τ 22 (27)

[0079] (4) The probability that a CAV in a mixed traffic flow follows a CAV in the same convoy is:

[0080]

[0081] (5) The probability that a CAV follows a CAV convoy that has reached its maximum size in a mixed traffic flow is:

[0082]

[0083] Further, in step S5:

[0084] p represents the vector composed of the proportions of different vehicle following modes in mixed traffic flow, that is, p = {p HH ,p HC ,p CH ,p CP ,p CC} T ;

[0085] c represents the lane capacity in the mixed traffic scenario of connected autonomous driving, that is, the maximum mixed traffic flow on a lane; therefore, according to the relationship between the average headway and traffic density and traffic flow, it is obtained that:

[0086]

[0087] Substituting the probabilities (25)-(29) of different headways in mixed traffic flow into equation (30), we can obtain the explicit expression of the mixed lane capacity:

[0088]

[0089] As shown in formula (31), the mixed lane capacity c(·) is the CAV penetration rate P C , a multivariate function of the upper limit of CAV fleet length L and CAV aggregation intensity E.

[0090] Compared with the prior art, the advantages of the present invention are:

[0091] (1) In order to deal with the relationship between the capacity of mixed lanes and the spatial distribution of heterogeneous vehicles, the present invention proposes a computable indicator (i.e., CAV aggregation intensity) with clear physical meaning and expression. It quantitatively characterizes the longitudinal distribution of HVs and CAVs under the assumption that the upper limit of the CAV fleet length is considered and the two types of vehicles are not completely randomly distributed on the lane.

[0092] (2) Aiming at the problem of calculating the random capacity of lanes in a mixed driving environment of HVs and CAVs, the present invention proposes a setting of a circular single lane to ensure that the headway number in the mixed traffic flow is equal to the number of vehicles, thereby establishing a relationship between the vehicle penetration rate and the proportion of different vehicle pairs. Based on the proposed CAV formation strength index, a Markov chain model is established, and an explicit expression of the mixed lane capacity is theoretically derived, and it is expressed as a multivariate function of CAV penetration rate, CAV clustering strength, and the upper limit of the CAV fleet length. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 , the following modes and safe headway time division diagrams of different types of vehicles in mixed traffic scenarios of connected autonomous driving;

[0094] Figure 2 , vehicle following mode and safe headway diagram in mixed traffic scenarios of connected autonomous driving;

[0095] Figure 3 , Schematic diagram of mixed traffic flow on a single-lane circular road;

[0096] Figure 4 , mixed lane capacity values ​​at different CAV penetration rates and CAV aggregation intensities. DETAILED DESCRIPTION

[0097] The specific implementation mode of the present invention is described below in conjunction with embodiments:

[0098] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification so that people familiar with this technology can understand and read them, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0099] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" cited in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0100] Embodiment 1:

[0101] The present invention proposes a method for calculating and analyzing lane capacity in a mixed-traffic scenario of connected autonomous driving. For a mixed-traffic scenario of connected autonomous driving composed of HVs and CAVs, a computable metric, CAV aggregation intensity, is first proposed to characterize the longitudinal spatial distribution of HVs and CAVs on the lane, and based on this, a calculation expression for lane capacity in a mixed-traffic scenario of connected autonomous driving is derived, which is expressed as an explicit expression of CAV penetration, CAV aggregation intensity, and the upper limit of the length of the CAV fleet. This can effectively calculate the lane capacity in a mixed-traffic scenario of connected autonomous driving, and can be used to analyze the impact of the above-mentioned multiple factors on lane capacity.

[0102] Step 1: Classify different types of vehicle following modes and define related symbols

[0103] like Figure 1 As shown in the figure, for the mixed traffic flow composed of HVs and CAVs, five different vehicle following modes are divided according to the types of the leading and trailing vehicles and whether the leading and trailing vehicles belong to the same CAV convoy during driving. Specifically, four vehicle pairs can be divided according to the types of the leading and trailing vehicles, including HV-HV vehicle pairs (i.e., one HV follows another HV), HV-CAV vehicle pairs (i.e., one HV follows a CAV), CAV-HV vehicle pairs (i.e., one CAV follows an HV) and CAV-CAV vehicle pairs (i.e., one CAV follows another CAV). The first three vehicle pairs correspond to three vehicle following modes respectively. Since there is an upper limit on the length of the CAV convoy, two adjacent CAVs may not belong to the same CAV convoy. Therefore, according to whether the leading and trailing vehicles belong to the same CAV convoy, the CAV-CAV vehicle pairs can be further divided into two types of vehicle following modes: one CAV follows a CAV convoy that has reached the maximum formation size, and one CAV follows another CAV in the same CAV convoy. During driving, the vehicle maintains different safe headway distances with the leading vehicle in different following modes. Therefore, in the mixed driving scenario of HV and CAV connected autonomous driving, there are five types of vehicle following modes, each corresponding to a safe headway.

