Intelligent network connection vehicle mixed traffic flow modeling and analysis method considering communication limitation

Abstract

The invention discloses an intelligent network connection vehicle mixed traffic flow modeling and analysis method considering communication limitation. The method comprises the steps that S1, three vehicle following models in a communication limitation environment are constructed and initialized; s2, substituting the three vehicle following models into the vehicle speed in the equilibrium state to obtain the average headstock distance of the three vehicle following models in the equilibrium state; s3, defining an average equilibrium state headstock distance of all vehicles in the mixed traffic flow; s4, dividing the mixed traffic flow into a free flow part and a non-free flow part based on the average equilibrium state headstock distance, and obtaining a flow-density relationship of the mixed traffic flow; s5, partial differential calculation is carried out on the three vehicle following models under communication limitation; and S6, defining an unstable discriminant of the mixed traffic flow model, and obtaining an unstable discriminant of the mixed traffic flow under communication limitation. The model obtained by the invention not only can accurately predict the traffic flow change in a non-ideal communication environment, but also improves the universality and practical application value of the model.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent transportation systems, and particularly relates to a method for modeling and analyzing the mixed traffic flow of intelligent connected vehicles considering communication constraints. Background Art

[0002] With the deep integration of intelligent vehicles and vehicle-to-everything (V2X) technologies, intelligent connected vehicles are expected to significantly improve road capacity and traffic flow stability. However, the full promotion of intelligent connected vehicles and the improvement of related infrastructure still take time, and relevant laws and regulations have not fully caught up. In the foreseeable future, the transportation system will present a mixed traffic flow form in which intelligent connected vehicles coexist with traditional human-driven vehicles. This form will significantly increase the complexity of the traffic environment and bring potential negative impacts on traffic safety, traffic efficiency, and environmental quality.

[0003] The stability and efficiency of mixed traffic flow are restricted by various factors. Among them, communication limitations such as communication latency and data packet loss between vehicles constitute the main technical challenges affecting the performance of intelligent connected vehicles. Currently, most research on mixed traffic flow focuses on the construction of fundamental diagram models and stability analysis, but few studies comprehensively consider the actual impact of communication latency and data packet loss on the performance of mixed traffic flow.

[0004] First, the mixed traffic environment where intelligent connected vehicles coexist with human-driven vehicles is extremely complex. Existing research has not fully addressed communication latency and data packet loss problems, which may seriously weaken the performance of intelligent connected vehicles and affect the stability of traffic flow in practical applications. Second, although some fundamental diagram models have considered the penetration rate of intelligent connected vehicles, these models often ignore the actual impact of communication quality on traffic flow and fail to provide an effective method for accurately predicting traffic flow changes under non-ideal communication conditions. In addition, existing models mostly focus on single scenarios and lack generality to adapt to various traffic conditions and different road types.

[0005] Due to the above technical limitations, the existing technology has not been able to provide an accurate and effective method for analyzing the stability and traffic capacity of mixed traffic flow in the context of high-penetration intelligent connected vehicles and unstable communication environments. In addition, existing methods for evaluating the safety and efficiency of mixed traffic flow lack a unified standard and are difficult to apply to various complex traffic environments. Summary of the Invention

[0006] The present invention provides a mixed traffic flow modeling and analysis method considering the performance degradation of intelligent networked vehicles under communication delay and data packet loss environment. The method can comprehensively evaluate the impact of communication delay and data packet loss on mixed traffic flow, and proposes a basic graph model applicable to a variety of communication conditions and traffic conditions. Compared with the prior art, the model of the present invention can not only accurately predict traffic flow changes under undesirable communication environments, but also improve the versatility and practical application value of the model.

[0007] In order to achieve the above object, the present invention adopts the following technical scheme:

[0008] A method for modeling and analyzing mixed traffic flow of intelligent connected vehicles considering communication constraints includes the following steps:

[0009] S1. Construct and initialize three types of vehicle following models in a communication-constrained environment. The three types of vehicles are respectively a manually driven vehicle, an intelligent connected vehicle, and a degraded intelligent connected vehicle. The degraded intelligent connected vehicle is an intelligent connected vehicle that is degraded to an autonomous driving vehicle due to communication constraints. The communication constraints include communication delay and data packet loss.

