Method for calculating capacity of highway merging area of mixed traffic flow with special lane

Abstract

The application is a method for calculating the capacity of a merging area of a highway with mixed traffic flow containing a special lane. First, the demand of autonomous vehicles and the capacity of the autonomous vehicle special lane are considered, the autonomous vehicles are allocated, and the traffic demand of each lane is obtained. Second, the objective function is proposed with the maximum capacity as the optimization objective, and the constraint conditions of the traffic flow in the merging area are given. Finally, the capacity model of the merging area is established according to the objective function and the constraint conditions, the capacity model of the merging area is solved through mathematical programming, and the capacity of the merging area is obtained. This method is under the condition of mixed traffic flow containing a special lane and autonomous vehicles and manually driven vehicles, and on the basis of considering the demand of autonomous vehicles and the capacity of the autonomous vehicle special lane, the capacity of the merging area is quantified by allocating autonomous vehicles and the constraint conditions that the traffic flow in the merging area needs to comply with. It has guiding significance for the management and control of future human-machine mixed driving traffic flow containing autonomous vehicle special lanes.

Description

Technical Field

[0001] This invention belongs to the field of autonomous driving technology, specifically a method for calculating the capacity of a merging zone of a highway with mixed traffic flow including dedicated lanes. Background Technology

[0002] The rapid development of information technology has laid the foundation for the high-speed development of autonomous driving technology. Compared with human-driving vehicles (HV), connected autonomous vehicles (CAV) possess the characteristics of objectively judging road conditions and driving rationally. Their driving behavior is not affected by subjective factors such as the driver's psychological state and driving habits. Therefore, autonomous vehicles have shorter reaction times, a wider speed range, and can achieve smaller headrooms than ordinary vehicles, theoretically improving the maximum service flow rate and capacity of mixed human-machine traffic flow. Considering my country's basic national conditions and regional development differences, the mixed driving state of autonomous and human-driving vehicles will exist in my country's urban road traffic system for a long time. In the mixed human-machine driving environment, the mutual interference between human-driving vehicles and autonomous vehicles will reduce the operating efficiency of both simultaneously. Moreover, the complex vehicle behavior and high conflict rate in the merging zone increase driving difficulty and lead to an increase in the traffic accident rate.

[0003] High-occupancy vehicle (HOV) lanes and dedicated bus lanes have been widely implemented in transportation systems, proving their feasibility. These dedicated lanes provide a reference for the development of dedicated lanes for autonomous driving. By spatially separating lanes through dedicated autonomous driving lanes, the interference between autonomous and human-driven vehicles can be significantly reduced, fully leveraging the advantages of autonomous vehicles such as energy conservation, environmental protection, intelligent sharing, and network connectivity. Furthermore, dedicated lanes for autonomous driving can improve the efficiency of autonomous vehicles, thus promoting their widespread adoption.

[0004] Existing literature has limited research on the merging capacity of mixed traffic flows, and there is a lack of research on the merging capacity after the establishment of dedicated lanes for autonomous driving. Therefore, it is impossible to obtain the impact of the commercialization of autonomous vehicles on the merging capacity of the future, and thus cannot provide a reference for the planning of dedicated lanes for autonomous driving. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the technical problem this invention aims to solve is to provide a method for calculating the capacity of merging zones of highways with mixed traffic flows including dedicated lanes.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for calculating the capacity of a merging zone on a highway with mixed traffic flow including a dedicated lane, wherein the dedicated lane is an autonomous driving lane adjacent to the central green belt of the highway, i.e., the lane farthest from the entrance and exit ramps of the merging zone; the method includes the following steps:

[0008] Step 1: Considering the demand for autonomous vehicles and the capacity of dedicated autonomous driving lanes, allocate autonomous vehicles to obtain the traffic demand for each lane, including the following scenarios:

[0009] 1) When the demand for autonomous vehicles is less than the capacity of the dedicated autonomous driving lane, all autonomous vehicles should be assigned to the dedicated autonomous driving lane. In this case, the traffic demand of all lanes on the main road and the dedicated autonomous driving lane should satisfy the following formula:

[0010]

[0011] In equation (1), Q i Q c Let i represent the traffic demand for the main road lane i and the dedicated lane for autonomous driving, i = 1, 2, ..., s, where s is the number of mixed lanes. Except for the dedicated lane for autonomous driving, all other lanes are mixed lanes. Along the direction from the merging area to the dedicated lane for autonomous driving, each mixed lane is sequentially denoted as main road lane 1, main road lane 2, ..., main road lane s. Traffic flow rates for the main road's i-lane and the dedicated autonomous driving lane, respectively; q rf φ is the traffic flow rate of ramps entering lane 1 of the main road; p is the market penetration rate of autonomous vehicles, 0≤p≤1, p=p′+p″, p′ is the autonomous vehicle entry rate of the dedicated autonomous vehicle lane, p″ is the autonomous vehicle entry rate of the mixed lane; D is the main road traffic demand, that is, the total traffic demand of all main road lanes; φ is the ramp traffic demand, and BFC′ is the single-lane capacity of the dedicated autonomous vehicle lane.

