Signal intersection pedestrian protection type phase setting method, road intersection signal control device, electronic equipment and computer readable storage medium
Through microscopic traffic simulation and data analysis, a pedestrian-protected phase setting method for signalized intersections was determined. This method addresses the issue of neglecting the characteristics of mixed traffic flow and different traffic participants, achieving a balance between pedestrian safety and efficiency, and providing a scientific basis for decision-making and a quantitative approach.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HOHAI UNIV
- Filing Date
- 2026-01-22
- Publication Date
- 2026-04-17
AI Technical Summary
Existing technologies for pedestrian protection phase settings at signalized intersections fail to fully consider the characteristics of mixed traffic flow and different traffic participants, making it difficult to balance pedestrian crossing efficiency and safety, and lacking scientific decision-making methods.
The microscopic traffic simulation software VISSIM was used to obtain simulation data of three signal control schemes (ordinary two-phase, early pedestrian phase, and pedestrian-only phase) under different traffic conditions. The equivalent expected pedestrian delay, mixed vehicle delay, and conflict amount were calculated. Combined with the unit time delay cost and conflict cost, the optimal signal control scheme was determined.
While ensuring pedestrian safety, we should also consider the traffic efficiency at intersections, provide quantitative methods and scientific decision-making basis, and reduce implementation costs.
Smart Images

Figure CN121884604A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of traffic engineering and urban road signal control technology, specifically relating to a method for setting pedestrian protection phases at signalized intersections, a road intersection signal control device, electronic equipment, and a computer-readable storage medium. Background Technology
[0002] Existing research fails to adequately consider the characteristics of mixed traffic flow and traffic participants, and cannot provide a decision-making method for setting signal control schemes that ensure pedestrian crossing efficiency and safety. While Chinese patent document CN114724353A, "Method and Device for Passive Priority Control of Bus Signals Considering Pedestrians," calculates the saturation flow rate and delay for mixed-traffic lanes for cars and buses, improving upon the traditional Webster model's method of "converting all to cars," it does not include electric bicycles in the discussion. Furthermore, this patent treats all types of pedestrians as a standard adult for calculating average delay, lacking equivalent analysis of pedestrians and vehicles based on real traffic and conflict characteristics, and also failing to consider safety evaluation indicators; it also lacks comparative analysis of the three phases. Chinese patent document CN110097751B, "A Dynamic Setting Method for Pedestrian-Dedicated Phases at Two-Phase Signal Control Intersections," dynamically determines whether to insert a "pedestrian-dedicated phase" into the intersection signal cycle based on real-time traffic data by comparing with ordinary two-phase signals, but it does not consider early-opening pedestrian phases, nor does it provide the applicable traffic conditions for different phases; therefore, it lacks an operational decision-making method. Chinese patent document CN112071068A, "Analysis Method of Pedestrian Crossing Efficiency and Safety Based on Symmetrical Intersections," compares three crossing modes from the perspectives of efficiency and safety based on symmetrical intersections and proposes a complete quantitative evaluation system for pedestrian crossing efficiency and safety. However, it does not provide a decision-making process or specific decision-making conditions that can be directly implemented. Furthermore, symmetrical intersections require vehicles to travel on the left and right sides, which is difficult to implement in reality. Summary of the Invention
[0003] To address the aforementioned technical problems, this invention provides a method for setting pedestrian-protected phases at signalized intersections, a road intersection signal control device, electronic equipment, and a computer-readable storage medium. Its signal control scheme fully considers the characteristics of mixed traffic flow and different traffic participants, ensuring pedestrian safety while also balancing intersection efficiency. It has low implementation costs, provides a quantitative approach for the design and optimization of pedestrian-protected phases at signalized intersections, and offers a scientific basis for decision-making by traffic management personnel.
[0004] To achieve the above technical objectives, the technical solution adopted by this invention is as follows: a method for setting pedestrian protection phases at signalized intersections, comprising the following steps: S1: Using microscopic traffic simulation, within the preset range of equivalent pedestrian flow and equivalent mixed turning conflict parameters, the simulation operation data of each approach lane under three signal control schemes: ordinary two-phase, pedestrian early opening phase, and pedestrian dedicated phase are obtained. The simulation operation data includes at least the average delay of pedestrians and the average delay of mixed vehicles. S2: Calculate the equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict amount based on the equivalent pedestrian flow, equivalent mixed turning conflict amount, average pedestrian delay, and average mixed vehicle delay of each approach lane; S3: Calculate the unit time delay cost for pedestrians, the unit time delay cost for mixed vehicles, and the unit cost of pedestrian-vehicle conflicts; based on the equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict amount of each approach lane obtained in step S2, calculate the total intersection cost of the three signal control schemes: ordinary two-phase, pedestrian early opening phase, and pedestrian dedicated phase. S4: Based on the total cost of the three signal control schemes obtained in step S3, calculate the total cost increment of the pedestrian early-opening phase and the pedestrian-dedicated phase relative to the ordinary two-phase phase, and determine the decision on the setting of the ordinary two-phase phase, the pedestrian early-opening phase and the pedestrian-dedicated phase according to the total cost increment.