[0010] S2, substituting the three vehicle following models constructed in S1 into the equilibrium vehicle speed, and obtaining the average headway distances of the three vehicle following models in equilibrium;

[0011] S3, based on the average headway distances of the three vehicle following models in equilibrium state obtained in S2, defines the average headway distances of all vehicles in the mixed traffic flow in equilibrium state;

[0012] S4, based on the average equilibrium headway obtained in S3, the mixed traffic flow is divided into free flow and non-free flow, and the flow-density relationship of the mixed traffic flow is obtained;

[0013] S5, performing partial differential calculations on the following models of manually driven vehicles, intelligent connected vehicles, and degraded intelligent connected vehicles under limited communication constructed in S1, respectively, to obtain partial differential calculation results;

[0014] S6. Define an unstable discriminant of the mixed traffic flow model, and substitute the partial differential calculation results of the three vehicle following models obtained in S5 into the unstable discriminant of the mixed traffic flow model to obtain the unstable discriminant of the mixed traffic flow under communication restriction.

[0015] Compared with the prior art, the present invention has the following beneficial technical effects:

[0016] The model design of the present invention takes into account different traffic conditions and provides a general solution applicable to various environments such as urban roads and highways. This flexibility and adaptability enable the present invention to provide effective traffic flow analysis and management in a wider range of application scenarios. Through the accurate analysis of the stability of mixed traffic flow, the present invention helps to identify and prevent factors that may lead to traffic accidents, such as instability caused by communication errors. Therefore, these risks can be avoided or reduced by taking measures in advance, thereby enhancing road safety.

[0017] In addition, the model of the present invention considers problems such as time delay and packet loss that may occur in actual communication, making the traffic flow modeling more accurate and capable of more precisely analyzing and predicting the traffic flow state under communication-limited conditions (including communication time delay and data packet loss). By comprehensively considering these influencing factors, the traffic flow capacity and stability can be effectively improved, especially in traffic environments with a high penetration rate of intelligent connected vehicles. This is of great significance for the design and optimization of traffic management systems, as well as the development and application of advanced driver assistance systems.

[0018] Thus, the present invention proposes a set of unified evaluation criteria applicable to evaluating the stability and safety of mixed traffic flow. This standardized method not only helps in comparative analysis in scientific research and engineering practice but also facilitates the formulation and implementation of traffic policies.

[0019] The above beneficial effects reflect the significant advantages of the present invention in improving the scientific and technological level and practical value of traffic flow management, especially in dealing with the complexity and challenges of future traffic environments. These advantages endow the present invention with high application potential and practical value in the field of intelligent transportation systems. Brief Description of the Drawings

[0020] Figure 1 is a schematic flow chart of the present invention;

[0021] Figure 2 is a comparison between the basic graph model of the present invention and the real data collected from the open-access PeMS database, where (a) is the flow-density graph under the change of the initial penetration rate of intelligent connected vehicles, (b) is the flow-density graph under the change of the degradation rate of intelligent connected vehicles, (c) is the flow-density curve of mixed traffic flow under the change of the reaction time delay of degraded intelligent connected vehicles, and (d) is the flow-density curve of mixed traffic flow under the change of the reaction time delay of human-driven vehicles;

[0022] Figure 3 is a heat map of the stability of the present invention changing with the initial penetration rate and degradation rate. Detailed Description of the Invention

[0023] Specifically, the model proposed by the present invention can effectively simulate the degradation behavior of connected and automated vehicles (CAVs) under different penetration rates and communication qualities, and consider the complex dynamic traffic flow when traditional human-driven vehicles and CAVs coexist. By introducing the factors of time delay and packet loss, the model of the present invention can more realistically reflect various potential problems in the actual traffic environment, thereby improving the prediction accuracy of the stability and traffic capacity of the mixed traffic flow. First, analyze three vehicle-following models considering communication constraints and the equilibrium headway. Secondly, derive the fundamental diagram model of the mixed traffic flow including time delay and packet loss, and establish a stability analysis framework. Then, analyze the stability of the mixed traffic flow under the influence of the initial penetration rate and the vehicle degradation factor caused by data packet loss, analyze the characteristics of the mixed traffic flow, and conduct numerical simulation verification. The present invention will be further described in detail below with reference to the accompanying drawings:

[0024] See Figure 1 , the method for modeling and analyzing the mixed traffic flow of CAVs considering communication constraints of the present invention includes the following steps:

[0025] S1. Construct and initialize three vehicle-following models in a communication-constrained environment. These three types of vehicles are human-driven vehicles, CAVs, and degraded CAVs (i.e., CAVs that degrade to autonomous driving vehicles due to communication constraints, where communication constraints include communication time delay and data packet loss).

[0026] The human-driven vehicle adopts the standard parameters of IDM, the CAV adopts the standard parameters of CACC, and the degraded CAV adopts the standard parameters of ACC. Each vehicle-following model is finely adjusted through sensitivity analysis to reflect its unique following dynamics under different communication conditions. Reduce the control gain k p (adjusted from 0.6 to 0.45) to compensate for the overshoot caused by communication time delay. Reduce the control gain k1 (adjusted from 0.3 to 0.23) to compensate for the overshoot caused by reaction time delay. Increase the reaction time delay τ1 (adjusted from 0.1 s to 0.2 s) to distinguish the perception performance between human-driven vehicles and degraded CAVs. This step provides an initial calculation framework for the analysis of the mixed traffic flow.

[0027] Construct a vehicle-following model for human-driven vehicles considering reaction time delay:

[0028]

[0029] Where: a n is the vehicle acceleration at the current moment, a m is the maximum acceleration, v n is the vehicle speed at the current moment, v f is the free-flow speed, s0 is the minimum safety distance, τ1 is the reaction time delay of human-driven vehicles, T is the safe headway, Δvn where \( \Delta v \) is the speed difference between the host vehicle and the leading vehicle, \( b \) is the comfortable deceleration, \( h \) is the headway, and \( l \) is the vehicle length.

[0030] Construct an intelligent connected vehicle following model:

[0031]

[0032] In the formula, \( v \) prev is the vehicle speed at the previous moment, \( k \) p = 0.45, \( k \) d = 0.25 are both control coefficients, \( e \) is the error between the actual headway and the desired headway, represents the differential of the headway error, \( \Delta x \) n is the position difference between the host vehicle and the leading vehicle, and \( t \) g is the desired headway time.

[0033] Construct a degraded intelligent connected vehicle following model considering reaction delay:

[0034] a n = \( k_1[\Delta x \) n - (t g + \( \tau_2)v \) n - \( l - s_0] + k_2\Delta v \) n

[0035] In the formula, \( \tau_2 \) is the reaction delay of the degraded intelligent connected vehicle, and \( k_1 = 0.23 \), \( k_2 = 0.07 \) are both control coefficients.

[0036] In this embodiment, \( k \) p = 0.45, \( k \) d = 0.25, \( k_1 = 0.23 \), \( k_2 = 0.07 \), \( a \) m = 1, \( b = 2 \), \( l = 5 \), \( \tau_1 = 0.2 \), \( T = 1.5 \), \( s_0 = 2.62 \), \( v \) f = 33.3, \( t \) g = 0.6, \( \tau_2 = 0.1 \), \( \Delta t = 0.01 \).

[0037] S2. Substitute the three vehicle following models constructed in S1 into the equilibrium vehicle speed \( v \) e to obtain the average headways of the three vehicle following models at equilibrium. Specifically, it is expressed as follows:

[0038]

[0039] In the formula, \( h_1 \) is the average headway of the human-driven vehicle, \( h_2 \) is the average headway of the intelligent connected vehicle, and \( h_3 \) is the average headway of the degraded intelligent connected vehicle. In this embodiment, \( \beta = 0.3 \), and \( v \) e is from 0 to 33.3 m / s.