[0012] 2) When the demand for autonomous vehicles exceeds the capacity of dedicated autonomous driving lanes, some autonomous vehicles will be allocated to mixed lanes. In this case, the traffic demand of the main road lanes and dedicated autonomous driving lanes should meet the following formula:

[0013]

[0014] In equations (1) and (2), the main road traffic demand D ≤ BFC′ + 2BFC, where BFC is the single-lane capacity of the mixed lanes, and the ramp traffic demand φ ≤ C. max C max This represents the maximum merging volume of vehicles from the ramp into the main road, which is related to the traffic demand of one lane on the main road.

[0015] 3) Before vehicles merge onto the main road from the ramp, the merging rate of autonomous vehicles in the dedicated autonomous driving lane and the mixed lane is determined by the autonomous vehicle allocation strategy, specifically:

[0016]

[0017] In equation (3), p′≤p and

[0018] 4) After vehicles merge onto the main road from the ramp, the merging rate of autonomous vehicles in the dedicated autonomous driving lanes and mixed lanes is also affected by the merging behavior from the ramp, causing certain changes in the number of autonomous vehicles in each main road lane. Specifically, this includes the following two scenarios:

[0019] ① The traffic flow in the dedicated autonomous driving lane consists of autonomous vehicles that were originally traveling in the dedicated autonomous driving lane and autonomous vehicles that changed lanes from the main road's S-lane to the dedicated autonomous driving lane. At this time, the autonomous vehicle mixing rate in the dedicated autonomous driving lane is:

[0020]

[0021] In the formula, The traffic flow rate of the main road S-lane changing lane merging into the dedicated lane for autonomous driving. The traffic flow rate for vehicles in dedicated autonomous driving lanes that do not change lanes and directly pass through the merging zone. The traffic flow rate of lane i changing lanes and merging into lane i+1 of the main road; The traffic flow rate of the main road i lane that does not change lanes and directly passes through the merging zone;

[0022] ② If all mixed lanes are considered as a whole, then the mixing rate of autonomous vehicles in the mixed lanes is:

[0023]

[0024] Step 2: Establish a merging zone capacity model, solve the merging zone capacity model, and obtain the merging zone capacity of the highway with mixed traffic flow including dedicated lanes.

[0025] First, with maximizing traffic capacity as the optimization objective, an objective function is proposed. The traffic capacity of a merging zone on a highway with dedicated lanes under mixed human-machine driving conditions refers to the sum of the main road traffic volume passing through the merging zone per unit time and the maximum traffic volume of ramps merging into the main road of the merging zone. Therefore, the objective function is:

[0026]

[0027] In equation (6), C represents the merging zone capacity;

[0028] Secondly, traffic flow within the merging zone must comply with certain constraints, including:

[0029] 1) If the capacity of each lane in the merging zone cannot exceed the capacity of the basic road section under the same conditions, then:

[0030]

[0031]

[0032]

[0033]

[0034]

[0035] in, Traffic flow rate of the main road lane 1 directly passing through the merging zone without changing lanes. The traffic flow rate of the main road i+1 lane that does not change lanes and directly passes through the merging zone;

[0036] 2) Since each variable in equation (6) cannot exceed the maximum merging volume of the corresponding lane, we have:

[0037] q rf ≤C max (12)

[0038]

[0039]

[0040] In the formula, C′ max The maximum merging volume of vehicles from main road lane i into main road lane i+1 is related to the traffic demand of main road lane i+1; C″ max The maximum number of vehicles merging into the dedicated autonomous driving lane is related to the traffic demand of the dedicated autonomous driving lane.

[0041] 3) The merging rate of autonomous vehicles in each lane within the merging zone must not exceed the market penetration rate p of autonomous vehicles, then:

[0042]

[0043]

[0044] Based on the objective function and constraints, the capacity model for the merging zone is obtained as follows:

[0045]

[0046] The capacity of the merging zone of a highway with a mixed traffic flow containing dedicated lanes is calculated by solving the optimization model of equation (17) through mathematical programming.