[0005] This invention obtains pedestrian delays and mixed vehicle delays for three signal control schemes under different traffic conditions through microscopic traffic simulation. It then calculates the equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict rate. Next, it uses statistical data to determine the unit time delay cost for pedestrians and mixed vehicles, as well as the unit cost of pedestrian-vehicle conflict, and calculates the total cost of the intersection. Finally, it calculates the total cost increment of the protective phase compared to the ordinary two-phase system. The optimal signal control scheme is determined based on this total cost increment. This scheme fully considers the characteristics of mixed traffic flow and different traffic participants, ensuring pedestrian safety while also balancing intersection efficiency. It has low implementation costs and provides a quantitative approach for the design and optimization of pedestrian-protective phases at signalized intersections, offering a scientific basis for decision-making by traffic management personnel.
[0006] Furthermore, the micro-traffic simulation in step S1 is performed using the micro-traffic simulation software VISSIM.
[0007] Furthermore, the equivalent pedestrian flow in step S1 is calculated by converting different types of people into the pedestrian flow of a standard adult. The formula for calculating the equivalent pedestrian flow of a single entrance is as follows: , in, The equivalent pedestrian flow at entrance i is expressed in eau / h. The actual number of pedestrians at entrance i, in person / hour; , , , These are the equivalent conversion factors for children, the elderly, the disabled, and adults, respectively, converted to one standard adult. , b , c , d The pedestrian flow rates are categorized into children, the elderly, the disabled, and adults, and are expressed as a percentage. The equivalent mixed steering conflict amount for a single approach lane is the equivalent mixed traffic volume for that approach lane multiplied by the steering ratio. The formula for calculating the equivalent mixed traffic volume for a single approach lane is: , in, The equivalent mixed traffic flow rate for lane i is expressed in pcu / h. The number of mixed-use vehicles entering lane i, in vehicles / hour; , These are the equivalent conversion factors for converting motor vehicles and electric bicycles into one standard passenger car, respectively. m , e The figures represent the proportions of traffic flow for motor vehicles and electric bicycles, expressed as a percentage.
[0008] Furthermore, in step S2, the formula for calculating the equivalent expected pedestrian delay for a single approach lane is: , in, Equivalent expected pedestrian delay for entrance lane i, in seconds per hour (s / eau). The average pedestrian delay in a certain direction at entrance i is expressed in seconds per person. The average delay for pedestrians in the opposite direction of entrance i is given in seconds per person; pedestrian flow is the same in both directions. The formula for calculating the equivalent expected mixed vehicle delay for a single import lane is as follows: , in, The equivalent expected mixed vehicle delay for lane i is expressed in seconds per cubic meter (pcu). , , The average delays for mixed vehicles traveling in the straight, left-turn, and right-turn directions at the i-entry lane are respectively, in seconds per vehicle. s , l , r These represent the percentages of vehicles going straight, turning left, and turning right in a mixed traffic system, expressed as a percentage.
[0009] Furthermore, in step S2, the equivalent expected conflict amount is calculated based on the pedestrian spacing theory. The equivalent expected conflict amount of the pedestrian early opening phase is the same as that of the ordinary two-phase phase, and the equivalent expected conflict amount of the pedestrian-dedicated phase is zero.
[0010] Furthermore, in step S3, the pedestrian unit time delay cost is calculated based on the per capita disposable wage income of residents; the mixed vehicle unit time delay cost is calculated by combining the motor vehicle unit time delay cost and the electric bicycle unit time delay cost, which is based on the pedestrian unit time delay cost and combined with the average number of occupants of motor vehicles and electric bicycles; the unit cost of pedestrian-vehicle conflict is calculated based on the average direct economic loss of road traffic accidents and the conversion relationship between conflict and accident.
[0011] Furthermore, the formula for calculating the total cost of the intersection in step S3 is as follows: , in, C The total cost of the four approach lanes at the intersection is expressed in yuan / hour. D v The total estimated delay for mixed vehicles is expressed in seconds per unit of cash. D p Equivalent expected total pedestrian delay, in seconds per hour (s / eau). P c The equivalent expected total number of conflicts is expressed in units per hour. S d The unit of time delay cost for mixed vehicles is: yuan / (vehicle / s); S p The cost of pedestrian delay per unit time is expressed in yuan per person per second. S c The unit cost of human-vehicle conflict is expressed in yuan per conflict.
[0012] Furthermore, in step S4, the decision to determine the settings of the ordinary two-phase, the pedestrian early-opening phase, and the pedestrian-dedicated phase based on the total cost increment is made by comparing the magnitude of the total cost increment with zero.