[0040] S3. Define the average headway \(h\) of all vehicles in the mixed traffic flow based on the average headways at the equilibrium states of the three vehicle-following models obtained in S2. e That is:

[0041]

[0042] In the formula, \(\beta\) is the degradation rate of connected and automated vehicles (CAVs), representing the proportion of CAVs that degrade into autonomous vehicles relying only on on-vehicle sensors due to communication limitations and lose their cooperative control capabilities; \(p_0\) is the initial penetration rate of CAVs, representing the proportion of CAVs in the mixed traffic flow at the initial moment; the proportion of CAVs in the mixed traffic flow is \(p_0(1 - \beta)\), the proportion of degraded CAVs is \(p_0\beta\), and the proportion of human-driven vehicles is \((1-(p_0(1 - \beta)) - p_0\beta)\). The above definition takes into account the degradation factor. In this embodiment, \(p_0 = 0.6\).

[0043] S4. Based on the average headway at the equilibrium state obtained in S3, divide the mixed traffic flow into two parts: free flow and non-free flow, and thus obtain the flow-density relationship of the mixed traffic flow.

[0044] At the equilibrium state, the equilibrium vehicle speed \(v\) of all vehicles e tends to the free-flow speed \(v\) f , and the density \(q\) of the mixed traffic flow at the equilibrium state e = \(v\) e / \(h\) e ; when the headway is less than the desired headway time and the desired distance , the vehicle starts the acceleration adjustment strategy, that is, dynamically adjusts the acceleration based on the vehicle-following model to maintain a safe distance.

[0045] Specifically, S4 is: Based on the average headway at the equilibrium state obtained in S3, divide the mixed traffic flow into two parts: free flow and non-free flow. When the traffic flow is free flow, the average headway at the equilibrium state is greater than or equal to the desired distance, that is At this time, the free-flow density is \(k\) free = 1 / \(h\) e , and the free-flow flow rate is the product of the speed and the density \(q\) free = \(k\) free · \(v\) f = \(v\) f / \(h\) e ; when the traffic flow is non-free flow, the average headway at the equilibrium state is less than the desired distance, that is At this time, the average speed of the mixed traffic flow in the non-free flow state is The non-free flow density is From the above, the flow-density relationship of the mixed traffic flow is obtained as:

[0046]

[0047] S5. Respectively perform partial differential calculations on the car-following models of manually driven vehicles, connected and automated vehicles, and degraded connected and automated vehicles constructed in S1 to obtain the partial differential calculation results:

[0048]

[0049] In the formula, are respectively the partial differentials of the car-following model of manually driven vehicles with respect to speed v, speed difference Δv, and headway x = Δx - l; are respectively the partial differentials of the car-following model of connected and automated vehicles with respect to speed, speed difference, and headway; are respectively the partial differentials of the car-following model of degraded vehicles with respect to speed, speed difference, and headway; Δt = 0.01 s is the sampling time.

[0050] S6. Define the instability discriminant of the mixed traffic flow model, and substitute the partial differential calculation results of the car-following models of the three types of vehicles obtained in S5 into the instability discriminant of the mixed traffic flow model to obtain the instability discriminant of the mixed traffic flow under communication constraints; specifically:

[0051] The defined instability discriminant of the mixed traffic flow model is:

[0052]

[0053] In the formula: F is the stability discriminant value of the mixed traffic flow, and F < 0 when the traffic flow is unstable; n, m are vehicle numbers; are respectively the partial differentials of the car-following model of the nth vehicle with respect to speed, speed difference, and headway; N is the total number of vehicles in the mixed traffic flow;

[0054] The obtained instability discriminant of the mixed traffic flow under communication constraints is:

[0055]

[0056] Cancel out N and simultaneously for the three terms, and the instability discriminant of the mixed traffic flow under communication constraints can be obtained:

[0057] p0(1 - β)S C +p0βS A +(1 - p0)S I <0

[0058]

[0059] In the formula, S C , S A , S IThey are the stability discriminants for intelligent connected vehicles, degraded intelligent connected vehicles, and human-driven vehicles respectively.