[0104] Let L represent the upper limit of the length of a CAV convoy. When the size of a CAV convoy reaches L, the subsequent CAVs can no longer join the convoy and can only travel alone or form a new CAV convoy with other subsequent CAVs. In the classification of vehicle pairs, in order to distinguish the two types of vehicles, "1" and "2" represent HV and CAV respectively. The proportion of the four types of vehicle pairs in mixed traffic flow can be represented by τ with different subscripts, where the combination of "1" and "2" and their sequence represent different types of vehicle pairs. Therefore, τ 11 , τ 12 , τ 21 and τ 22 They respectively represent the proportions of HV-HV vehicle pairs, HV-CAV vehicle pairs, CAV-HV vehicle pairs and CAV-CAV vehicle pairs in mixed traffic flows.

[0105] Since there is not a one-to-one mapping relationship between vehicle pairs and vehicle following modes, "H" and "C" are used to represent HV and CAV respectively when classifying vehicle following modes. "P" is used to represent a CAV fleet that has reached the maximum formation size. The combination of "H", "C", and "P" represents different types of vehicle following modes as superscripts. Specifically, "HH" refers to an HV following another HV, "HC" refers to an HV following a CAV, "CP" refers to a CAV following a CAV fleet that has reached the maximum size, and "CC" refers to a CAV in the same CAV fleet following another CAV. Therefore, the variables and parameters related to the five vehicle following modes are distinguished by these superscripts. Figure 2 As shown in the figure, different subscripts of h represent the safe headway time under different vehicle following modes, that is, h HH 、h HC 、h CH 、h CP 、h CC ; Different subscripts p represent the proportions of different vehicle following modes in mixed traffic flow, that is, p HH 、p HC 、p CH 、p CP 、p CC .

[0106] Step 2: Propose a computable quantitative indicator (i.e., CAV aggregation intensity) to characterize the longitudinal spatial distribution of the two types of vehicles on the lane

[0107] Given the external CAV penetration rate, the CAV aggregation intensity is introduced to quantitatively characterize the spatial distribution of heterogeneous vehicles on the longitudinal lanes, and is defined as the degree of CAV aggregation on the longitudinal lanes in the mixed traffic scenario of connected autonomous driving. Let E represent the CAV aggregation intensity, which can be measured by the ratio of the number of vehicle pairs in which both the front and rear vehicles are CAVs to the total number of CAVs in the mixed traffic flow. Therefore, it is mathematically expressed as follows:

[0108]

[0109] where τ 22 is the ratio of CAV-CAV vehicle pairs in mixed traffic flow.

[0110] Step 3: Build a Markov chain model to model the spatial distribution of mixed traffic

[0111] Step 3.1 Build a Markov chain model

[0112] Since the spatial distribution of HVs and CAVs on the longitudinal lanes is uncertain, the vehicle type at each position in the mixed traffic flow can be regarded as a set of random variables, that is, a discrete random process, for which a Markov chain model is constructed. For a mixed traffic flow consisting of a column of HVs and CAVs, all vehicles are numbered in order from front to back, and the index n∈{1,2,…} is used to represent the nth vehicle in the mixed traffic flow. n A represents the type of the nth vehicle and can be regarded as the state variable of the nth step. n =1 indicates that the nth vehicle is a HV, A n = 2 indicates that the nth vehicle is a CAV. Therefore, a discrete random variable sequence corresponds to the vehicle type at each position on the longitudinal lane {A n ,n∈1,2,…} can be regarded as a Markov chain.