[0013] Furthermore, in step S4, the specific method for determining the settings of the ordinary two-phase, pedestrian early-opening phase, and pedestrian-dedicated phase based on the total cost increment is as follows: When the equivalent pedestrian flow is less than the first threshold, select normal two-phase; When the equivalent pedestrian flow is not less than the first threshold and less than the second threshold, and the total cost increment of the early pedestrian phase relative to the ordinary two-phase phase is less than zero, the early pedestrian phase is selected. When the equivalent pedestrian flow is not less than the second threshold, and the total cost increment of the pedestrian-dedicated phase relative to the ordinary two-phase phase is less than zero, and the total cost increment of the pedestrian-dedicated phase relative to the pedestrian early-opening phase is less than zero, the pedestrian-dedicated phase is selected.
[0014] Further, the first threshold is 700 eau / h; the second threshold is 900 eau / h; the setting range for the early pedestrian phase is: 800≤P<900 and 280≤V<480; the setting range for the dedicated pedestrian phase is: P=1000 and 40≤V<560, where P is the equivalent pedestrian flow rate in eau / h; and V is the equivalent mixed turning conflict rate in pcu / h.
[0015] The present invention also provides a road intersection signal control device, the signal control scheme of which can fully consider the characteristics of mixed traffic flow and different traffic participants, and take into account the traffic efficiency of the intersection while ensuring pedestrian safety; it has low implementation cost, can provide a quantitative approach for the design and optimization of pedestrian protection phases at signalized intersections, and provide scientific decision-making basis for traffic managers.
[0016] To achieve this technical objective, the technical solution adopted by the present invention is: the road intersection signal control device, comprising: Data acquisition module: configured to acquire simulation operation data of each approach lane under three signal control schemes: ordinary two-phase, pedestrian early opening phase, and pedestrian dedicated phase, within the preset range of equivalent pedestrian flow and equivalent mixed turning conflict parameters through micro traffic simulation. The simulation operation data includes at least the average delay of pedestrians and the average delay of mixed vehicles. Data calculation module: configured to calculate equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict amount based on the equivalent pedestrian flow, equivalent mixed turning conflict amount, average pedestrian delay, and average mixed vehicle delay of each approach lane; Cost Analysis Module: Configured to calculate the unit time delay cost of pedestrians, the unit time delay cost of mixed vehicles, and the unit cost of pedestrian-vehicle conflicts; based on the equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict amount of each approach lane, calculate the total intersection cost of three signal control schemes: ordinary two-phase, pedestrian early-opening phase, and pedestrian-dedicated phase. Decision module: Configured to calculate the total cost of the intersection based on three signal control schemes, calculate the total cost increment of the pedestrian early-opening phase and the pedestrian-dedicated phase relative to the ordinary two-phase phase, and determine the decision of setting the ordinary two-phase phase, the pedestrian early-opening phase and the pedestrian-dedicated phase based on the total cost increment.
[0017] The present invention also provides an electronic device, the signal control scheme of which can fully consider the characteristics of mixed traffic flow and different traffic participants, ensuring pedestrian safety while taking into account the traffic efficiency of the intersection; it has low implementation cost, can provide a quantitative approach for the design and optimization of pedestrian protection phases at signalized intersections, and provide scientific decision-making basis for traffic managers.
[0018] To achieve this technical objective, the present invention employs the following technical solution: the electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor in executing any of the methods described above, and the processor is configured to execute the program stored in the memory.
[0019] The present invention also provides a computer-readable storage medium, wherein the obtained signal control scheme can fully consider the characteristics of mixed traffic flow and different traffic participants, and take into account the traffic efficiency of the intersection while ensuring pedestrian safety; the implementation cost is low, and it can provide a quantitative approach for the design and optimization of pedestrian protection phases at signalized intersections, and provide scientific decision-making basis for traffic managers.
[0020] To achieve this technical objective, the present invention employs the following technical solution: a computer-readable storage medium having a computer program stored thereon, wherein the computer program is executed by a processor to perform any of the methods described above. Attached Figure Description
[0021] The following detailed description, in conjunction with the accompanying drawings and embodiments of the present invention, is as follows: Figure 1 This is a simulation diagram of the present invention; Figure 2 This is a heatmap of the total inter-phase delay cost difference according to the present invention; Figure 3 This is a heatmap of the total conflict cost of the three phases in this invention; Figure 4 This is a surface plot showing the total cost increment of the pedestrian early-opening phase versus ordinary two-phase phase of the present invention. Figure 5 This is a surface plot showing the total cost increment of the pedestrian-specific phase versus ordinary two-phase phase of the present invention. Figure 6 This is a surface plot showing the total cost increment of the pedestrian-specific phase-pedestrian early-opening phase of the present invention. Figure 7 This is a flowchart of the pedestrian protection phase setting decision method of the present invention; Figure 8 This is an aerial photograph of an intersection according to an embodiment of the present invention. Detailed Implementation
[0022] To enhance understanding of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. These embodiments are only used to explain the invention and do not limit the scope of protection of the invention.
