Method and system for calculating minimum separation distance of urban expressway under heterogeneous traffic flow

Abstract

The application discloses a kind of minimum clear distance calculation method and system of urban expressway under heterogeneous traffic flow, the method includes the following steps: according to the driving speed of each lane vehicle of current urban expressway traffic speed regulation setting, calculate the critical safety vehicle distance between the front and rear vehicles of target lane in the lane changing process of lane changing vehicle;According to the type of lane changing vehicle and the front and rear vehicles of target lane, several lane changing scenarios are constructed, the minimum lane changing gap between the front and rear vehicles of target lane and lane changing vehicle under each lane changing scenario is calculated according to the critical safety vehicle distance, the minimum lane changing gap is used as the driving constraint of lane changing vehicle, the driving scene of lane changing vehicle and the front and rear vehicles of target lane under all lane changing scenarios is simulated;According to the simulation result, the minimum clear distance under all lane changing scenarios is calculated, and the maximum value in all minimum clear distances is taken as the minimum clear distance of current urban expressway.The minimum clear distance calculated by the application fully considers the difference of driving vehicle type, and is more practical.

Description

Technical Field

[0001] This invention belongs to the field of road traffic design technology, specifically relating to a method and system for calculating the minimum clearance of urban expressways under heterogeneous traffic flow. Background Technology

[0002] The minimum clearance at interchanges on urban expressways directly impacts the overall road safety and traffic efficiency. With the continuous development and advancement of autonomous driving technology, the penetration rate of autonomous vehicles is gradually increasing. Road traffic will consist of both autonomous and human-driven vehicles, forming a persistent heterogeneous traffic flow. Against this backdrop, research on whether and how road geometry design indicators are adapted to this environment becomes crucial. The clearance section between adjacent interchanges is the core area of ​​this research. Specifically, it refers to the section from the end of the acceleration lane transition section of the previous interchange to the beginning of the deceleration lane transition section of the next interchange. This is a critical area for frequent vehicle interactions such as following and lane changes. Traffic flow in this area is susceptible to conflicts and interference, often leading to traffic chaos and frequent accidents, thus becoming a bottleneck affecting the overall operational quality of the urban expressway network. Under heterogeneous traffic flow conditions, factors such as differences in driving behavior between autonomous and human-driven vehicles, clearance section length, traffic volume, vehicle speed, and the penetration rate of autonomous vehicles all have complex impacts on traffic flow, making the scientific and accurate calculation of the minimum clearance a prerequisite for ensuring safety and efficiency.

[0003] To solve for the minimum clearance mentioned above, existing research has evolved from theoretical models to simulation verification: early work simply built clearance calculation models based on acceptable clearance theory, vehicle kinematics, probability theory and other methods; in recent years, with the development of calculation methods, research has further introduced traffic conflict simulation methods to verify and correct the model results.

[0004] While these findings provide fundamental theoretical support for the minimum clearance design of urban expressway interchanges, their focus is primarily on the operational characteristics of manually driven vehicles. The characterization of clearance segment traffic characteristics and lane-changing behavior remains insufficient, particularly regarding the interaction and strategic game behavior between manually and autonomous vehicles. Furthermore, there is a lack of systematic research on clearance segment length under heterogeneous traffic flow conditions. On the one hand, most studies only consider the assumptions of manually driven vehicles and fixed clearances, failing to fully reflect the complex traffic environment after the incorporation of autonomous vehicles. On the other hand, the models do not adequately characterize the key behavioral differences between manually and autonomous vehicles in terms of reaction time, acceleration / deceleration capabilities, and lane-changing strategies, resulting in an inability to accurately reflect the core characteristics such as the interaction, acceleration / deceleration behavior, and lane-changing behavior between different types of vehicles in heterogeneous traffic flows. Therefore, the applicability and accuracy of existing methods in the context of heterogeneous traffic flows still need improvement. Summary of the Invention

[0005] This invention proposes a method and system for calculating the minimum clearance of urban expressways under heterogeneous traffic flow, which solves the problem of poor applicability and accuracy of existing technologies in the context of heterogeneous traffic flow.

[0006] To address the aforementioned technical problems, this invention provides a method for calculating the minimum clearance of urban expressways under heterogeneous traffic flow, comprising the following steps:

[0007] Step S1: Set the driving speed of vehicles in each lane according to the current driving speed regulations of the urban expressway, and calculate the critical safe distance between the lane-changing vehicle and the vehicles in front and behind in the target lane during the lane-changing process based on the vehicle speed.

[0008] Step S2: Construct several lane-changing scenarios based on the types of lane-changing vehicles and vehicles in front and behind the target lane. Calculate the minimum lane-changing gap between the lane-changing vehicle and vehicles in front and behind the target lane in each lane-changing scenario based on the critical safe distance. Use the minimum lane-changing gap as the driving constraint for the lane-changing vehicle and simulate the driving scenarios of the lane-changing vehicle and vehicles in front and behind the target lane in all lane-changing scenarios.

[0009] Step S3: Based on the simulation results, determine the braking reaction distance of lane-changing vehicles, the distance traveled when searching for lane-changing gaps, and the lane-changing distance for all lane-changing scenarios. Calculate the minimum clearance for all lane-changing scenarios and take the maximum value among all minimum clearances as the current minimum clearance for the urban expressway.

[0010] Preferably, the expression for calculating the critical safe distance between the lane-changing vehicle and the vehicles in front and behind in the target lane during the lane-changing process based on the vehicle's speed in step S1 is as follows:

[0011] ;

[0012] In the formula, For vehicles n The critical safe following distance; , They are respectively t Time and t +1 moment vehicle n speed; , vehicles n The reaction time and braking time; For vehicles n The maximum braking deceleration.