[0113] All possible vehicle types at each position constitute the state space of the Markov chain model, and its state space is expressed as:

[0114] S=[1,2] (2)

[0115] The initial state of the Markov chain model is the type of the first vehicle in the longitudinal lane. In mixed traffic flow, the probability that a vehicle is a CAV is P C , the probability of being HV is 1-P C . Therefore, the initial state is:

[0116]

[0117] The one-step transition probability matrix of the Markov chain model is defined as the probability of the current vehicle type transitioning to the subsequent vehicle type, and its expression is:

[0118]

[0119] Among them, t sr represents the probability that a type r vehicle is followed by a type s vehicle. Therefore,

[0120] In order to calculate the one-step transition probability between different states, it is assumed that all vehicles travel on a single-lane circular road and form a sequence from the beginning to the end (such as Figure 3 As shown), the number of headways is equal to the number of vehicles.

[0121] Because only in the vehicle pairs “11” and “12”, the following vehicle is a HV, the sum of the proportions of these two vehicle pairs on the road should be equal to the HV penetration rate in the mixed traffic flow (i.e., 1-P C ), so we have the following equation:

[0122] τ 11 +τ 12 =1-P C (5)

[0123] Similarly, only in the “21” and “22” vehicle pairs is the following vehicle a CAV, so the sum of the proportions of these two vehicle pairs should be equal to the penetration rate of CAVs in the mixed traffic flow:

[0124] τ 21 +τ 22 =P C (6)

[0125] Since only the leading vehicles in vehicle pairs “11” and “21” are HVs among all vehicle pairs, the sum of the proportions of these two vehicle pairs on the road should be equal to the HV penetration rate in the mixed traffic flow, which can be expressed as:

[0126] τ 11 +τ 21 =1-P C (7)

[0127] Similarly, among all vehicle pairs, only the leading vehicles in the “12” and “22” vehicle pairs are CAVs, and the sum of the proportions of these two vehicle pairs on the road should be equal to the penetration rate of CAVs in the mixed traffic flow:

[0128] τ 12 +τ 22 =P C (8)

[0129] According to the above established formulas (5)-(8), the ratio of vehicle pairs of different types can be expressed as τ 22 and P C Function:

[0130] τ 11 =1-2P C +τ 22 (9)

[0131] τ 21 =P C -τ 22 (10)

[0132] τ 12 =P C -τ 22 (11)

[0133] Therefore, the external given P C Under the condition of sr Expressed as a function of CAV aggregation strength:

[0134]

[0135]

[0136] Step 3.2 Calculate the probability of a CAV being at different positions in the CAV fleet in mixed traffic flow

[0137] Let p m represents the probability that a vehicle is the mth vehicle in a CAV convoy, m∈{1,2,…,L}. Depending on whether the vehicle is the leading vehicle in the CAV convoy, the value of m is divided into two categories: m∈{2,…L} and m=1.

[0138] (1)m∈{2,3,…,L}

[0139] This means that a vehicle is in a CAV convoy but is not the leading vehicle in the convoy. At this point, the probability that the vehicle is the mth vehicle in the CAV convoy can be expressed as:

[0140] p m =Pr{A m =2,A m-1 =2,…,A1=2} (16)

[0141] According to the conditional probability formula and Markov property, we can infer the following:

[0142] p m =Pr{A m =2|A m-1 =2,…,A1=2}Pr{A m-1=2,…,A1=2}

[0143] =Pr{A m =2|A m-1 =2}Pr{A m-1 =2,…,A1=2}

[0144] =t 22 p m-1 (17)

[0145] Since Equation (17) is applicable to all m∈{2,3,…,L}, according to mathematical induction, the probability that a vehicle is the mth vehicle in a CAV queue can be expressed as:

[0146] p m =(t 22 ) 2 p m-2 =(t 22 ) m-1 p1 (18)

[0147] (2) m = 1

[0148] It indicates that a vehicle is the leading vehicle in a CAV convoy. At this time, the vehicle in front of it should be an HV or a CAV convoy that has reached its maximum size, so p1 = p CP +p CH .like Figure 1 As shown in Figure 2, the proportion of certain types of vehicle pairs in a mixed traffic flow is directly equal to the probability of the corresponding vehicle following mode, as τ 12 =p HC , τ 21 =p CH Therefore, according to equations (9)-(11), we can deduce that p CH =p HC In addition, according to formula (14), we can get p HC =τ 12 =Pr(A n+1 =1,A n =2) = P C t 12 Therefore, the following equation can be obtained:

[0149] p1=p CP +p CH =p CP +p HC =p CP +P C t 12 (19)

[0150] According to equations (15) and (18), the probability that a CAV follows a CAV fleet that has reached its maximum size is:

[0151] p CP =Pr{A L+1 =2,A L =2,…,A1=2}=(t 22 ) L p1 (20)

[0152] Substituting equation (20) into equation (19), if t 22 ≠1, we can get:

[0153]

[0154] According to formula (15), we know that t 22 = 1 is equivalent to E = 1, which represents the extreme case where all CAVs are clustered together in the longitudinal lane. Considering that the maximum number of platoons L is relatively small relative to the number of vehicles on the lane, or all CAVs can form an integer maximum platoon size, when t 22 =1 (i.e. E=1), we can get the following formula:

[0155]

[0156] In summary, we can get the probability that a vehicle is the leading vehicle in a CAV fleet:

[0157]

[0158] Substituting formula (23) into formula (20), we can get:

[0159]

[0160] Step 3.3 Calculate the probability of each headway

[0161] According to equations (12)-(15), (18), (23), and (24), the probabilities of different vehicle following modes in mixed traffic flow can be derived. The variable h represents the headway between any two adjacent vehicles in mixed traffic flow. Due to the one-to-one mapping relationship between vehicle following modes and headway, the probability distribution of headway in mixed traffic flow can be obtained as follows:

[0162] (1) The probability of an HV following an HV in a mixed traffic flow is:

[0163] Pr{h=h HH =p HH =(1-P C )t 11 =1-2P C +τ 22 (25)

[0164] (2) The probability of an HV following a CAV in mixed traffic flow is:

[0165] Pr{h=h HC =P HC =P C t 12 =P C -τ 22 (26)

[0166] (3) The probability of a CAV following an HV in mixed traffic flow is:

[0167] Pr{h=h CH =p CH =(1-P C )t 21 =P C -τ 22 (27)

[0168] (4) The probability that a CAV in a mixed traffic flow follows a CAV in the same convoy is:

[0169]

[0170] (5) The probability that a CAV follows a CAV convoy that has reached its maximum size in a mixed traffic flow is:

[0171]

[0172] Step 3.4 Calculation expression of mixed lane capacity in mixed HV and CAV environment

[0173] p represents the vector composed of the proportions of different vehicle following modes in mixed traffic flow, that is, p = {p HH ,p HC ,p CH ,p CP ,p CC} T , c represents the lane capacity in the mixed traffic scenario of connected autonomous driving, that is, the maximum mixed traffic flow on a lane. Therefore, based on the relationship between the average headway and traffic density and traffic flow, it can be concluded that:

[0174]

[0175] Substituting the probabilities (25)-(29) of different headways in mixed traffic flow into equation (30), we can obtain the explicit expression of the mixed lane capacity:

[0176]

[0177] As shown in formula (31), the mixed lane capacity c(·) is the CAV penetration rate (PC ), the upper limit of CAV fleet length (L) and the multivariate function of CAV aggregation intensity (E).

[0178] Given different parameter values, the corresponding mixed lane capacity can be directly calculated according to formula (31), and used to analyze the impact of CAV penetration, CAV aggregation intensity, and CAV fleet length upper limit on mixed lane capacity. The specific values ​​of different headway times are: h HH =2s,h HC =1.8s,h CH =1.6s,h CC =0.8s,h CP =1s, and the upper limit of the CAV fleet length is set to 5, that is, L=5. Figure 4 The variation of mixed lane capacity with CAV penetration and CAV clustering intensity is shown. The dotted lines in the figure indicate the maximum and minimum values ​​of CAV clustering intensity as the CAV penetration changes.

[0179] The present invention firstly gives a calculation expression for lane capacity in a mixed traffic scenario of connected autonomous driving, and expresses it as an explicit expression for CAV penetration rate, CAV aggregation intensity, and the upper limit of CAV fleet length, so as to effectively calculate the lane capacity in a mixed traffic scenario of connected autonomous driving, and use it to analyze the influence of the above-mentioned multiple factors on lane capacity. Compared with the existing technology, this technology fully considers the driving characteristics of CAV platoons and the upper limit of CAV fleet length, and does not rely on the assumption that the two types of vehicles are completely randomly distributed on the lane.