[0023] This embodiment provides a method for setting pedestrian protection phases at a signalized intersection, including the following steps: S1: Using microscopic traffic simulation, within the preset range of equivalent pedestrian flow and equivalent mixed turning conflict parameters, the simulation operation data of each approach lane under three signal control schemes: ordinary two-phase, pedestrian early opening phase, and pedestrian dedicated phase are obtained. The simulation operation data includes at least the average delay of pedestrians and the average delay of mixed vehicles. S2: Calculate the equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict amount based on the equivalent pedestrian flow, equivalent mixed turning conflict amount, average pedestrian delay, and average mixed vehicle delay of each approach lane; S3: Calculate the unit time delay cost for pedestrians, the unit time delay cost for mixed vehicles, and the unit cost of pedestrian-vehicle conflicts; based on the equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict amount of each approach lane obtained in step S2, calculate the total intersection cost of the three signal control schemes: ordinary two-phase, pedestrian early opening phase, and pedestrian dedicated phase. S4: Based on the total cost of the three signal control schemes obtained in step S3, calculate the total cost increment of the pedestrian early-opening phase and the pedestrian-dedicated phase relative to the ordinary two-phase phase, and determine the decision on the setting of the ordinary two-phase phase, the pedestrian early-opening phase and the pedestrian-dedicated phase according to the total cost increment.
[0024] This invention obtains pedestrian delays and mixed vehicle delays for three signal control schemes under different traffic conditions through microscopic traffic simulation. It then calculates the equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict rate. Next, it uses statistical data to determine the unit time delay cost for pedestrians and mixed vehicles, as well as the unit cost of pedestrian-vehicle conflict, and calculates the total cost of the intersection. Finally, it calculates the total cost increment of the protective phase compared to the ordinary two-phase system. The optimal signal control scheme is determined based on this total cost increment. This scheme fully considers the characteristics of mixed traffic flow and different traffic participants, ensuring pedestrian safety while also balancing intersection efficiency. It has low implementation costs and provides a quantitative approach for the design and optimization of pedestrian-protective phases at signalized intersections, offering a scientific basis for decision-making by traffic management personnel.
[0025] The micro-traffic simulation in step S1 is performed using the micro-traffic simulation software VISSIM.
[0026] Specifically, using VISSIM microscopic traffic simulation software, pedestrian delays and mixed vehicle delays for three signal control schemes (ordinary two-phase, early pedestrian phase, and dedicated pedestrian phase) were obtained within the parameter range of 100-1000 eau / h equivalent pedestrian flow and 40-560 pcu / h equivalent mixed turning conflict at a single approach lane. Figure 1 As shown.
[0027] The VISSIM simulation parameters are set as follows: This is a two-way, four-lane intersection, with each lane 500 m long and 3.5 m wide. Each approach lane is divided into straight / right-turn lanes and straight / left-turn lanes. The pedestrian crossing is 20 m long and 4 m wide. The expected speed for motor vehicles is 48-58 km / h, for electric bicycles it is 15-20 km / h, and for pedestrians it is 2.09-5.51 km / h. Different pedestrian types are assigned different expected speeds: adults 68%, elderly 20%, children 10%, and disabled 2%. Among mixed traffic, 60% of vehicles go straight, and 20% each turn left and right. The simulation time is set to 3600 s. Each simulation uses the same pedestrian flow and mixed traffic flow for all four approach lanes, with motor vehicles accounting for 80% and electric bicycles for 20%. Based on the calculation formulas for equivalent pedestrian flow and equivalent mixed turning conflict, the actual pedestrian flow and actual mixed vehicle flow required for simulation are calculated. The simulation input parameter range for a single approach lane is: actual pedestrian flow of 82-820 people / h and actual mixed vehicle flow of 45-636 vehicles / h. The timing settings for the three signal control schemes are shown in Tables 1, 2, and 3 below.
[0028] Table 1. Ordinary two-phase timing settings with a period of 90 s
[0029] In Table 1, 01 for vehicles refers to the first phase of the signal control scheme used for vehicles, which allows vehicles to travel in the east-west direction; 02 for vehicles refers to the second phase, which allows vehicles to travel in the north-south direction; 01 for pedestrians refers to the first phase of the signal control scheme used for pedestrians, which allows pedestrians to travel in the east-west direction; 02 refers to the second phase, which allows pedestrians to travel in the north-south direction. Pedestrian traffic lights are equipped with flashing green and flashing red lights, but no yellow lights or all-red lights.
[0030] Table 2. Early Opening Phase Timing Settings for Downstream Pedestrians with a Period of 90 s
[0031] The meanings of phase references in Table 2 are the same as those in Table 1.