[0013] Preferably, the lane-changing vehicle and the vehicles in front and behind the target lane in step S2 are either autonomous or manually driven vehicles. Several lane-changing scenarios are constructed based on the types of the lane-changing vehicle and the vehicles in front and behind the target lane, including:

[0014] Lane change scenario 1: The vehicle changing lanes and the vehicles in front and behind in the target lane are all manually driven;

[0015] Lane change scenario 2: The vehicle changing lanes and the vehicle behind in the target lane are manually driven vehicles, while the vehicle in front in the target lane is an autonomous vehicle;

[0016] Lane change scenario 3: The vehicle changing lanes and the vehicle in front of the target lane are manually driven vehicles, while the vehicle behind the target lane is an autonomous vehicle.

[0017] Lane change scenario 4: The vehicle changing lanes is a manually driven vehicle, while the vehicles in front and behind the target lane are autonomous vehicles;

[0018] Lane change scenario 5: The vehicle changing lanes is an autonomous vehicle, while the vehicles in front and behind the target lane are manually driven vehicles;

[0019] Lane change scenario 6: The vehicle changing lanes and the vehicle in front of the target lane are both autonomous vehicles; the vehicle behind the target lane is also an autonomous vehicle.

[0020] Lane change scenario 7: The vehicle changing lanes and the vehicle behind in the target lane are autonomous vehicles, and the vehicle in front in the target lane is an autonomous vehicle;

[0021] Lane change scenario 8: The vehicle changing lanes and the vehicles in front and behind the target lane are all autonomous vehicles.

[0022] Preferably, each lane-changing scenario also includes direct lane-changing scenarios and collaborative lane-changing scenarios;

[0023] The direct lane-changing scenario is as follows: when the vehicle changing lanes changes lanes, the vehicles in front and behind in the target lane maintain their original driving speeds;

[0024] The cooperative lane-changing scenario is as follows: when the lane-changing vehicle changes lanes, the vehicle in front of the target lane accelerates or the vehicle behind accelerates or the vehicle in front accelerates and the vehicle behind accelerates.

[0025] Preferably, the expression for calculating the minimum lane-changing clearance between the lane-changing vehicle and the vehicles in front and behind the target lane in each lane-changing scenario based on the critical safe following distance in step S2 is as follows:

[0026] (1) When the lane-changing vehicle is an autonomous vehicle and the current scenario is a direct lane change, the expression for the minimum lane-changing gap is:

[0027] ;

[0028] ;

[0029] ;

[0030] In the formula, The minimum lane-changing clearance required for autonomous vehicles to make direct lane changes; after the lane change is completed, the following behavior of the vehicles in front and behind is established. The critical safe distance between the following vehicle and the vehicle in front during car-following behavior; The critical safe distance between the following vehicle and the vehicle in front in car-following behavior; , These represent the travel distances of vehicles in front and behind the target lane during the lane-changing process in a direct lane-changing scenario. The length of the vehicle changing lanes; , These represent the speeds of the vehicles in front and behind in the target lane before the lane change; The lane-changing time for vehicles changing lanes;

[0031] (2) When the lane-changing vehicle is an autonomous vehicle and the current lane-changing scenario is cooperative, the expression for the minimum lane-changing gap is:

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] In the formula, The minimum lane change interval required for autonomous vehicles to perform cooperative lane changes; , These represent the travel distances of vehicles in front and behind in the target lane during the lane-changing process in a collaborative lane-changing scenario. The distance traveled to maintain the original speed of the vehicle in front; For the comfort acceleration of the vehicle ahead in the target lane; To reduce the speed for the comfort of vehicles following in the target lane;

[0037] (3) When the lane-changing vehicle is a manually driven vehicle and the current scenario is a direct lane change, the expression for the minimum lane-changing gap is:

[0038] ;

[0039] In the formula, The minimum lane change clearance required for a manually driven vehicle to make a direct lane change;

[0040] (4) When the lane-changing vehicle is a manually driven vehicle and the current scenario is a cooperative lane-changing scenario, the expression for the minimum lane-changing gap is:

[0041] ;

[0042] In the formula, The minimum lane change interval required for collaborative lane changing for manually driven vehicles.

[0043] Preferably, in step S2, when simulating the driving scenarios of lane-changing vehicles and vehicles in front and behind the target lane under all lane-changing scenarios, the headway of the target lane is fitted using the Erlang distribution. In step S3, the distance traveled by the lane-changing vehicle when searching for a lane-changing gap is calculated based on the headway. The expression for fitting the headway of the target lane using the Erlang distribution is:

[0044] ;

[0045] In the formula, This represents the probability distribution of the headway between the train and the train. The acceptable headway for lane-changing vehicles; The headway to the target lane; The average arrival rate of vehicles in the target lane; Let be the specific order of the Erlang distribution.

[0046] Preferably, the braking reaction distance in step S3 includes the sign reaction distance and the exit confirmation distance, and the expression for calculating the minimum clearance under all lane-changing scenarios is:

[0047] (1) When the lane-changing vehicle is a manually driven vehicle, the expression for the minimum clearance is:

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] ;

[0055] In the above formula, Minimum clearance; To indicate the reaction distance; The speed of vehicles changing lanes at the starting point of the clearance section; Reading time; For decision-making time; The distance traveled when finding a lane-changing gap for a vehicle changing lanes; For vehicles changing lanes i During the next lane change, the distance the vehicle travels while waiting for an acceptable lane change interval; The driving speed during the acceptable lane-changing interval for vehicles to change lanes; This represents the average waiting time for vehicles changing lanes. n The number of unacceptable lane-changing gaps that a vehicle must pass through from the moment it decides to change lanes; For vehicles changing lanes i Vehicle adjustment distance during lane change; The critical safe following distance between a vehicle changing lanes and the vehicle following in the target lane; The length of the vehicle changing lanes; The speed of the vehicle behind in the target lane; This refers to the distance traveled by a vehicle in the direction of travel during the lane-changing process. The longitudinal speed of the vehicle changing lanes; It equals the lane width divided by the vehicle's lateral speed; Before a vehicle enters the next ramp exit, confirm the safe distance from the exit location; The speed at which a vehicle changing lanes approaches the end of the clearance section;

[0056] (2) When the lane-changing vehicle is an automated driving vehicle, the expression for the minimum clearance is:

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] in .