[0060] S7. To analyze the influence of the initial penetration rate of intelligent connected vehicles, communication delay, and data packet loss on the flow of mixed traffic, based on the flow-density relationship obtained in S4, draw the basic flow-density diagrams of intelligent connected vehicles with different initial penetration rates and degradation rates, human-driven vehicles, and degraded intelligent connected vehicles under different time delays. Specifically:

[0061] Draw the basic flow-density diagram of intelligent connected vehicles under the change of the initial penetration rate according to the flow-density relationship obtained in S4. Among them, drawing the basic flow-density diagram according to the flow-density relationship is a well-known method in this field and will not be elaborated here. Under the change of the initial penetration rate of intelligent connected vehicles, take the degradation rate β = 0.3, and take the time delays τ1 = 0.2 s and τ2 = 0.1 s.

[0062] Draw the basic flow-density diagram of intelligent connected vehicles under the change of the degradation rate according to the flow-density relationship obtained in S4. Under the change of the degradation rate of intelligent connected vehicles, take the initial penetration rate p0 = 0.6, the time delay of human-driven vehicles τ1 = 0.2 s, and the time delay of degraded intelligent connected vehicles τ2 = 0.1 s.

[0063] Draw the basic flow-density diagram of human-driven vehicles under the change of the time delay according to the flow-density relationship obtained in S4. Under the change of the time delay of human-driven vehicles, take the initial penetration rate p0 = 0.6 of intelligent connected vehicles, the degradation rate β = 0.3, and the time delay of degraded intelligent connected vehicles τ2 = 0.1.

[0064] Draw the basic flow-density diagram of degraded intelligent connected vehicles under the change of the time delay according to the flow-density relationship obtained in S4. Under the change of the time delay of degraded intelligent connected vehicles, take the initial penetration rate p0 = 0.6 of intelligent connected vehicles, the degradation rate β = 0.3, and the time delay of human-driven vehicles τ1 = 0.2.

[0065] S8. To analyze the influence of the initial penetration rate and degradation rate of intelligent connected vehicles on the stability of mixed traffic, based on the instability discriminant of mixed traffic flow under communication constraints obtained in S7, draw the stability heat maps of intelligent connected vehicles with different initial penetration rates and degradation rates. Among them, drawing the stability heat map according to the instability discriminant of mixed traffic flow is a well-known method in this field and will not be elaborated here.

[0066] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the descriptions and parameters of the embodiments of the present invention shown in the accompanying drawings here can be designed through various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0067] Please refer to Figure 2 , the research scenario of the present invention is a single-lane highway with a maximum speed limit of 120 km / h, and the value range of the equilibrium speed v e is set to 0 - 33.3 m / s. The present invention collected 18,144 sets of speed and density data detected by 63 loop detectors on the US101-S highway from the open-access PeMS database. According to the traffic flow theory q = kv, the macroscopic traffic flow volume value can be obtained. Considering the functional relationship between the traffic flow volume and density of the mixed traffic flow under communication constraints, the impact of connected and autonomous vehicles on the road traffic capacity is analyzed. Figure 2 (a)-(d) compare the real data and the simulation values.

[0068] It can be seen from the simulation results that due to the small inter-vehicle distance, high sensitivity, and good safety of connected and autonomous vehicles, the higher their proportion, the stronger the traffic capacity. However, as the degradation rate increases, the traffic flow volume decreases accordingly. When the traffic flow volume is large, the degradation rate has a significant impact on the traffic state, and has a smaller impact when the vehicle approaches the free flow speed or congestion state. Degraded connected and autonomous vehicles have a stronger ability to suppress interference compared to manually driven vehicles. In addition, as the time delay increases, the maximum traffic flow volume decreases. Therefore, the existence of time delay will reduce the traffic flow volume. And the time delay has a smaller impact on the traffic flow volume of the mixed traffic flow when the vehicle is in a low density and congestion state.