[0047] Specifically, calculating the basic traffic capacity of highway sections includes the following:

[0048] 1) The single-lane capacity (BFC) for mixed lanes is:

[0049]

[0050] In the formula, t cc t represents the expected headway between autonomous vehicles. cm t represents the expected headway between autonomous vehicles and manually driven vehicles. mm The expected headway between manually driven vehicles;

[0051] 2) The single-lane capacity (BFC′) of the dedicated autonomous driving lane is:

[0052]

[0053] Based on the acceptable gap theory and probability theory, the maximum lane merging volume includes the following two scenarios:

[0054] ① Maximum merging volume of mixed lanes

[0055] Taking the merging of a ramp into the first lane of the main road as an example, assuming the critical clearance for a type k (k=1,2) vehicle is t ck Let k = 1 represent an autonomous vehicle and k = 2 represent a manually driven vehicle, with a following distance of t. fk The headway of a vehicle in lane 1 of the main road is... According to the acceptable gap theory, when At that time, one K-type vehicle is allowed to merge from the ramp into lane 1 of the main road; when At that time, one K-type vehicle is allowed to line up at the ramp, followed immediately by another vehicle merging into lane 1 of the main road; generally, when At that time, one K-type vehicle is allowed to line up at the ramp, followed by R1 manually driven vehicle and R2 autonomous vehicle to merge into the main road lane 1.

[0056] Since the random events of manually driven vehicles and autonomous vehicles in the ramp traffic flow finding suitable gaps to merge into the main road are independent of each other, the possible queuing configurations of ramp vehicles and their probabilities are studied, and the maximum merging volume of ramp lanes into lane 1 of the main road is calculated based on the queuing configurations and probabilities.

[0057] When the queue leader is 1, there are two queue configurations: one with a manually driven vehicle and the other with an autonomous vehicle as the queue leader.

[0058] When the queue length is 2, there are 4 possible queue configurations: manually driven vehicle ~ manually driven vehicle, manually driven vehicle ~ autonomous vehicle, autonomous vehicle ~ manually driven vehicle, and autonomous vehicle ~ autonomous vehicle; the probability of these four queue configurations is (1-p). 2 p(1-p), p(1-p) and p 2 The sum of the four probability values ​​is 1;

[0059] Generally, when the queue length is r, the queue configuration is: vehicle type k ~ queue configuration with a queue length of r-1. Since vehicle type k is at the head of the queue, the subsequent queue configuration with a queue length of r-1 contains r1 manually driven vehicles and r2 autonomous vehicles. The total number of different queue configurations is... There are r1 vehicles, where r1 + r2 = r - 1; the probability that a vehicle of type k is at the head of the queue and there are r1 manually driven vehicles and r2 autonomous vehicles in the queue configuration with a length of r - 1 is: p k Let represent the probability of vehicle type k; the sum of all probability values ​​is 1, then:

[0060]

[0061] The headway of vehicles in lane 1 of the main road follows a second-order Erlang distribution, and its probability distribution function is:

[0062]

[0063] In the formula, λ is the vehicle arrival rate, m represents the order, and t represents the headway between two vehicles.

[0064] The headway of a vehicle in lane 1 of the main road is sufficient to pass the ramp. A vehicle of type k is at the head of the queue. The probability that there are r1 manually driven vehicles and r2 autonomous vehicles in the queue configuration with a length of r-1 is:

[0065]

[0066] The headway of a vehicle in lane 1 of the main road is sufficient to allow it to pass through the ramp in one go. The probability that a vehicle of type k, at the head of the queue, will have r1 manually driven vehicles and r2 autonomous vehicles in a queue configuration with a length of r-1 is:

[0067]

[0068] The probability that the headway of a vehicle in lane 1 of the main road can guarantee the passage of r vehicles from the ramp in one go is:

[0069]

[0070] The mathematical expectation of mixed traffic flow merging into the main road from a ramp within a one-lane gap is:

[0071]

[0072] Assuming the traffic demand for lane 1 of the main road is Q1, meaning there are Q1 gaps in lane 1 of the main road, then the maximum merging capacity of vehicles from the ramp into the main road is:

[0073]

[0074] Among them, t c1 t c2 The critical gaps for autonomous vehicles and manually driven vehicles, respectively, t f1 t f2 These are the following distances for autonomous vehicles and manually driven vehicles, respectively;

[0075] Assume the traffic demand for lane i+1 of the main road is Q. i+1 Similarly, we can derive the maximum merging volume C′ of vehicles merging from lane i of the main road into lane i+1 of the main road. max for:

[0076]

[0077] Q2 is the traffic demand for the two lanes of the main road;

[0078] ② Maximum merging volume C″ of the dedicated lane for autonomous driving max

[0079] From the above, it can be concluded that only autonomous vehicles have the motivation to enter the dedicated autonomous driving lane, and in this case, the following distance t of the autonomous vehicle is... f1 and critical gap t c1 The change occurs because it does not involve manually driven vehicles; therefore, the maximum merging volume C″ into the dedicated autonomous driving lane is [not specified]. max The calculation process is as follows:

[0080] According to the acceptable gap theory, when At any time, one autonomous vehicle is allowed to merge into the dedicated autonomous driving lane; when At any given time, n autonomous vehicles are allowed to merge into the dedicated autonomous driving lane;

[0081] The probability P of n autonomous vehicles merging into the dedicated autonomous driving lane within a headway of lane s on the main road is given by the following information. n for:

[0082]

[0083] The traffic demand for dedicated lanes for autonomous driving is Q. c That is, the total headway between vehicles in the dedicated autonomous driving lane is Q. cAssume that the main road has s lanes that can accommodate a maximum of o vehicles queuing in a line, among which... The number of times is P n Q c ,Appear The number of times Therefore, the total number of vehicles allowed to merge from lane S on the main road into the dedicated lane for automated driving within 1 hour should be:

[0084]

[0085] Let o→∞, then we obtain the maximum merging volume C″ of the main road lane s merging into the dedicated autonomous driving lane. max for:

[0086]

[0087] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0088] 1. A merging zone capacity model was established based on linear optimization. The model aims to maximize capacity and proposes an objective function. It also considers scenarios involving dedicated lanes and mixed traffic of autonomous vehicles and human-autonomous vehicles. In this case, autonomous vehicles merging from ramps continuously change lanes to enter the dedicated autonomous driving lanes, directly impacting traffic flow on all main road lanes. Therefore, considering the demand for autonomous vehicles and the capacity of dedicated autonomous driving lanes, the capacity of merging zones with dedicated lanes is quantified by allocating autonomous vehicles and defining constraints for traffic flow within the merging zone. This provides a foundation for vehicle control and autonomous driving strategies in merging zones of highways with dedicated autonomous driving lanes, offers solutions for improving the efficiency and capacity of mixed traffic flow in highway merging zones, and provides guidance for the future management of mixed human-machine traffic flow under dedicated autonomous driving lanes.

[0089] 2. Since each variable in the objective function cannot exceed the maximum merging volume of its corresponding lane, the maximum merging volume of the lane was calculated based on the acceptable gap theory and probability theory. The maximum merging volume of the mixed lanes considers different queuing configurations for the two vehicle types. The maximum merging volume was calculated using probability theory and the acceptable gap theory, more comprehensively considering the possible queuing configurations of ramp vehicles, making the calculated maximum merging volume of the mixed lanes closer to reality. The maximum merging volume of the dedicated lane for autonomous driving was also calculated based on the acceptable gap theory. Attached Figure Description

[0090] Figure 1 This is a schematic diagram of a merging zone containing dedicated lanes under mixed traffic flow;

[0091] Figure 2 This is a flowchart of the method of the present invention;

[0092] Figure 3 This is a graph showing the relationship between the rate of autonomous vehicles entering the merging zone and the capacity of the merging area.

[0093] Figure 4 This is a graph showing the relationship between the maximum merging volume of mixed lanes and the merging rate of autonomous vehicles under different main road traffic demands.

[0094] Figure 5 This is a graph showing the relationship between the maximum number of autonomous driving lanes that can merge and the merging rate of autonomous vehicles under different main road traffic demands. Detailed Implementation

[0095] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments, but this does not limit the scope of protection of this application.

[0096] like Figure 1 As shown, the CAV dedicated lane is adjacent to the central green belt of the highway (i.e., the lane furthest from the merging area entrance / exit ramps). The remaining lanes are mixed lanes, and along the direction from the merging area to the CAV dedicated lane, each mixed lane is sequentially labeled as Main Road Lane 1, Main Road Lane 2, ..., Main Road Lane s. This embodiment uses a three-lane highway in one direction as an example to illustrate the method for calculating the capacity of the merging area of ​​a highway with mixed traffic flow including dedicated lanes. Therefore, s = 2. The specific steps include:

[0097] Step 1: Consider the demand for autonomous vehicles and the capacity of dedicated autonomous driving lanes, and allocate autonomous vehicles accordingly. The principle for allocating autonomous vehicles is: priority is given to dedicated autonomous driving lanes, and the allocation of autonomous vehicles is carried out using the principle of fixed traffic flow management. Under the premise of ensuring that the total number of autonomous vehicles allocated to dedicated autonomous driving lanes does not exceed the capacity of dedicated autonomous driving lanes, as many autonomous vehicles as possible should be allocated to dedicated autonomous driving lanes.