[0032] Table 3. Pedestrian-only phase timing settings for a 90 s period
[0033] Table 3 uses a single signal control scheme for pedestrians and vehicles. 01 Vehicles refers to the first phase for east-west traffic, 02 Vehicles refers to the second phase for north-south traffic, and 03 Pedestrians refers to the third phase for all-directional pedestrian traffic.
[0034] The equivalent pedestrian flow in step S1 is calculated by converting different types of people into the pedestrian flow of a standard adult. The formula for calculating the equivalent pedestrian flow of a single entrance is as follows: , in, The equivalent pedestrian flow at entrance i is expressed in eau / h. The actual number of pedestrians at entrance i, in person / hour; , , , These are the equivalent conversion factors for children, the elderly, the disabled, and adults, respectively, converted to one standard adult. , b , c , d The percentages of pedestrian traffic for children, the elderly, the disabled, and adults are shown in Table 4. The equivalent pedestrian traffic conversion factor is shown in Table 4.
[0035] Table 4 Conversion Factors for Equivalent Pedestrian Flow
[0036] Right now, , , , They are 2, 1.5, 2, and 1 respectively; a , b , c , d They are 10%, 20%, 2%, and 68% respectively.
[0037] The formula for calculating the equivalent mixed traffic flow of a single approach lane is: , in, The equivalent mixed traffic flow rate for lane i is expressed in pcu / h. The number of mixed-use vehicles entering lane i, in vehicles / hour; , These are the equivalent conversion factors for converting motor vehicles and electric bicycles into one standard passenger car, respectively. m , eThe traffic flow ratios for motor vehicles and electric bicycles are represented as percentages, respectively. The equivalent mixed turning conflict amount for a single approach lane is calculated by multiplying the equivalent mixed traffic flow of that approach lane by the turning ratio. During simulation, the equivalent turning conflict amount for a single approach lane can be obtained by inputting the equivalent mixed traffic flow and turning ratio, thereby analyzing the delay under different turning conflict amounts.
[0038] In this embodiment, , They are 1 and 0.3 respectively; m , e The percentages are 80% and 20% respectively; the steering ratio is 40%.
[0039] The types of simulated vehicles, their expected speeds and proportions, and the types of simulated pedestrians, their expected speeds and proportions are shown in Tables 5 and 6 below.
[0040] Table 5. Simulated vehicle types, expected speeds, and proportions
[0041] Table 6 Simulated Pedestrian Types, Expected Speeds, and Proportions
[0042] In step S2, the formula for calculating the equivalent expected pedestrian delay for a single approach lane is as follows: , in, Equivalent expected pedestrian delay for entrance lane i, in seconds per hour (s / eau). The average pedestrian delay in a certain direction at entrance i is expressed in seconds per person. The average delay for pedestrians in the opposite direction of entrance i is given in seconds per person; pedestrian flow is the same in both directions. The total equivalent expected pedestrian delay at the intersection under the three signal control schemes are shown in Tables 7, 8, and 9, where P is the equivalent pedestrian flow rate in eau / h and V is the equivalent mixed turning conflict in pcu / h.
[0043] Table 7. Total Equivalent Expected Pedestrian Delay for Ordinary Two-Phase Vehicles (s / eau)
[0044] Table 8. Total Equivalent Expected Pedestrian Delay for Early Pedestrian Opening Phases (s / eau)
[0045] Table 9. Expected Pedestrian Delay (s / eau) based on Total Equivalent of Pedestrian-Specific Phase
[0046] The formula for calculating the equivalent expected mixed vehicle delay for a single import lane is as follows: , in, The equivalent expected mixed vehicle delay for lane i is expressed in seconds per cubic meter (pcu). , , The average delays for mixed vehicles traveling in the straight, left-turn, and right-turn directions at the i-entry lane are respectively, in seconds per vehicle. s , l , r These represent the percentages of vehicles going straight, turning left, and turning right in a mixed traffic system, expressed as a percentage.
[0047] In this embodiment, the s , l , r They are 60%, 20%, and 20% respectively.
[0048] The total equivalent expected mixed vehicle delays at the intersection under the three signal control schemes are shown in Tables 10, 11, and 12.
[0049] Table 10. Total Equivalent Expected Mixed Vehicle Delay (s / pcu) for Ordinary Two-Phase Vehicles
[0050] Table 11 Total Equivalent Expected Mixed Vehicle Delay for Early Pedestrian-Opening Phases (s / pcu)
[0051] Table 12 Total Equivalent Expected Mixed Vehicle Delay (s / pcu) for Pedestrian-Dedicated Phases
[0052] In step S2, the equivalent expected conflict amount is calculated based on the pedestrian spacing theory in Yuan Li et al.'s "Research on the Evaluation Method of Safety Benefits of Pedestrian-Dedicated Phase at Signalized Intersections". The equivalent expected conflict amount of the pedestrian early opening phase is the same as that of the ordinary two-phase phase, and the equivalent expected conflict amount of the pedestrian-dedicated phase is zero.