[0069] Please refer to Figure 3 , as the speed gradually increases, the stability of the mixed traffic flow gradually increases. At the same time, as the degree of data packet loss increases, under the conditions of the same speed and the initial penetration rate of connected and autonomous vehicles, the area of the unstable region of the traffic flow increases. When the vehicle speed is low, the change of the degradation rate has a small impact on the stability of the mixed traffic flow. When the vehicle driving speed is greater than 15 m / s, the change of the degradation rate has an increasing impact on the stability of the mixed traffic flow, and the greater the degradation rate, the more significant the impact effect. Therefore, the penetration rate of connected and autonomous vehicles, the packet loss rate, and the vehicle speed are the factors affecting the stability of the traffic flow.

[0070] In summary, compared with the traditional mixed traffic flow modeling and analysis methods, the present invention comprehensively considers the impact of communication constraints on the flow, density, and stability of mixed traffic flow, and can improve the accuracy of the flow-density-speed relationship to a certain extent. It is of great significance for the management and optimization of mixed traffic flow in intelligent transportation systems. In addition, the model of the present invention is not only applicable to a single traffic scenario, but also can be widely applied to various road types and traffic conditions, greatly enhancing the practicability and accuracy of the model. Therefore, the present invention provides a scientific theoretical basis for the design, optimization, and practical application of intelligent transportation systems in complex traffic environments.

[0071] The present invention provides a method for modeling and analyzing mixed traffic flow of connected and autonomous vehicles considering communication constraints. First, for the mixed traffic flow composed of human-driven vehicles and connected and autonomous vehicles, a vehicle-following model under communication constraints is established and the equilibrium headway is analyzed. Secondly, communication delay and packet loss are introduced, and the fundamental diagram model of the mixed traffic flow including human-driven vehicles, connected and autonomous vehicles, and their degraded vehicles under communication constraints is derived, and an analytical framework for the stability of the mixed traffic flow is established. Then, the influence of vehicle degradation factors caused by the initial penetration rate and packet loss on the stability of the mixed traffic flow is analyzed. Finally, the effectiveness of the model proposed in the present invention is verified through numerical simulation, showing how communication delay and packet loss reduce the traffic capacity and stability of the mixed traffic flow, and at the same time indicating that as the penetration rate of connected and autonomous vehicles increases, the traffic flow fluctuation elimination time decreases and the stability level is significantly improved.

[0072] The present invention is applicable to professional technicians in the field of traffic model theory and methods, and demonstrates a technology that can be implemented as a theoretical method or operation process. Therefore, the present invention can be realized in the form of a series of specialized technical tutorials or implementation guide books, aiming to provide a detailed analysis of the mixed traffic flow model and its application in a specific communication-constrained environment.

[0073] The present invention is specifically described step by step, including but not limited to flowcharts, diagrams, and theoretical analysis models. Each step can be realized through theoretical calculations and model derivations, and these theoretical calculations and model derivations can be carried out according to the method manuals or tutorials provided by the present invention to ensure that these methods can be effectively applied to predict and analyze traffic flow dynamics under different traffic environments and communication restriction conditions.

[0074] Each step of the present invention can also be taught through training courses or seminars in traffic engineering, enabling traffic system planners and engineers to use these methods to optimize the management and control of traffic flow. In addition, these methods can also be integrated into advanced traffic management systems to achieve dynamic adjustment and optimization of traffic conditions by directly applying them to traffic flow monitoring and control devices.

[0075] In summary, by providing a series of methods and theoretical guidance, the present invention not only enhances the accuracy and practicality of traffic flow analysis, but also provides a scientific basis for the design and optimization of traffic management systems, and is particularly suitable for analyzing the stability and efficiency of traffic flow in environments with limited communication.

[0076] The above content is only to illustrate the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the claims of the present invention.