[0063] This invention also provides a minimum clearance calculation system for urban expressways under heterogeneous traffic flow, which is based on the above-mentioned minimum clearance calculation method for urban expressways under heterogeneous traffic flow, and includes: a scene generation module, a lane-changing behavior simulation module, a minimum clearance calculation module, and a verification and optimization module;

[0064] The scenario generation module constructs lane-changing scenarios based on the penetration rate of autonomous vehicles, historical traffic flow, and urban expressway design specifications, calculates the probability of each scenario occurring within the entire net distance segment, and forms a scenario-probability matrix.

[0065] The lane-changing behavior simulation module simulates the longitudinal displacement, acceleration and deceleration process, and time required for a vehicle to complete one or more lane changes between different lanes in each lane-changing scenario, and outputs the single lane-changing distance required for a single lane change in all lane-changing scenarios.

[0066] The minimum clearance calculation module: accumulates the single lane change distance according to the number of lane changes, and superimposes the sign reaction distance, gap finding distance, vehicle adjustment distance and exit confirmation distance to finally obtain the minimum clearance length corresponding to the current lane change scenario; and performs a weighted summation of all minimum clearance lengths according to the scenario probability to obtain the comprehensive minimum clearance design value under the current autonomous driving penetration rate.

[0067] The verification and optimization module compares the calculation results with current standards or historical accident data to verify the rationality of the simulation. If the deviation exceeds the set threshold, it backtracks to check the parameters or scenario weights.

[0068] Preferably, the expression for the single lane change distance required for a single lane change in all lane change scenarios output by the lane change behavior simulation module is:

[0069] ;

[0070] ;

[0071] ;

[0072] ;

[0073] In the above formula, The distance traveled when finding a lane-changing gap for a vehicle changing lanes; For vehicles changing lanes i During the next lane change, the distance the vehicle travels while waiting for an acceptable lane change interval; The driving speed during the acceptable lane-changing interval for vehicles to change lanes; This represents the average waiting time for vehicles changing lanes. n The number of unacceptable lane-changing gaps that a vehicle must pass through from the moment it decides to change lanes; This represents the probability distribution of the headway between the train and the train. The acceptable headway for lane-changing vehicles; The headway to the target lane; The average arrival rate of vehicles in the target lane; For the specific order of the Erlang distribution; For vehicles changing lanes i Vehicle adjustment distance during lane change; The critical safe following distance between a vehicle changing lanes and the vehicle following in the target lane; The length of the vehicle changing lanes; The speed of the vehicle behind in the target lane.

[0074] Preferably, after obtaining the minimum clearance design value for each autonomous driving penetration rate, the minimum clearance calculation module uses the maximum value among all minimum clearance design values ​​as the comprehensive minimum clearance design value for the current urban expressway.

[0075] The beneficial effects of the present invention include at least the following:

[0076] 1. Set vehicle speeds based on the current legal speed limits for urban expressways to ensure that the calculation of critical safe following distances is dynamically linked to actual traffic regulations, and avoid the failure of safety thresholds due to deviations in vehicle speed assumptions.

[0077] 2. In heterogeneous traffic flow environments, by fully considering the differences between manually driven vehicles and autonomous vehicles, and by accurately calculating the minimum clearance after taking into account the differences between vehicles, the risk of collision that may be caused by the different characteristics of vehicles can be effectively avoided. When a manually driven vehicle changes lanes in front of an autonomous vehicle, an appropriate clearance is determined based on the rapid response characteristics of the autonomous vehicle to ensure a sufficient safe distance and reduce the accident rate. Attached Figure Description

[0078] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0079] Figure 2 This is a schematic diagram illustrating safe car-following in an embodiment of the present invention;

[0080] Figure 3 This is a schematic diagram of the lane-changing process in an embodiment of the present invention;

[0081] Figure 4 This is a schematic diagram illustrating the classification of heterogeneous flow lane-changing scenarios in an embodiment of the present invention;

[0082] Figure 5 This is a schematic diagram of the diversion vehicle's travel path in the clearance section of this invention.

[0083] Figure 6 This is a schematic diagram of the minimum clearance composition model of the interchange in an embodiment of the present invention. Detailed Implementation

[0084] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0085] like Figure 1As shown in the figure, this embodiment of the invention provides a method for calculating the minimum clearance of urban expressways under heterogeneous traffic flow, including the following steps:

[0086] Step S1: Set the driving speed of vehicles in each lane according to the current driving speed regulations of the urban expressway, and calculate the critical safe distance between the lane-changing vehicle and the vehicles in front and behind in the target lane during the lane-changing process based on the vehicle speed.

[0087] Specifically, when calculating the minimum clearance length of interchanges on urban expressways, the 85th percentile of the lane speed required by road specifications is used as the operating speed of vehicles in that lane. A model is then constructed to calculate the critical safe following distance, such as... Figure 2 As shown, the critical safe following distance can be expressed as:

[0088] ;

[0089] In the formula, For vehicles n The critical safe following distance, and must meet the following requirements. The critical safe following distance between a vehicle changing lanes and the vehicle following it in the target lane is The critical safe distance between a vehicle changing lanes and the vehicle in front in the target lane ; , They are respectively t Time and t +1 moment vehicle n speed; , vehicles n The reaction time and braking time of autonomous and manually driven vehicles differ. For vehicles n The maximum braking deceleration.