[0053] Specifically, the formula for calculating the equivalent expected conflict amount for a single approach lane is as follows (taking the north approach lane as an example): , in, , b These are the pedestrian row conflict equivalent and column conflict equivalent, respectively, in units / h; W The width for pedestrian crossing, in meters; L The pedestrian crossing length is taken as the road width, in meters. l1 =1 m is the lateral movement range of a pedestrian. l 2 =1 m is the longitudinal range of pedestrian movement; The total expected conflict quantity of the northern entrance is expressed as units per hour. The equivalent mixed right-turn conflict amount from east to west, pcu / h; The equivalent mixed left-turn conflict amount from west to east, pcu / h; Equivalent pedestrian crossing volume on the north side from east to west, eau / h; Equivalent pedestrian crossing volume on the north side from west to east, eau / h.
[0054] In this embodiment, the W , L The values are 4 m and 20 m respectively; taking a single approach lane with an equivalent pedestrian flow of 100 eau / h and an equivalent turning conflict of 40 pcu / h as an example. , , , The corresponding values are 20 pcu / h, 20 pcu / h, 50 eau / h, and 50 eau / h. The equivalent pedestrian flow in different directions is the same for a single pedestrian crossing, and the conflict volume for left and right turns at a single approach is the same.
[0055] Within the equivalent pedestrian flow range of this invention, VISSIM assumes that pedestrian arrivals follow a Poisson distribution. When using the early pedestrian phase, almost no pedestrians arrive in the first 5 seconds of the simulation. Therefore, the equivalent expected conflict amount of the early pedestrian phase is the same as that of the ordinary two-phase phase, and the equivalent expected conflict amount of the pedestrian-dedicated phase is zero.
[0056] The total expected conflict amount of the intersection under the normal two-phase and pedestrian early opening phase conditions is shown in Table 13.
[0057] Table 13 Total Equivalent Expected Conflict Quantity for Ordinary Two-Phase and Pedestrian Early Opening Phase (Number of Conflicts / h)
[0058] In step S3, the pedestrian unit time delay cost is calculated based on the per capita disposable wage income of residents; the mixed vehicle unit time delay cost is calculated by combining the motor vehicle unit time delay cost and the electric bicycle unit time delay cost, which is based on the pedestrian unit time delay cost and combined with the average number of occupants of motor vehicles and electric bicycles; the unit cost of pedestrian-vehicle conflict is calculated based on the average direct economic loss of road traffic accidents and the conversion relationship between conflict and accident.
[0059] Specifically, the unit value of time is calculated using the latest resident income statistics to determine the unit time delay cost for pedestrians, motor vehicles, and electric bicycles, and thus the unit time delay cost for mixed vehicles. The average direct economic loss per accident is calculated using the latest road traffic accident statistics, and the unit cost of pedestrian-vehicle conflict is determined by combining this with the conflict-accident conversion relationship.
[0060] Unit time delay cost for pedestrians, motor vehicles, electric bicycles, and mixed vehicles S p , S m , S e , S d The unit costs for personnel-vehicle conflicts are 0.0031 yuan / (person / s), 0.0047 yuan / (vehicle / s), 0.0037 yuan / (vehicle / s), and 0.0045 yuan / (vehicle / s), respectively. S c The cost is 0.0579 yuan per conflict. The calculation process is as follows: Based on the 2023 resident income data, the time value of money is estimated using wage income. In 2023, the national per capita disposable income was approximately 39,218 yuan, of which wage income was approximately 22,053 yuan. The working hours in 2023 were 2008 hours. Therefore, the time value per hour is: , The cost of pedestrian delay per unit time is: , Considering the impact of vehicle passenger numbers, with an average passenger number of 1.5 people per motor vehicle and 1.2 people per electric bicycle, we get: The unit time delay cost for motor vehicles is: , The unit time delay cost for electric bicycles is: , The unit time delay cost for hybrid vehicles is: , According to publicly available data such as the China Statistical Yearbook, there were approximately 255,000 road traffic accidents nationwide in 2023, resulting in direct economic losses of approximately 1.18 billion yuan. This leads to the following average direct economic loss per accident: , Based on domestic traffic conflict theories and relevant research, the probability that a pedestrian-vehicle conflict will escalate into a traffic accident can be taken as: , The unit cost of pedestrian-vehicle conflict is: , The formula for calculating the total cost of the intersection in step S3 is as follows: , in, C The total cost of the four approach lanes at the intersection is expressed in yuan / hour. D v The total estimated delay for mixed vehicles is expressed in seconds per unit of cash. D p Equivalent expected total pedestrian delay, in seconds per hour (s / eau). P c The equivalent expected total number of conflicts is expressed in units per hour. S d The unit of time delay cost for mixed vehicles is: yuan / (vehicle / s); S p The cost of pedestrian delay per unit time is expressed in yuan per person per second. S c The unit cost of human-vehicle conflict is expressed in yuan per conflict.