Claims

1. Modeling and analysis method of mixed traffic flow of intelligent connected vehicles with limited communication, characterized by: The specific steps include: S1. Construct and initialize three types of vehicle following models in a communication-constrained environment. The three types of vehicles are respectively a manually driven vehicle, an intelligent connected vehicle, and a degraded intelligent connected vehicle. The degraded intelligent connected vehicle is an intelligent connected vehicle that is degraded to an autonomous driving vehicle due to communication constraints. The communication constraints include communication delay and data packet loss. S2. Substitute the three vehicle following models constructed in S1 into the equilibrium vehicle speed v e In the above equation, the average headway distances of the three vehicle following models in equilibrium are obtained; S3, based on the average headway distances of the three vehicle following models in equilibrium state obtained in S2, defines the average headway distances of all vehicles in the mixed traffic flow in equilibrium state; S4, based on the average equilibrium headway obtained in S3, the mixed traffic flow is divided into free flow and non-free flow, and the flow-density relationship of the mixed traffic flow is obtained; S5, performing partial differential calculations on the following models of manually driven vehicles, intelligent connected vehicles, and degraded intelligent connected vehicles under limited communication constructed in S1, respectively, to obtain partial differential calculation results; S6. Define an unstable discriminant of the mixed traffic flow model, and substitute the partial differential calculation results of the three vehicle following models obtained in S5 into the unstable discriminant of the mixed traffic flow model to obtain the unstable discriminant of the mixed traffic flow under communication restriction.

2. The method for modeling and analyzing mixed traffic flow of intelligent connected vehicles considering communication constraints as claimed in claim 1, characterized in that: The three vehicle following models constructed in S1 are as follows: Constructing a car-following model for human-driven vehicles taking into account reaction delay: Where: a n is the vehicle acceleration at the current moment, a m is the maximum acceleration, v n is the vehicle speed at the current moment, v f is the free flow speed, s0 is the minimum safe distance, τ1 is the reaction delay of the manually driven vehicle, T is the safe headway, Δv n is the speed difference between the vehicle and the preceding vehicle, b is the comfortable deceleration, h is the headway between the vehicles, and l is the vehicle length; Building a car-following model for intelligent connected vehicles: In the formula, v prev is the vehicle speed at the last moment, k p =0.45, k d =0.25 are control coefficients, e is the error between the actual vehicle spacing and the expected vehicle spacing, Denotes the differential of the inter-vehicle distance error, Δx n is the position difference between the vehicle in front and the vehicle in front, t g is the expected workshop time interval; Constructing a degraded intelligent connected vehicle following model considering reaction delay: a n =k1[Δx n -(t g +τ2)v n -l-s0]+k2Δv n Where τ2 is the reaction delay of the degraded intelligent connected vehicle, k1=0.23 and k2=0.07 are both control coefficients.

3. The method for modeling and analyzing mixed traffic flow of intelligent connected vehicles considering communication limitations as claimed in claim 2, characterized in that: k p =0.45,k d =0.25,k1=0.23,k2=0.07,a m =1,b=2,l=5,τ1=0.2,T=1.5,s0=2.62,v f =33.3,t g =0.6,τ2=0.1,Δt=0.01。 4. The method for modeling and analyzing mixed traffic flow of intelligent connected vehicles considering communication limitations as claimed in claim 2 or 3, characterized in that: The average headway distances of the three vehicle following models in equilibrium state obtained by S2 are expressed as follows: Where h1 is the average headway of manually driven vehicles, h2 is the average headway of intelligent connected vehicles, and h3 is the average headway of degraded intelligent connected vehicles.

5. The method for modeling and analyzing mixed traffic flow of intelligent connected vehicles considering communication limitations as claimed in claim 4, characterized in that: The average equilibrium headway h of all vehicles in the mixed traffic flow defined by S3 e It is expressed as follows: Where β is the degradation rate of intelligent connected vehicles, which indicates the proportion of intelligent connected vehicles that degenerate into autonomous driving vehicles that rely only on on-board sensors after losing their collaborative control capabilities due to limited communication; p0 is the initial penetration rate of intelligent connected vehicles, which indicates the proportion of intelligent connected vehicles in the mixed traffic flow at the initial moment; the proportion of intelligent connected vehicles in the mixed traffic flow is p0(1-β), the proportion of degraded intelligent connected vehicles is p0β, and the proportion of manually driven vehicles is (1-(p0(1-β))-p0β).