[0090] Step S2: Construct several lane-changing scenarios based on the types of lane-changing vehicles and vehicles in front and behind the target lane. Calculate the minimum lane-changing gap between the lane-changing vehicle and vehicles in front and behind the target lane in each lane-changing scenario based on the critical safe following distance. Use the minimum lane-changing gap as the driving constraint for the lane-changing vehicle and simulate the driving scenarios of the lane-changing vehicle and vehicles in front and behind the target lane in all lane-changing scenarios.

[0091] Specifically, eight heterogeneous flow lane-changing scenarios are constructed based on combinations of lane-changing vehicle types and the types of vehicles preceding and following the target lane. Each scenario considers both direct lane-changing and cooperative lane-changing behavior modes. The eight heterogeneous flow lane-changing scenarios are as follows:

[0092] Lane change scenario 1: The vehicle changing lanes and the vehicles in front and behind in the target lane are all manually driven;

[0093] Lane change scenario 2: The vehicle changing lanes and the vehicle behind in the target lane are manually driven vehicles, while the vehicle in front in the target lane is an autonomous vehicle;

[0094] Lane change scenario 3: The vehicle changing lanes and the vehicle in front of the target lane are manually driven vehicles, while the vehicle behind the target lane is an autonomous vehicle.

[0095] Lane change scenario 4: The vehicle changing lanes is a manually driven vehicle, while the vehicles in front and behind the target lane are autonomous vehicles;

[0096] Lane change scenario 5: The vehicle changing lanes is an autonomous vehicle, while the vehicles in front and behind the target lane are manually driven vehicles;

[0097] Lane change scenario 6: The vehicle changing lanes and the vehicle in front of the target lane are both autonomous vehicles; the vehicle behind the target lane is also an autonomous vehicle.

[0098] Lane change scenario 7: The vehicle changing lanes and the vehicle behind in the target lane are autonomous vehicles, and the vehicle in front in the target lane is an autonomous vehicle;

[0099] Lane change scenario 8: The vehicle changing lanes and the vehicles in front and behind the target lane are all autonomous vehicles.

[0100] like Figure 3 As shown, by analyzing the positional relationship between the lane-changing vehicle and the adjacent vehicles in the deceleration lane before and after the lane change, a basic minimum lane-changing clearance model for lane-changing vehicles is constructed as follows:

[0101] ;

[0102] In the formula, The minimum acceptable lane-changing clearance for vehicles changing lanes; The safe following distance between the vehicle changing lanes and the vehicle following in the target lane after a lane change; The safe following distance between the vehicle changing lanes and the leading vehicle in the target lane after a lane change; , These represent the longitudinal travel distances of the leading vehicle and the following vehicle in the target lane during the lane change process, respectively. This refers to the length of the vehicle.

[0103] In practice, lane-changing vehicles may use direct or cooperative lane changing. When direct lane changing is used, the travel distance of the vehicle in the target lane can be expressed as:

[0104] ;

[0105] ;

[0106] In the above formula, , These represent the travel distances of vehicles in front and behind the target lane during the lane-changing process in a direct lane-changing scenario. The length of the vehicle changing lanes; , These represent the speeds of the vehicles in front and behind in the target lane before the lane change; This refers to the lane-changing time for vehicles changing lanes.

[0107] When cooperative lane changing is adopted, vehicles cannot change lanes directly; cooperation between vehicles in front and behind is required to complete the lane change. The cooperative lane changing behavior in each heterogeneous flow lane changing scenario is as follows: Figure 4 As shown.

[0108] from Figure 4 As can be seen, when the lane-changing vehicle is a manually driven vehicle (HV), if the vehicle following in the target lane is also a manually driven vehicle (HV), as shown in scenarios 1 and 2, during the lane-changing process, the manually driven vehicle may maintain its original speed, refuse to cooperate with the lane-changing vehicle, or choose to slow down and give way. If the vehicle following in the target lane is an autonomous vehicle (AV), the autonomous vehicle will accept the lane-changing request and cooperate with the lane-changing vehicle. Regarding the decision-making behavior of the vehicle in front in the target lane, if the vehicle in front in the target lane is an HV, since the lane-changing vehicle is not within its field of vision, there is almost no interaction between the two vehicles. Therefore, the lane-changing vehicle only needs to treat it as an obstacle vehicle, just like the vehicle in front in its current lane. If the vehicle in front in the target lane is an AV, since the lane-changing vehicle is an HV, it cannot communicate with other vehicles and therefore cannot recognize the lane-changing behavior, and will continue to travel at its original speed.

[0109] When the lane-changing vehicle is an autonomous vehicle (AV), if the vehicle behind in the target lane is a manually driven vehicle (HV), as shown in scenarios 5 and 6, the HV may choose to refuse the lane-changing vehicle's request or decelerate to cooperate. If the vehicle in front of the target lane is a manually driven HV, as shown in scenarios 7 and 8, the vehicle in front of the target lane cannot make a decision because the lane-changing vehicle is not within its field of vision and will continue to travel at its original speed. If there is an AV in the target lane, as shown in scenarios 6 and 7, the vehicles in the target lane can communicate with the AV that needs to change lanes and adjust their distance from the vehicles in front and behind by accelerating or decelerating to assist the lane-changing vehicle. If both vehicles in front and behind the target lane are AVs, as shown in scenario 8, the problem becomes a multi-vehicle cooperative lane-changing problem in a fully connected autonomous driving environment, which can achieve safer and more efficient lane changing.