[0061] The total cost of the intersection under the three signal control schemes is shown in Tables 14, 15, and 16.
[0062] Table 14 Total Cost of Ordinary Two-Phase (Yuan / h)
[0063] Table 15 Total Cost of Early Pedestrian Opening Phase (Yuan / h)
[0064] Table 16 Total Cost of Pedestrian-Dedicated Phase (Yuan / h)
[0065] Among them, a heatmap analysis was conducted to examine the differences in total delay costs between early pedestrian phase, dedicated pedestrian phase, and ordinary two-phase phase. The results are as follows: Figure 2 As shown in the figure, a heatmap analysis was performed to examine the differences in total conflict costs between pedestrian early-opening phases, pedestrian-dedicated phases, and ordinary two-phase phases. The results are as follows: Figure 3 As shown.
[0066] In step S4, the decision to determine the settings of the ordinary two-phase, pedestrian early-opening phase, and pedestrian-dedicated phase based on the total cost increment is made by comparing the magnitude of the total cost increment with zero.
[0067] In step S4, the specific method for determining the settings of the ordinary two-phase, pedestrian early-opening phase, and pedestrian-dedicated phase based on the total cost increment is as follows: When the equivalent pedestrian flow is less than the first threshold, select normal two-phase; When the equivalent pedestrian flow is not less than the first threshold and less than the second threshold, and the total cost increment of the early pedestrian phase relative to the ordinary two-phase phase is less than zero, the early pedestrian phase is selected. When the equivalent pedestrian flow is not less than the second threshold, and the total cost increment of the pedestrian-dedicated phase relative to the ordinary two-phase phase is less than zero, and the total cost increment of the pedestrian-dedicated phase relative to the pedestrian early-opening phase is less than zero, the pedestrian-dedicated phase is selected.
[0068] Further, the first threshold is 700 eau / h; the second threshold is 900 eau / h; the preferred setting area for the early pedestrian phase is: 800≤P<900 and 280≤V<480; the preferred setting area for the dedicated pedestrian phase is: P=1000 and 40≤V<560, where P is the equivalent pedestrian flow rate in eau / h; and V is the equivalent mixed turning conflict amount in pcu / h.
[0069] In this embodiment, the total cost increment surface plot is used, such as Figure 4-6 As shown, the setting areas for ordinary two-phase, pedestrian early-opening phase and pedestrian-dedicated phase are divided to obtain a decision-making method for pedestrian protection phase setting.
[0070] From the appendix Figure 2 Appendix Figure 3 Appendix Figure 4 Appendix Figure 5 Appendix Figure 6 It can be seen that, when only considering the total delay cost, within the scope of all equivalent pedestrian flow P and equivalent mixed turning conflict V, the pedestrian-only phase has the highest cost, far exceeding the other two phases. The cost of the early-opening pedestrian phase is slightly higher than that of the ordinary two-phase phase, but in some cases, it is lower than that of the ordinary two-phase phase under medium-to-high pedestrian flow or medium-to-high mixed vehicle flow. The cost of the ordinary two-phase phase is the lowest in most cases. When only considering the total cost of pedestrian-vehicle conflict, the costs of the ordinary two-phase phase and the early-opening pedestrian phase are the same, while the cost of the pedestrian-only phase is zero. In practice, the early-opening pedestrian phase can improve pedestrian safety and enhance pedestrian experience, making it a suitable choice that comprehensively considers delay and conflict. The pedestrian-only phase can completely isolate pedestrian-vehicle conflict, making it the best phase choice for protecting pedestrians. To simultaneously consider delay costs and safety costs, and to implement the "people-oriented" traffic concept, this patent first determines the pedestrian flow and then calculates the total cost increment between phases. Value, when pedestrian early phase - total cost increment of ordinary two-phase When the cost is RMB / h, the pedestrian early-opening phase is preferred, and the total cost increase between the pedestrian-dedicated phase and the ordinary two-phase phase is calculated. Yuan / h and pedestrian-dedicated phase - pedestrian early opening phase total cost increment When the cost is 1 yuan / h, the pedestrian-only phase should be selected first.
[0071] In this embodiment, the preferred setting area for the ordinary two-phase is: P < 700 people / h; the main setting area for the pedestrian early-opening phase is: 700 ≤ P < 900 people / h, and the preferred setting area is: 800 ≤ P < 900 people / h and 280 ≤ V < 480 pcu / h; the main setting area for the pedestrian-dedicated phase is: 900 ≤ P ≤ 1000 people / h, and the preferred setting area is: P = 1000 people / h and 40 ≤ V < 560 pcu / h.