[0180] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0181] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0182] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0183] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0184] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

[0185] Many other changes and modifications may be made without departing from the concept and scope of the present invention.It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A method for calculating and analyzing lane capacity in a mixed traffic scenario of connected autonomous driving, characterized in that: The method comprises: S1: Classification of vehicle pairs and vehicle following modes: vehicle pairs are divided according to different vehicle types, and then further divided into different types of vehicle following modes according to whether the front and rear adjacent vehicles belong to the same CAV fleet. Each mode corresponds to a different safe headway time. S2: Definition of CAV aggregation intensity: The concept of CAV aggregation intensity E is introduced, which is defined as the ratio of the proportion of CAV-CAV vehicle pairs in mixed traffic flow to the total number of CAVs, to quantify the distribution characteristics of CAVs on the longitudinal lanes; S3: Establishment of Markov chain model: Use Markov chain to model the spatial distribution of mixed vehicle types, define the state space and state transition probability matrix to describe the changes of vehicle types at different positions, and calculate the probability of CAVs being at different positions in the CAV fleet in mixed traffic flow; S4: Calculate the probability of various safe headway distances: By constructing the probability of following modes for different types of vehicles, the probability distribution of headway distances in mixed traffic scenarios is derived; S5: Calculation of lane capacity: Based on the proportion of different vehicle following modes, the relationship between lane capacity and CAV penetration rate, CAV aggregation intensity, and CAV fleet length is derived to provide calculation support for practical applications; The step S2 comprises: Given the CAV penetration rate, the CAV aggregation intensity is introduced to quantitatively characterize the spatial distribution of heterogeneous vehicles on the longitudinal lanes. It is defined as the degree of CAV aggregation on the longitudinal lanes in the mixed traffic scenario of connected autonomous driving. Let E denote the aggregation intensity of CAVs, measured by the ratio of the number of vehicle pairs whose leading and trailing vehicles are both CAVs to the total number of CAVs in the mixed traffic flow; therefore, it is mathematically expressed as follows: where τ 22 is the ratio of CAV-CAV vehicle pairs in mixed traffic flow; The step S3 comprises: Considering the uncertainty of the spatial distribution of HVs and CAVs on the longitudinal lanes, the vehicle types at each position in the mixed traffic flow are regarded as a set of random variables, that is, a discrete random process, and a Markov chain model is constructed for this purpose; for a mixed traffic flow composed of a column of HVs and CAVs, all vehicles are numbered in order from front to back, and the index n∈{1,2,…} is used to represent the nth vehicle in the mixed traffic flow; A n Represents the type of the nth vehicle, which is regarded as the state variable of the nth step, A n =1 indicates that the nth vehicle is a HV, A n = 2 indicates that the nth vehicle is a CAV, so a discrete random variable sequence corresponds to the vehicle type at each position on the longitudinal lane {A n ,n∈1,2,…} is regarded as a Markov chain; All possible vehicle types at each position constitute the state space of the Markov chain model, and its state space is expressed as: S＝[1,2] (2) The initial state of the Markov chain model is the type of the first vehicle in the longitudinal lane. In mixed traffic flow, the probability that a vehicle is a CAV is P C , the probability of being HV is 1-P C ; Therefore, the initial state is: The one-step transition probability matrix of the Markov chain model is defined as the probability of the current vehicle type transitioning to the subsequent vehicle type, and its expression is: Among them, t sr represents the probability that a type r vehicle is followed by a type s vehicle, so, To calculate the one-step transition probability between different states, it is assumed that all vehicles travel on a single-lane circular road and form a sequence from the beginning to the end, and the number of headways is equal to the number of vehicles; Because only in the "11" and "12" vehicle pairs, the rear vehicle is a HV, so the sum of the proportions of these two vehicle pairs on the road should be equal to the HV penetration rate in the mixed traffic flow, that is, 1-P C , so the following equation: t 11 +v 12 =1-P C (5) Similarly, only in the "21" and "22" vehicle pairs is the following vehicle a CAV, so the sum of the proportions of these two vehicle pairs should be equal to the penetration rate of CAVs in the mixed traffic flow: t 21 +t 22 =P C (6) Since only the leading vehicles in vehicle pairs "11" and "21" are HVs among all vehicle pairs, the sum of the proportions of these two vehicle pairs on the road should be equal to the HV penetration rate in the mixed traffic flow, which can be expressed as: t 11 +t 21 =1-P C (7) Similarly, among all vehicle pairs, only the leading vehicles in vehicle pairs "12" and "22" are CAVs, and the sum of the proportions of these two vehicle pairs on the road should be equal to the penetration rate of CAVs in the mixed traffic flow: t 12 +t 22 =P C (8) According to the above established formulas (5)-(8), the ratio of vehicle pairs of different types can be expressed as τ 22 and P C Function: t 11 =1-2P C +t 22 (9) t 21 =P C -t 22 (10) t 12 =P C -t 22 (11) Therefore, the external given P C Under the condition of sr Expressed as a function of CAV aggregation strength:

2. The method for calculating and analyzing lane capacity in a mixed traffic scenario of a networked autonomous driving system according to claim 1, characterized in that: The step S1 comprises: For the mixed traffic flow composed of HVs and CAVs, five different vehicle following modes are divided according to the types of front and rear vehicles during driving and whether the front and rear vehicles belong to the same CAV fleet. Specifically, four types of vehicle pairs are divided according to the types of front and rear vehicles, including HV-HV vehicle pairs, that is, one HV follows another HV; HV-CAV vehicle pairs, that is, one HV follows a CAV; CAV-HV vehicle pairs, that is, one CAV follows an HV; CAV-CAV vehicle pairs, that is, one CAV follows another CAV; The first three types of vehicle pairs correspond to three types of vehicle following modes respectively; According to whether the front and rear vehicles belong to the same CAV fleet, the CAV-CAV vehicle pairs are further divided into two types of vehicle following modes: a CAV follows a CAV fleet that has reached the maximum formation size, and a CAV follows another CAV in the same CAV fleet; In the mixed driving scenario of HV and CAV connected autonomous driving, there are five types of vehicle following modes, each corresponding to a safe headway; Let L represent the upper limit of the length of a CAV convoy. When the size of a CAV convoy reaches L, the following CAVs can no longer join the convoy and can only travel alone or form a new CAV convoy with other subsequent CAVs. In the classification of vehicle pairs, in order to distinguish the two types of vehicles, "1" and "2" represent HV and CAV respectively. The proportions of the four types of vehicle pairs in the mixed traffic flow can be represented by τ with different subscripts, where the combination and sequence of "1" and "2" represent different types of vehicle pairs. Therefore, τ 11 , τ 12 , τ 21 and τ 22 They represent the proportions of HV-HV vehicle pairs, HV-CAV vehicle pairs, CAV-HV vehicle pairs, and CAV-CAV vehicle pairs in mixed traffic flows; When classifying vehicle following modes, "H" and "C" are used to represent HV and CAV respectively, "P" is used to represent a CAV convoy that has reached the maximum platoon size, and the combination of "H", "C", and "P" represents different types of vehicle following modes as superscripts; specifically, "HH" refers to an HV following another HV, "HC" refers to an HV following a CAV, "CP" refers to a CAV following a CAV convoy that has reached the maximum size, and "CC" refers to a CAV in the same CAV convoy following another CAV. Therefore, the variables and parameters related to the five vehicle following modes are distinguished by these superscripts, and different subscripts of h represent the safe headway time under different vehicle following modes, that is, h HH 、h HC 、h CH 、h CP 、h CC ; Different subscripts p represent the proportions of different vehicle following modes in mixed traffic flow, that is, p HH 、p HC 、p CH 、p CP 、p CC .