[0098] 1) When the demand for autonomous vehicles is less than the capacity of the dedicated autonomous driving lane, all autonomous vehicles are allocated to the dedicated autonomous driving lane. According to equation (1), the traffic demand for main road lane 1, main road lane 2, and the dedicated autonomous driving lane are obtained, i.e., the traffic volume is:

[0099]

[0100] In equation (31), Q1 represents the traffic demand for one lane of the main road, Q2 represents the traffic demand for two lanes of the main road, and q f1 Traffic flow rate of a single lane on the main road, q f2φ is the traffic flow rate of the two lanes of the main road; p is the market penetration rate of autonomous vehicles, 0≤p≤1, p=p′+p″, p′ is the autonomous vehicle mixing rate of the dedicated autonomous driving lane, p″ is the autonomous vehicle mixing rate of the mixed lane; D is the traffic demand of the main road, that is, the total traffic demand of all lanes of the main road; φ is the traffic demand of the ramp; BFC′ is the single lane capacity of the dedicated autonomous driving lane.

[0101] 2) When the demand for autonomous vehicles exceeds the capacity of the dedicated autonomous driving lanes, some autonomous vehicles are allocated to the mixed lanes. According to equation (2), the traffic demand for main road lane 1, main road lane 2, and the dedicated autonomous driving lanes is as follows:

[0102]

[0103] In equations (31) and (32), the main road traffic demand D ≤ BFC′ + 2BFC, where BFC is the single-lane capacity of the mixed lanes, and the ramp traffic demand φ ≤ C. max C max This represents the maximum merging volume of vehicles from the ramp onto the main road.

[0104] 3) Before vehicles merge into the main road from the ramp, the merging rate of autonomous vehicles in the dedicated autonomous driving lane and the mixed lane is shown in Equation (3);

[0105] 4) After vehicles merge onto the main road from the ramp, the merging rate of autonomous vehicles in the dedicated autonomous driving lanes and mixed lanes is also affected by the merging behavior from the ramp, resulting in certain changes in the number of autonomous vehicles in each lane, specifically:

[0106] ① The traffic flow in the dedicated autonomous driving lane consists of autonomous vehicles that were originally traveling in the dedicated lane and autonomous vehicles that changed lanes from the main road lane 2 to the dedicated autonomous driving lane. According to equation (4), the mixing rate of autonomous vehicles in the dedicated autonomous driving lane is:

[0107]

[0108] In the formula, q rf This refers to the traffic flow rate of vehicles entering the main road from the ramp. The traffic flow rate of changing lanes from lane 1 on the main road to lane 2 on the main road. Traffic flow rate merging from the two-lane main road changing lane into the dedicated autonomous driving lane. Traffic flow rate of the main road lane 1 directly passing through the merging zone without changing lanes. Traffic flow rate of two lanes on the main road directly passing through the merging zone without changing lanes. Traffic flow rate for vehicles in dedicated lanes for autonomous driving that do not change lanes and directly pass through merging areas;

[0109] ② Treating lane 1 and lane 2 of the main road as a single unit, the mixing rate of autonomous vehicles in the mixed lane is obtained according to equation (5):

[0110]

[0111] Step 2: Establish a merging zone capacity model, solve the merging zone capacity model, and obtain the merging zone capacity of the highway with mixed traffic flow including dedicated lanes.

[0112] First, with maximizing traffic capacity as the optimization objective, an objective function is proposed. The traffic capacity of a merging zone on a highway with dedicated lanes under mixed human-machine driving conditions refers to the sum of the main road traffic volume passing through the merging zone per unit time and the maximum traffic volume of ramps merging into the main road of the merging zone. Based on equation (6), the objective function is:

[0113]

[0114] In the formula, C represents the merging zone capacity;

[0115] Secondly, traffic flow within the merging zone must comply with certain constraints, specifically:

[0116] 1) The capacity of each lane in the merging zone shall not exceed the capacity of the basic road section under the same conditions, that is:

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] 2) Each variable in equation (35) must not exceed the maximum merging volume of the corresponding lane, that is:

[0124] q rf ≤C max (12)

[0125]

[0126]

[0127] 3) The merging rate of autonomous vehicles in each lane within the merging zone shall not exceed the market penetration rate p of autonomous vehicles. According to equations (15) and (16):

[0128]

[0129]

[0130] Based on the above objective function and constraints, the merging zone capacity model of this embodiment is obtained as follows:

[0131]

[0132] Solving equation (44) yields the merging zone capacity for this example.

[0133] Calculating the basic traffic capacity of highway sections includes:

[0134] 1) The single-lane capacity (BFC) for mixed lanes is:

[0135]

[0136] In the formula, t cc Let t be the expected headway of the autonomous vehicle, taken as 0.6s; cm Let t be the expected headway between the autonomous vehicle and the manually driven vehicle, taken as 1.2s; mm The expected headway for a manually driven vehicle is set to 1.8 seconds.