[0110] During the lane-changing vehicle re-decision phase, if both the leading and following vehicles in the target lane refuse the lane-changing request, the lane-changing vehicle will choose to abandon the lane-changing; if either the leading or following vehicle in the target lane accepts the lane-changing request, the lane-changing vehicle will choose to continue to complete the lane-changing.

[0111] In a cooperative lane-changing scenario, the travel distance of a vehicle in the target lane can be expressed as:

[0112] ;

[0113] ;

[0114] ;

[0115] In the above formula, , These represent the travel distances of vehicles in front and behind in the target lane during the lane-changing process in a collaborative lane-changing scenario. The distance traveled to maintain the original speed of the vehicle in front; For the comfort acceleration of the vehicle ahead in the target lane; To provide a comfortable deceleration for vehicles following in the target lane.

[0116] Based on the above formula, when the lane-changing vehicle is an autonomous vehicle, the minimum lane-changing gap required for a direct lane change is... It can be represented as:

[0117] ;

[0118] After the lane change is completed, the vehicles in front and behind will follow each other. The critical safe distance between the following vehicle and the vehicle in front during car-following behavior; The critical safe distance between the following vehicle and the vehicle in front during car-following behavior in autonomous driving.

[0119] When the lane-changing vehicle is an autonomous vehicle, the minimum lane-changing clearance required for cooperative lane changing. It can be represented as:

[0120] .

[0121] When the lane-changing vehicle is manually driven, the minimum lane-changing clearance for direct lane changing and cooperative lane changing can be expressed as follows: and :

[0122] ;

[0123] .

[0124] Step S3: Based on the simulation results, determine the braking reaction distance of lane-changing vehicles, the distance traveled when searching for lane-changing gaps, and the lane-changing distance for all lane-changing scenarios. Calculate the minimum clearance for all lane-changing scenarios and take the maximum value among all minimum clearances as the current minimum clearance for the urban expressway.

[0125] Specifically, as Figure 5Taking a one-way three-lane interchange as an example, the vehicles affecting the clearance section length are mainly diverting vehicles. Vehicles entering the clearance section are restricted by the exit ramp location and must change lanes to the outermost lane (lane 1) before the end of the clearance section. Therefore, within the clearance section of a one-way three-lane interchange, diverting vehicles that need to change lanes can leave the main line via the following three main paths:

[0126] Route A: Vehicles located in lane 3 of the main line at the starting point of the clearance section, such as Figure 5 As shown in (a), the vehicle changes lanes to the outermost lane and enters the exit ramp following the path of lane 3 → lane 2 → lane 1.

[0127] Route B: Vehicles located in lane 2 of the main line at the starting point of the clearance section, such as Figure 5 As shown in (b), the vehicle changes lanes from lane 2 to lane 1 to the outermost lane and enters the exit ramp. Although lane 3 is more efficient, it is rare for diverting vehicles to change lanes from lane 2 to the inner lane and then to the outer lane. Moreover, frequent lane changes of this kind would affect traffic order. Therefore, this lane-changing behavior will not be discussed in the lane-changing scenario.

[0128] Route C: Vehicles located in mainline lane 1 at the start of the clearance section, such as... Figure 5 As shown in (c), this may come from mainline lane 1 or vehicles entering the mainline from the entrance ramp. These vehicles could have continued to travel in lane 1 until they exited the clearance section before entering the exit ramp, but due to the influence of the free lane-changing motive, in order to pursue traffic efficiency, the vehicles first changed lanes to the middle lane, i.e., lane 2, and then changed lanes to the outermost lane 1 when they were closer to the end of the clearance section.

[0129] Considering the worst-case scenario, paths A and C involve two lane changes, requiring a longer distance than path B. The main reason for the difference in minimum clearance between paths A and C is the lane change (lane 1). Speed ​​characteristic analysis shows that lane 3 has a higher speed than lane 1, therefore the distance required for lane change 1 on path A is longer than on path C. Therefore, in this embodiment of the invention, the worst-case scenario of path A is selected as the research scenario for the minimum clearance calculation model. Figure 6 The minimum clearance length of an urban expressway interchange under heterogeneous traffic flow is shown as a component. The formula for calculating the minimum clearance length can be expressed as:

[0130] ;

[0131] In the formula, Minimum clearance; To indicate the reaction distance; The distance a vehicle travels when changing lanes from lane 3 to lane 2 to find a lane change gap; The distance a vehicle travels when changing lanes from lane 2 to lane 1 to find a lane change gap; The distance traveled along the direction of travel during the lane change process for a vehicle moving from lane 3 to lane 2; The distance traveled along the direction of travel during the lane change process for a vehicle moving from lane 2 to lane 1; Before a vehicle enters the next ramp exit, confirm the safe distance from the exit location.

[0132] When the lane-changing vehicle is manually driven, the sign reaction distance is... It can be represented as:

[0133] ;

[0134] In the formula, The speed of vehicles changing lanes at the starting point of the clearance section; The reading time is 2.6 seconds in this embodiment of the invention; The decision time is set to 2.6 seconds in this embodiment of the invention.

[0135] The distance traveled by a vehicle changing lanes while searching for a lane-changing gap. It can be represented as:

[0136] ;

[0137] ;

[0138] ;

[0139] In the above formula, The distance a vehicle travels during the acceptable lane-changing interval when a vehicle is changing lanes; The speed at which vehicles wait for an acceptable lane-changing interval is generally 0.76 times the mainline operating speed. This represents the average waiting time for vehicles changing lanes. n The number of unacceptable lane-changing gaps that a vehicle must pass through from the moment it decides to change lanes; The distance that a vehicle adjusts its body distance when changing lanes; This refers to the critical safe following distance between a vehicle changing lanes and the vehicle following in the target lane.