3. The method for calculating and analyzing lane capacity in a mixed traffic scenario of a networked autonomous driving system according to claim 1, characterized in that: Calculate the probability of a CAV being at different positions in a CAV fleet in mixed traffic flow, including: Let p m represents the probability that a vehicle is the mth vehicle in a CAV convoy, m∈{1,2,…,L}; depending on whether the vehicle is the leading vehicle in the CAV convoy, the value of m is divided into two categories: m∈{2,…L} and m=1; (1)m∈{2,3,…,L} Indicates that a vehicle is in a CAV convoy, but is not the leading vehicle of the CAV convoy; at this time, the probability that the vehicle is the mth vehicle in the CAV convoy is expressed as: p m =Pr{A m =2,A m-1 =2,…,A1=2} (16) According to the conditional probability formula and Markov property, the following inferences can be made: p m =Pr{A m =2|A m-1 =2,…,A1=2}Pr{A m-1 =2,…,A1=2} =Pr{A m =2|A m-1 =2}Pr{A m-1 =2,…,A1=2} =t 22 p m-1 (17) Since Equation (17) is applicable to all m∈{2,3,…,L}, according to mathematical induction, the probability that a vehicle is the mth vehicle in a CAV queue is expressed as: p m =(t 22 ) 2 p m-2 =(t 22 ) m-1 p1 (18) (2)m＝1 It indicates that a vehicle is the leading vehicle in a CAV convoy; at this time, the vehicle in front of it is an HV or a CAV convoy that has reached its maximum size, so p1 = p CP +p CH ; The proportion of certain types of vehicle pairs in a mixed traffic flow is directly equal to the probability of the corresponding vehicle following mode, such as τ 12 =p HC , τ 21 =p CH Therefore, according to equations (9)-(11), p CH =p HC In addition, according to formula (14), we get p HC =τ 12 =Pr(A n+1 =1,A n =2) = P C t 12 ; Therefore, the following equation is obtained: p1=p CP +p CH =p CP +p HC =p CP +P C t 12 (19) According to equations (15) and (18), the probability that a CAV follows a CAV fleet that has reached its maximum size is: p CP =Pr{A L+1 =2,A L =2,…,A1=2}=(t 22 ) L p1 (20) Substituting equation (20) into equation (19), if t 22 ≠1, we can get: According to formula (15), we know that t 22 = 1 is equivalent to E = 1, which represents the extreme case where all CAVs are clustered together in the longitudinal lane; considering that the maximum number of rows L is relatively small relative to the number of vehicles on the lane, or all CAVs form an integer maximum-scale platoon, when t 22 =1, that is, when E=1, the following formula is obtained: To sum up, the probability of a vehicle being the leading vehicle in a CAV fleet is: Substituting formula (23) into formula (20), we can get:

4. The method for calculating and analyzing lane capacity in a mixed traffic scenario of a networked autonomous driving system according to claim 3, characterized in that: In step S4: according to equations (12)-(15), (18), (23) and (24), the probabilities of different vehicle following modes in the mixed traffic flow are derived.

5. The method for calculating and analyzing lane capacity in a mixed traffic scenario of a networked autonomous driving system according to claim 1, characterized in that: In step S4: The variable h is used to represent the headway time between any two adjacent vehicles in the mixed traffic flow. Based on the one-to-one mapping relationship between the vehicle following mode and the headway time, the probability distribution of the headway time in the mixed traffic flow is obtained as follows: (1) The probability of an HV following an HV in a mixed traffic flow is: Pr{h=h HH }=p HH =(1-P C )t 11 =1-2P C +τ 22 (25) (2) The probability of an HV following a CAV in mixed traffic flow is: Pr{h=h HC }=p HC =P C t 12 =P C -τ 22 (26) (3) The probability of a CAV following an HV in mixed traffic flow is: Pr{h=h CH }=p CH =(1-P C )t 21 =P C -τ 22 (27) (4) The probability that a CAV in a mixed traffic flow follows a CAV in the same convoy is: (5) The probability that a CAV follows a CAV convoy that has reached its maximum size in a mixed traffic flow is:

6. The method for calculating and analyzing lane capacity in a mixed traffic scenario of a networked autonomous driving system according to claim 5, characterized in that: In step S5: ρ represents the vector composed of the proportions of different vehicle following modes in mixed traffic flow, that is, p = {p HH ,p HC ,p CH ,p CP ,p CC } T ; c represents the lane capacity in the mixed traffic scenario of connected autonomous driving, that is, the maximum mixed traffic flow on a lane; therefore, according to the relationship between the average headway and traffic density and traffic flow, it is obtained that: Substituting the probabilities (25)-(29) of different headways in mixed traffic flow into equation (30), we can obtain the explicit expression of the mixed lane capacity: As shown in formula (31), the mixed lane capacity c(·) is the CAV penetration rate P C , a multivariate function of the upper limit of CAV fleet length L and CAV aggregation intensity E.

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