[0137] 2) The single-lane capacity (BFC′) of the dedicated autonomous driving lane is:

[0138]

[0139] Based on the acceptable gap theory and probability theory, the maximum lane merging volume includes the following two scenarios:

[0140] 1) Maximum merging volume of mixed lanes

[0141] When vehicles from the ramp merge into lane 1 of the main road, assuming the critical clearance for type k (k=1,2) vehicles is t ck Let k = 1 represent an autonomous vehicle, and k = 2 represent a manually driven vehicle. The following distance for a type k vehicle is t. fk The headway of a vehicle in lane 1 of the main road is... According to the acceptable gap theory, when At that time, one K-type vehicle is allowed to merge from the ramp into lane 1 of the main road; when At that time, one K-type vehicle is allowed to line up at the ramp, followed immediately by another vehicle merging into lane 1 of the main road; generally, when At that time, one K-type vehicle is allowed to line up at the ramp, followed by R1 manually driven vehicle and R2 autonomous vehicle to merge into the main road lane 1.

[0142] Since the random events of manually driven vehicles and autonomous vehicles in the ramp traffic flow finding suitable gaps to merge into the main road are independent of each other, the possible queuing configurations of ramp vehicles and their probabilities are studied, and the maximum merging volume of ramp lanes into lane 1 of the main road is calculated based on the queuing configurations and probabilities.

[0143] When the queue leader is 1, there are two queue configurations: one with a manually driven vehicle and the other with an autonomous vehicle as the queue leader.

[0144] When the queue length is 2, there are 4 possible queue configurations: manually driven vehicle ~ manually driven vehicle, manually driven vehicle ~ autonomous vehicle, autonomous vehicle ~ manually driven vehicle, and autonomous vehicle ~ autonomous vehicle; the probability of these four queue configurations is (1-p). 2 p(1-p), p(1-p) and p 2 The sum of the four probability values ​​is 1;

[0145] Generally, when the queue length is r, the queue configuration is: vehicle type k ~ queue configuration with a queue length of r-1. Since vehicle type k is at the head of the queue, the subsequent queue configuration with a queue length of r-1 contains r1 manually driven vehicles and r2 autonomous vehicles. The total number of different queue configurations is... There are r1 vehicles, where r1 + r2 = r - 1; the probability that a vehicle of type k is at the head of the queue and there are r1 manually driven vehicles and r2 autonomous vehicles in the queue configuration with a length of r - 1 is: p k Let represent the probability of vehicle type k; the sum of all probability values ​​is 1, then:

[0146]

[0147] The headway of vehicles in lane 1 of the main road follows a second-order Erlang distribution, and its probability distribution function is:

[0148]

[0149] In the formula, λ is the vehicle arrival rate, m represents the order, and t represents the headway between two vehicles.

[0150] The headway of a vehicle in lane 1 of the main road is sufficient to pass the ramp. A vehicle of type k is at the head of the queue. The probability that there are r1 manually driven vehicles and r2 autonomous vehicles in the queue configuration with a length of r-1 is:

[0151]

[0152] In equation (22), t c1 Take 2.4s, t c2 Take 3 seconds;

[0153] The headway of a vehicle in lane 1 of the main road is sufficient to allow it to pass through the ramp in one go. The probability that a vehicle of type k, at the head of the queue, will have r1 manually driven vehicles and r2 autonomous vehicles in a queue configuration with a length of r-1 is:

[0154]

[0155] The probability that the headway of a vehicle in lane 1 of the main road can guarantee the passage of r vehicles from the ramp in one go is:

[0156]

[0157] The mathematical expectation of mixed traffic flow merging into the main road from a ramp within a one-lane gap is:

[0158]

[0159] Assuming the traffic demand for lane 1 of the main road is Q1, meaning there are Q1 gaps in lane 1 of the main road, then the maximum merging capacity of vehicles from the ramp into the main road is:

[0160]

[0161] Among them, t c1 t c2 The critical gaps for autonomous vehicles and manually driven vehicles, respectively, t f1 t f2 These are the following distances for autonomous vehicles and manually driven vehicles, respectively;

[0162] Assume the traffic demand for lane i+1 of the main road is Q. i+1 Similarly, we can derive the maximum merging volume C′ of vehicles merging from lane i of the main road into lane i+1 of the main road. max for:

[0163]

[0164] ③ Maximum merging volume C″ of dedicated lanes for autonomous driving max

[0165] From the above, it can be concluded that only autonomous vehicles have the motivation to enter the dedicated autonomous driving lane, and in this case, the following distance t of the autonomous vehicle is... f1 and critical gap t c1 The change occurs because it does not involve manually driven vehicles; therefore, the maximum merging volume C″ into the dedicated autonomous driving lane is [not specified]. max The calculation process is as follows:

[0166] According to the acceptable gap theory, when At any time, one autonomous vehicle is allowed to merge into the dedicated autonomous driving lane; when At any given time, n autonomous vehicles are allowed to merge into the dedicated autonomous driving lane;

[0167] The probability P of n autonomous vehicles merging into the dedicated autonomous driving lane within a headway of lane s on the main road is given by the following information. n for:

[0168]

[0169] The traffic demand for dedicated lanes for autonomous driving is Q. c That is, the total headway between vehicles in the dedicated autonomous driving lane is Q. c Assume that the main road has s lanes that can accommodate a maximum of o vehicles queuing in a line, among which... The number of times is P n Q c ,Appear The number of times Therefore, the total number of vehicles allowed to merge from lane S on the main road into the dedicated lane for automated driving within 1 hour should be:

[0170]

[0171] Let o→∞, then we obtain the maximum merging volume C″ of the main road lane s merging into the dedicated autonomous driving lane. max for:

[0172]

[0173] To verify the effectiveness of this method, the merging capacity model was solved using Matlab software. The relationship between the merging rate of autonomous vehicles and the merging capacity of the merging area was analyzed, as well as the impact of different main road traffic demands and the merging rate of autonomous vehicles on the maximum merging volume.

[0174] Figure 3 This is a graph showing the relationship between the merging zone capacity and the rate of autonomous vehicles entering the area. Figure 3 It can be seen that the traffic capacity of the merging zone increases with the increase of the mixing rate of autonomous vehicles, eventually reaching the limit that the road can bear, indicating that autonomous vehicles can improve the traffic capacity of the road.

[0175] Figure 4 This is a graph showing the relationship between the maximum merging volume of mixed lanes and the merging rate of autonomous vehicles under different main road traffic demands. Figure 4It can be seen that under low traffic demand (D = 1800–3600 veh / h), the maximum merging volume of the mixed lanes decreases with the increase of the autonomous vehicle merging rate. This is because when the traffic demand does not exceed the basic capacity of the dedicated autonomous vehicle lanes, the traffic demand allocated to the mixed lanes decreases as the autonomous vehicle merging rate increases. Under medium traffic demand (D = 5400–12600 veh / h), the maximum merging volume of the mixed lanes first increases and then decreases with the increase of the autonomous vehicle merging rate. This indicates that when the traffic demand is close to or greater than the basic capacity of the dedicated autonomous vehicle lanes, the traffic demand allocated to the mixed lanes increases with the increase of the autonomous vehicle merging rate. However, when the main road traffic demand reaches a certain value, the maximum merging volume of the mixed lanes will decrease with the increase of the main road traffic demand. This result is consistent with relevant research findings. When traffic demand approaches saturation (D = 14400veh / h), the traffic volume on the main road is basically saturated. As the merging rate of autonomous vehicles increases, the maximum merging volume also increases slowly, indicating that autonomous vehicles have a certain positive impact on vehicle merging.

[0176] Figure 5 This graph shows the relationship between the maximum merging volume of dedicated autonomous driving lanes and the merging rate of autonomous vehicles under different main road traffic demands. When traffic demand is constant, the maximum merging volume of autonomous driving lanes decreases as the merging rate of autonomous vehicles increases, indicating that the maximum merging volume continuously decreases as the traffic volume of dedicated autonomous driving lanes increases, which is consistent with relevant research. When traffic demand increases, the maximum merging volume gradually decreases to 0, indicating that the traffic volume of dedicated autonomous driving lanes has reached saturation, and autonomous vehicles in mixed lanes can no longer merge into dedicated lanes.