[0140] The distance traveled by a vehicle in the direction of travel during a lane change. It can be represented as:

[0141] ;

[0142] In the formula, The longitudinal speed of the vehicle changing lanes; It equals the lane width divided by the vehicle's lateral speed, where the vehicle's lateral speed is taken as 1 m / s and the lane width as 3.75 m. It equals 3.75s.

[0143] Before entering the next exit ramp, confirm the safe distance from the exit ramp location. It can be represented as:

[0144] ;

[0145] In the formula, The speed at which a vehicle changing lanes approaches the end of the clearance section.

[0146] When lane-changing vehicles are autonomous vehicles, they can obtain real-time traffic information such as the distance from the end of the interchange clearance section and the lane occupancy rate of the interchange clearance section through high-precision maps. They do not need to react to or make decisions based on signs, thus eliminating the need for signs to respond at a specific distance. And confirm the safe distance at the exit of the ramp. Set the value to 0m.

[0147] Find the gap distance Distance between vehicles The calculation method is the same as when the lane-changing vehicle is a manually driven vehicle.

[0148] In the specific simulation process, the headway distribution function conforming to the three main lanes of the clearance section is first analyzed. Then, the parameter values ​​in the model are determined. Taking a clearance section of an urban expressway with three main lanes and a design speed of 80 km / h as an example, the penetration rate of autonomous vehicles is analyzed. The minimum net clearance length was calculated for 0%, 20%, 40%, 60%, 80%, and 100% of the lane change scenarios. The distribution ratios for different lane change scenarios are shown in Table 1.

[0149] Table 1 Distribution ratio of different lane-changing scenarios

[0150]

[0151] Under low traffic flow conditions, headway can be represented by a negative exponential distribution, and its probability density function is expressed as follows:

[0152] ;

[0153] In the formula, This refers to the headway of the train. Let be the probability density function of the headway. This represents the average arrival rate of vehicles.

[0154] As traffic flow increases, the headway distribution is typically determined by fitting the Erlang distribution, and its probability density function is expressed as:

[0155] ;

[0156] In the formula, The acceptable headway for lane-changing vehicles; Let be the specific order of the Erlang distribution, taken as a positive integer.

[0157] Under conditions of high traffic volume or congestion, the headway between vehicles tends to stabilize at a relatively fixed value:

[0158] ;

[0159] In the formula, This refers to the actual traffic capacity of the road.

[0160] In this embodiment of the invention, the Erlang distribution is selected for fitting the headway distance. The headway distance distributions for all three lanes are of order 2 Erlang. The parameter values ​​involved in the simulation model are summarized in Table 2.

[0161] Table 2 Summary of Model Parameter Values

[0162]

[0163] When calculating the minimum clearance length of interchanges on urban expressways, based on speed characteristic surveys, the 85th percentile speed of each lane is taken as the operating speed of vehicles in that lane. That is, the operating speed of lane 3 is 18.57 m / s, the operating speed of lane 2 is 18.01 m / s, and the operating speed of lane 1 is 16.93 m / s. The minimum lane change clearances calculated according to the minimum lane change clearance calculation model for different lane change scenarios are summarized in Table 3.

[0164] Table 3 Summary of Minimum Lane Changing Clearance Calculation Results

[0165]

[0166] Based on the distribution ratio of different lane-changing scenarios, The distribution ratios of the eight lane-changing scenarios in heterogeneous traffic flow are shown in Table 4 when the values ​​are 0, 0.2, 0.6, 0.8, and 1.

[0167] Table 4 Summary of Lane Change Scenarios

[0168]

[0169] Based on the minimum clearance length calculation model, by substituting the vehicle headway distribution function and model parameters, the minimum clearance length under different autonomous driving penetration rates can be simulated. The calculation results after rounding to 10m are shown in Table 5.

[0170] Table 5 Calculation results of minimum clear distance length

[0171]

[0172] According to the current technical standards and specifications in my country, when the main line is a one-way three-lane road with a design speed of 80 km / h, the minimum clearance between adjacent interchanges should not be less than 800m. This is basically consistent with the calculated minimum clearance length in the purely manual driving traffic flow in Table 5. Therefore, the model calculation is considered to be relatively reasonable.

[0173] This invention also provides a minimum clearance calculation system for urban expressways under heterogeneous traffic flow, which is based on the above-mentioned minimum clearance calculation method for urban expressways under heterogeneous traffic flow, and includes: a scene generation module, a lane-changing behavior simulation module, a minimum clearance calculation module, and a verification and optimization module.

[0174] Scene generation module: Construct lane-changing scenarios based on the penetration rate of autonomous vehicles, historical traffic flow, and urban expressway design specifications, calculate the probability of each scenario occurring within the entire net distance segment, and form a scene-probability matrix.

[0175] Lane change behavior simulation module: In each lane change scenario, it simulates the longitudinal displacement, acceleration and deceleration process and time required for a vehicle to complete one or more lane changes between different lanes, and outputs the single lane change distance required for a single lane change in all lane change scenarios.

[0176] Minimum clearance calculation module: Accumulate the single lane change distance according to the number of lane changes, and superimpose the sign reaction distance, gap finding distance, vehicle adjustment distance and exit confirmation distance to finally obtain the minimum clearance length corresponding to the current lane change scenario; and perform a weighted summation of all minimum clearance lengths according to the scenario probability to obtain the comprehensive minimum clearance design value under the current autonomous driving penetration rate.

[0177] Verification and optimization module: The calculation results are compared with current standards or historical accident data to verify the rationality of the simulation. If the deviation exceeds the set threshold, the parameters or scenario weights are checked back.