6. The method for modeling and analyzing mixed traffic flow of intelligent connected vehicles considering communication limitations as claimed in claim 5, characterized in that: The specific operation of S4 is as follows: Based on the average equilibrium headway obtained in S3, the mixed traffic flow is divided into free flow and non-free flow. When the traffic flow is free flow, the average equilibrium headway is greater than or equal to the expected distance, that is, At this time, the free flow density is k free =1 / h e , the free stream flow is the product of velocity and density q free =k free ·v f =v f / h e ; When the traffic flow is non-free flow, the average equilibrium headway is less than the expected distance, that is, At this time, the average speed of mixed traffic flow in the non-free flow state is The non-free flow density is From the above, the relationship between mixed traffic flow and density is:

7. The method for modeling and analyzing mixed traffic flow of intelligent connected vehicles considering communication limitations as claimed in claim 6, characterized in that: The partial differential calculation results of S5 are as follows: In the formula, are the partial differentials of the artificial driving vehicle following model with respect to speed v, speed difference Δv and headway x = Δx-l respectively; They are the partial differentials of the intelligent connected vehicle following model for speed, speed difference and headway distance respectively; are the partial derivatives of the degraded vehicle following model with respect to speed, speed difference and headway distance respectively; Δt=0.01s is the sampling time.

8. The method for modeling and analyzing mixed traffic flow of intelligent connected vehicles considering communication limitations as claimed in claim 7, characterized in that: In S6, the instability discriminant of the mixed traffic flow model is defined as: Where: F is the mixed traffic flow stability judgment value, when the traffic flow is unstable, F<0; n, m are vehicle numbers; are the partial differentials of the vehicle following model of the nth vehicle with respect to speed, speed difference and headway; N is the total number of vehicles in the mixed traffic flow; The obtained mixed traffic flow instability discriminant under communication constraints is: p0(1-β)S C +p0βS A +(1-p0)S I <0 In the formula, S C , S A , S I They are the stability discriminants for intelligent connected vehicles, degraded intelligent connected vehicles and manually driven vehicles respectively.

9. The method for modeling and analyzing mixed traffic flow of intelligent connected vehicles considering communication limitations as claimed in claim 8, characterized in that: The following steps are also included: S7. To analyze the impact of the initial penetration rate of intelligent connected vehicles and the communication delay and data packet loss on the mixed traffic flow, a basic flow-density diagram of different initial penetration rates and degradation rates of intelligent connected vehicles, manually driven vehicles and degraded intelligent connected vehicles under different delays is drawn according to the flow-density relationship obtained in S4; S8. In order to analyze the impact of the initial penetration rate and degradation rate of intelligent connected vehicles on the stability of mixed traffic flow, according to the instability discriminant of mixed traffic flow under communication restriction obtained in S7, the stability heat map of intelligent connected vehicles under different initial penetration rates and degradation rates is drawn.

10. The method for modeling and analyzing mixed traffic flow of intelligent connected vehicles considering communication limitations as claimed in claim 9, characterized in that: Specific operation of S7: According to the traffic-density relationship obtained in S4, the traffic-density basic diagram under the change of the initial penetration rate of intelligent connected vehicles is drawn. Under the change of the initial penetration rate of intelligent connected vehicles, the degradation rate β = 0.3, the delay τ1 = 0.2s, τ2 = 0.1s are taken; According to the traffic-density relationship obtained in S4, the traffic-density basic diagram under the change of the degradation rate of intelligent connected vehicles is drawn. Under the change of the degradation rate of intelligent connected vehicles, the initial penetration rate p0 = 0.6, the time delay of the manually driven vehicle τ1 = 0.2s, and the time delay of the degraded intelligent connected vehicle τ2 = 0.1s are taken; According to the traffic-density relationship obtained in S4, the basic traffic-density diagram under the delay change of manually driven vehicles is drawn. Under the delay change of manually driven vehicles, the initial penetration rate of intelligent connected vehicles p0 = 0.6, the degradation rate β = 0.3, and the degraded intelligent connected vehicle delay τ2 = 0.1; According to the traffic-density relationship obtained in S4, a basic traffic-density diagram is drawn under the delay change of degraded intelligent connected vehicles. Under the delay change of degraded intelligent connected vehicles, the initial penetration rate of intelligent connected vehicles is p0=0.6, the degradation rate β=0.3, and the delay τ1=0.2 of manually driven vehicles.

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