[0177] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for calculating the capacity of a merging zone of mixed traffic flow on a highway, including a dedicated lane, wherein the dedicated lane is an autonomous driving lane adjacent to the central green belt of the highway; characterized in that, The method includes the following steps: Step 1: Considering the demand for autonomous vehicles and the capacity of dedicated autonomous driving lanes, allocate autonomous vehicles to obtain the traffic demand for each lane, including the following scenarios: 1) When the demand for autonomous vehicles is less than the capacity of the dedicated autonomous driving lane, all autonomous vehicles should be assigned to the dedicated autonomous driving lane. In this case, the traffic demand of all lanes on the main road and the dedicated autonomous driving lane should satisfy the following formula: In equation (1), Q i Q c Let i represent the traffic demand for the main road lane i and the dedicated lane for autonomous driving, i = 1, 2, ..., s, where s is the number of mixed lanes. Except for the dedicated lane for autonomous driving, all other lanes are mixed lanes. Along the direction from the merging area to the dedicated lane for autonomous driving, each mixed lane is sequentially denoted as main road lane 1, main road lane 2, ..., main road lane s. Traffic flow rates for the main road's i-lane and the dedicated autonomous driving lane, respectively; q rf denoted as φ, where φ is the traffic flow rate from the ramp into the main road lane 1; p is the market penetration rate of autonomous vehicles, 0≤p≤1; D is the main road traffic demand; φ is the ramp traffic demand; and BFC′ is the single-lane capacity of the dedicated autonomous driving lane. 2) When the demand for autonomous vehicles exceeds the capacity of dedicated autonomous driving lanes, some autonomous vehicles will be allocated to mixed lanes. In this case, the traffic demand of the main road lanes and dedicated autonomous driving lanes should meet the following formula: In equations (1) and (2), the main road traffic demand D ≤ BFC′ + 2BFC, where BFC is the single-lane capacity of the mixed lanes, and the ramp traffic demand φ ≤ C. max C max The maximum merging volume of vehicles from the ramp into the main road is related to the traffic demand of lane 1 on the main road; the market penetration rate of autonomous vehicles p = p′ + p″, where p′ is the autonomous vehicle merging rate in the dedicated autonomous vehicle lane and p″ is the autonomous vehicle merging rate in the mixed lane. Before vehicles merge onto the main road from the ramp, the merging rate of autonomous vehicles in the dedicated autonomous driving lane and the mixed lane is: After vehicles merge onto the main road from the ramp, the merging rate of autonomous vehicles in the dedicated autonomous driving lane and the mixed lane is affected by the merging behavior of the ramp vehicles, including the following two scenarios: ① The traffic flow in the dedicated autonomous driving lane consists of autonomous vehicles that were originally traveling in the dedicated autonomous driving lane and autonomous vehicles that changed lanes from the main road's S-lane to the dedicated autonomous driving lane. At this time, the autonomous vehicle mixing rate in the dedicated autonomous driving lane is: In the formula, The traffic flow rate of the main road S-lane changing lane merging into the dedicated lane for autonomous driving. The traffic flow rate for vehicles in dedicated autonomous driving lanes that do not change lanes and directly pass through the merging zone. The traffic flow rate of lane i changing lanes and merging into lane i+1 of the main road; The traffic flow rate of the main road i lane that does not change lanes and directly passes through the merging zone; ② If all mixed lanes are considered as a whole, then the mixing rate of autonomous vehicles in the mixed lanes is: Step 2: Establish the merging capacity model of equation (17), and solve the merging capacity model by mathematical programming to obtain the merging capacity of the highway with dedicated lanes for mixed traffic flow. In the formula, Traffic flow rate of the main road lane 1 directly passing through the merging zone without changing lanes. Traffic flow rate of lane i+1 on the main road directly passing through the merging zone without changing lanes; C′ max The maximum merging volume of vehicles from main road lane i into main road lane i+1 is related to the traffic demand of main road lane i+1; C″ max The maximum number of vehicles merging into the dedicated autonomous driving lane is related to the traffic demand of the dedicated autonomous driving lane.

2. The method for calculating the capacity of the merging zone of a highway with mixed traffic flow including dedicated lanes as described in claim 1, characterized in that, Maximum merging volume C of vehicles merging from ramps into the main road max for: Q1 represents the traffic demand for lane 1 of the main road; k represents type k vehicles, k = 1, 2, k = 1 for autonomous vehicles and k = 2 for manually driven vehicles; p k Let λ represent the probability of vehicle type k, λ be the vehicle arrival rate, and t be the probability of vehicle type k. ck For the critical clearance of type K vehicles, t c1 t c2 These represent the critical gaps between autonomous vehicles and manually driven vehicles, respectively; t fk For vehicle type K, the following distance is t. f1 t f2 These are the following distances for autonomous vehicles and manually driven vehicles, respectively; The maximum merging volume C′ of vehicles merging from lane i of the main road into lane i+1 of the main road max for: Among them, Q i+1 The traffic demand for the main road i+1 lane in Q2 is the traffic demand for the main road 2 lanes in Q2. Maximum merging volume C″ into the dedicated autonomous driving lane max for: Among them, Q c For the traffic demand of the dedicated autonomous driving lane, m represents the order of the second-order Erlang distribution, and n is the number of autonomous vehicles allowed to merge into the dedicated autonomous driving lane.

3. The method for calculating the capacity of the merging zone of a highway with mixed traffic flow including dedicated lanes as described in claim 1 or 2, characterized in that, The single-lane capacity (BFC) for mixed lanes is: In the formula, t cc t represents the expected headway between autonomous vehicles. cm t represents the expected headway between autonomous vehicles and manually driven vehicles. mm The expected headway between manually driven vehicles; The single-lane capacity (BFC′) of the dedicated autonomous driving lane is:

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