[0178] Application examples demonstrate that the minimum clearance model for urban expressway interchanges based on probabilistic methods and acceptable gap theory, proposed in this invention, under the game-theoretic behavior of hybrid driving traffic flow, overcomes the limitations of current models that only consider manually driven vehicles and fixed gaps. By fully considering the differences between manually driven and autonomous vehicles, the calculated minimum clearance is more in line with actual needs. This calculation model can provide a reference for determining the minimum length of clearance segments for future urban expressway interchanges.

[0179] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described; only preferred embodiments of the present invention are illustrated. The descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. As long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0180] It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept, and these all fall within the scope of protection of this invention. Therefore, the scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for calculating the minimum clearance of urban expressways under heterogeneous traffic flow, characterized in that, Includes the following steps: Step S1: Set the driving speed of vehicles in each lane according to the current driving speed regulations of the urban expressway, and calculate the critical safe distance between the lane-changing vehicle and the vehicles in front and behind in the target lane during the lane-changing process based on the vehicle speed. Step S2: Construct several lane-changing scenarios based on the types of lane-changing vehicles and vehicles in front and behind the target lane. Calculate the minimum lane-changing gap between the lane-changing vehicle and vehicles in front and behind the target lane in each lane-changing scenario based on the critical safe distance. Use the minimum lane-changing gap as the driving constraint for the lane-changing vehicle. Fit the headway of the target lane using the Erlang distribution to simulate the driving scenarios of lane-changing vehicles and vehicles in front and behind the target lane in all lane-changing scenarios. Step S3: Based on the simulation results, determine the braking reaction distance of lane-changing vehicles, the distance traveled when searching for lane-changing gaps, and the lane-changing distance for all lane-changing scenarios. Calculate the minimum clearance for all lane-changing scenarios and take the maximum value among all minimum clearances as the minimum clearance for the current urban expressway. The distance traveled by the lane-changing vehicle while searching for a lane-changing gap is calculated based on the headway. The expression for the headway of the target lane fitted using the Erlang distribution is as follows: ； In the formula, This represents the probability distribution of the headway between the train and the train. The acceptable headway for lane-changing vehicles; The headway to the target lane; The average arrival rate of vehicles in the target lane; For the specific order of the Erlang distribution; The braking reaction distance includes the sign reaction distance and the exit confirmation distance. The expression for calculating the minimum clearance in all lane-changing scenarios is as follows: (1) When the lane-changing vehicle is a manually driven vehicle, the expression for the minimum clearance is: ； ； ； ； ； ； ； In the above formula, Minimum clearance; To indicate the reaction distance; The speed of vehicles changing lanes at the starting point of the clearance section; Reading time; For decision-making time; The distance traveled when finding a lane-changing gap for a vehicle changing lanes; For the i-th lane-changing vehicle, the distance the vehicle travels during the acceptable lane-changing interval. The driving speed during the acceptable lane-changing interval for vehicles to change lanes; is the average waiting time for lane-changing vehicles; n is the number of unacceptable lane-changing gaps that a lane-changing vehicle passes through from the time it decides to change lanes. The vehicle body adjustment distance for the i-th lane change of the vehicle; The critical safe following distance between a vehicle changing lanes and the vehicle following in the target lane; The length of the vehicle changing lanes; The speed of the vehicle behind in the target lane; This refers to the distance traveled by a vehicle in the direction of travel during the lane-changing process. The longitudinal speed of the vehicle changing lanes; It equals the lane width divided by the vehicle's lateral speed; Before a vehicle enters the next ramp exit, confirm the safe distance from the exit location; The speed at which a vehicle changing lanes approaches the end of the clearance section; (2) When the lane-changing vehicle is an automated driving vehicle, the expression for the minimum clearance is: ； ； ； ； ； in .

2. The method for calculating the minimum clearance of an urban expressway under heterogeneous traffic flow according to claim 1, characterized in that: The expression for calculating the critical safe following distance between the lane-changing vehicle and the vehicles in front and behind in the target lane during the lane-changing process, based on the vehicle's speed, as described in step S1, is as follows: ； In the formula, Let n be the critical safe following distance for vehicle n. , Let be the speeds of vehicle n at time t and time t+1, respectively. , These are the reaction time and braking time of vehicle n, respectively; Let n be the maximum braking deceleration of vehicle n.

3. The method for calculating the minimum clearance of an urban expressway under heterogeneous traffic flow according to claim 1, characterized in that: In step S2, the lane-changing vehicle and the vehicles in front and behind in the target lane are either autonomous or manually driven. Several lane-changing scenarios are constructed based on the types of the lane-changing vehicle and the vehicles in front and behind in the target lane, including: Lane change scenario 1: The vehicle changing lanes and the vehicles in front and behind in the target lane are all manually driven; Lane change scenario 2: The vehicle changing lanes and the vehicle behind in the target lane are manually driven vehicles, while the vehicle in front in the target lane is an autonomous vehicle; Lane change scenario 3: The vehicle changing lanes and the vehicle in front of the target lane are manually driven vehicles, while the vehicle behind the target lane is an autonomous vehicle. Lane change scenario 4: The vehicle changing lanes is a manually driven vehicle, while the vehicles in front and behind the target lane are autonomous vehicles; Lane change scenario 5: The vehicle changing lanes is an autonomous vehicle, while the vehicles in front and behind the target lane are manually driven vehicles; Lane change scenario 6: The vehicle changing lanes and the vehicle in front of the target lane are both autonomous vehicles; the vehicle behind the target lane is also an autonomous vehicle. Lane change scenario 7: The vehicle changing lanes and the vehicle behind in the target lane are autonomous vehicles, and the vehicle in front in the target lane is an autonomous vehicle; Lane change scenario 8: The vehicle changing lanes and the vehicles in front and behind the target lane are all autonomous vehicles.

4. The method for calculating the minimum clearance of an urban expressway under heterogeneous traffic flow according to claim 3, characterized in that: Each lane-changing scenario also includes direct lane-changing scenarios and collaborative lane-changing scenarios; The direct lane-changing scenario is as follows: when the lane-changing vehicle changes lanes, the vehicles in front and behind in the target lane maintain their original driving speeds; The cooperative lane-changing scenario is as follows: when the lane-changing vehicle changes lanes, the vehicle in front of the target lane accelerates or the vehicle behind accelerates or the vehicle in front accelerates and the vehicle behind accelerates.

5. The method for calculating the minimum clearance of an urban expressway under heterogeneous traffic flow according to claim 4, characterized in that: In step S2, the expression for calculating the minimum lane-changing clearance between the lane-changing vehicle and the vehicles in front and behind in the target lane under each lane-changing scenario based on the critical safe following distance is as follows: (1) When the lane-changing vehicle is an autonomous vehicle and the current scenario is a direct lane change, the expression for the minimum lane-changing gap is: ； ； ； In the formula, The minimum lane change clearance required for autonomous vehicles to make direct lane changes; After the lane change is completed, the vehicles in front and behind will follow each other. The critical safe distance between the following vehicle and the vehicle in front during car-following behavior; The critical safe distance between the following vehicle and the vehicle in front in car-following behavior; , These represent the travel distances of vehicles in front and behind the target lane during the lane-changing process in a direct lane-changing scenario. The length of the vehicle changing lanes; , These represent the speeds of the vehicles in front and behind in the target lane before the lane change; The lane-changing time for vehicles changing lanes; (2) When the lane-changing vehicle is an autonomous vehicle and the current lane-changing scenario is cooperative, the expression for the minimum lane-changing gap is: ； ； ； ； In the formula, The minimum lane change interval required for autonomous vehicles to perform cooperative lane changes; , These represent the travel distances of vehicles in front and behind in the target lane during the lane-changing process in a collaborative lane-changing scenario. The distance traveled to maintain the original speed of the vehicle in front; For the vehicle ahead in the target lane, the comfortable acceleration; To reduce the speed for the comfort of vehicles following in the target lane; (3) When the lane-changing vehicle is a manually driven vehicle and the current scenario is a direct lane change, the expression for the minimum lane-changing gap is: ； In the formula, The minimum lane change clearance required for a manually driven vehicle to make a direct lane change; (4) When the lane-changing vehicle is a manually driven vehicle and the current scenario is a cooperative lane-changing scenario, the expression for the minimum lane-changing gap is: ； In the formula, The minimum lane change interval required for collaborative lane changing for manually driven vehicles.

6. A minimum clearance calculation system for urban expressways under heterogeneous traffic flow, implemented based on the minimum clearance calculation method for urban expressways under heterogeneous traffic flow as described in any one of claims 1-5, characterized in that, include: The module includes a scene generation module, a lane-changing behavior simulation module, a minimum clearance calculation module, and a verification and optimization module. The scenario generation module constructs lane-changing scenarios based on the penetration rate of autonomous vehicles, historical traffic flow, and urban expressway design specifications, calculates the probability of each scenario occurring within the entire net distance segment, and forms a scenario-probability matrix. The lane-changing behavior simulation module simulates the longitudinal displacement, acceleration and deceleration process, and time required for a vehicle to complete one or more lane changes between different lanes in each lane-changing scenario, and outputs the single lane-changing distance required for a single lane change in all lane-changing scenarios. The minimum clearance calculation module: accumulates the single lane change distance according to the number of lane changes, and superimposes the sign reaction distance, gap finding distance, vehicle adjustment distance and exit confirmation distance to finally obtain the minimum clearance length corresponding to the current lane change scenario; and performs a weighted summation of all minimum clearance lengths according to the scenario probability to obtain the comprehensive minimum clearance design value under the current autonomous driving penetration rate. The verification and optimization module compares the calculation results with current standards or historical accident data to verify the rationality of the simulation. If the deviation exceeds the set threshold, it backtracks to check the parameters or scenario weights.

7. The minimum clearance calculation system for urban expressways under heterogeneous traffic flow according to claim 6, characterized in that: The expression for the single lane change distance required for a single lane change in all lane change scenarios output by the lane change behavior simulation module is as follows: ； ； ； ； In the above formula, The distance traveled when finding a lane-changing gap for a vehicle changing lanes; For the i-th lane-changing vehicle, the distance the vehicle travels during the acceptable lane-changing interval. The driving speed during the acceptable lane-changing interval for vehicles to change lanes; is the average waiting time for lane-changing vehicles; n is the number of unacceptable lane-changing gaps that a lane-changing vehicle passes through from the time it decides to change lanes. This represents the probability distribution of the headway between the train and the train. The acceptable headway for lane-changing vehicles; The headway to the target lane; The average arrival rate of vehicles in the target lane; For the specific order of the Erlang distribution; The vehicle body adjustment distance for the i-th lane change of the vehicle; The critical safe following distance between a vehicle changing lanes and the vehicle following in the target lane; The length of the vehicle changing lanes; The speed of the vehicle behind in the target lane.

8. The minimum clearance calculation system for urban expressways under heterogeneous traffic flow according to claim 6, characterized in that: After obtaining the minimum clearance design value for each autonomous driving penetration rate, the minimum clearance calculation module uses the maximum value among all minimum clearance design values ​​as the comprehensive minimum clearance design value for the current urban expressway.

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