[0072] In summary, the method for setting up pedestrian-protected phases at signalized intersections as described in this invention first obtains pedestrian delays and mixed vehicle delays under different traffic conditions using VISSIM simulation. Then, it calculates the equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict rate. Next, it uses the latest statistical data to determine the unit time delay cost for pedestrians, motor vehicles, electric bicycles, and mixed vehicles, as well as the unit cost of pedestrian-vehicle conflict. Finally, it calculates the total cost increment of the protected phase relative to the ordinary two-phase phase using the total cost increment surface diagram. The optimal setting areas for the ordinary two-phase phase, the early pedestrian opening phase, and the pedestrian-dedicated phase are then divided using the total cost increment surface diagram, resulting in a decision-making method for setting up pedestrian-protected phases. The flowchart of this decision-making method is shown below. Figure 7 As shown, this invention is a method for setting pedestrian-protected phases at signalized intersections based on a comprehensive optimization of pedestrian-vehicle conflict costs and delay costs. It is applicable to urban at-grade intersections that consider pedestrian priority and mixed traffic flow characteristics.
[0073] This embodiment also provides a road intersection signal control device, including: Data acquisition module: configured to acquire simulation operation data of each approach lane under three signal control schemes: ordinary two-phase, pedestrian early opening phase, and pedestrian dedicated phase, within the preset range of equivalent pedestrian flow and equivalent mixed turning conflict parameters through micro traffic simulation. The simulation operation data includes at least the average delay of pedestrians and the average delay of mixed vehicles. Data calculation module: configured to calculate equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict amount based on the equivalent pedestrian flow, equivalent mixed turning conflict amount, average pedestrian delay, and average mixed vehicle delay of each approach lane; Cost Analysis Module: Configured to calculate the unit time delay cost of pedestrians, the unit time delay cost of mixed vehicles, and the unit cost of pedestrian-vehicle conflicts; based on the equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict amount of each approach lane, calculate the total intersection cost of three signal control schemes: ordinary two-phase, pedestrian early-opening phase, and pedestrian-dedicated phase. Decision module: Configured to calculate the total cost of the intersection based on three signal control schemes, calculate the total cost increment of the pedestrian early-opening phase and the pedestrian-dedicated phase relative to the ordinary two-phase phase, and determine the decision of setting the ordinary two-phase phase, the pedestrian early-opening phase and the pedestrian-dedicated phase based on the total cost increment.
[0074] This embodiment also provides an electronic device, including a memory and a processor. The memory is used to store a program that supports the processor in executing the above-described phase setting decision method, and the processor is configured to execute the program stored in the memory.
[0075] This embodiment also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, performs the aforementioned phase setting decision method.
[0076] This embodiment also provides a method for determining (deciding on) a typical two-way four-lane intersection based on actual measurements and signal control schemes, specifically including the following steps: Step 1: On-site data collection, selecting the intersection of Songshan Road and Shuanghe Street in Nanjing City, such as... Figure 8 As shown, an on-site investigation was conducted, and a drone was used to continuously film for 1 hour during the evening rush hour, recording the current signal control scheme at the intersection.
[0077] The intersection parameters are as follows: This intersection is a two-way, four-lane, four-entry secondary arterial road-to-secondary arterial road intersection with mixed traffic of motor vehicles and non-motor vehicles. Each approach lane is divided into one straight-left lane and one straight-right lane, with a lane width of 3 m. The pedestrian crossings at each approach lane are 4 m wide and 22 m long. The existing signal control scheme is a conventional two-phase control with a cycle of 70 s. The green light time, yellow light time, and all-red light time are 30 s, 3 s, and 2 s, respectively. There are kindergartens, primary schools, subway stations, and numerous residential areas near this intersection, resulting in a large volume of pedestrian and mixed vehicle traffic.
[0078] Step 2: Count the number of pedestrians at each crosswalk and the proportion of different pedestrian types. Based on the pedestrian protection phase setting decision method of this invention, pedestrian flow is the primary condition, and the southwest-facing approach with the highest pedestrian flow is selected as the analysis object to calculate the equivalent pedestrian flow. According to the equivalent pedestrian flow calculation formula, the equivalent pedestrian flow of this intersection is 920 eau / h ≥ 900 eau / h, specifically calculated as follows: , in, , , , They are 2, 1.5, 2, and 1 respectively; , b , c , d They were 21%, 0%, 0%, and 79% respectively; It is 720 people / hour.
[0079] Step 3: The mixed traffic flow, turning ratio, and non-motorized vehicle proportion of the four approach lanes are statistically analyzed, as shown in Table 17. The average delays for pedestrians and vehicles in different directions at each approach lane under ordinary two-phase and pedestrian-only phase signal control were obtained through VISSIM simulation. The green light time for the pedestrian-only phase was set to 20 seconds. The total equivalent expected pedestrian delays for ordinary two-phase and pedestrian-only phases were calculated to be 20645 s / eau and 27097 s / eau, respectively; the total equivalent expected mixed vehicle delays were 632000 s / pcu and 717111 s / pcu, respectively; and the equivalent expected conflict quantities were 161883 / h and 0 / h, respectively. Finally, the total cost increment between the pedestrian-only phase and ordinary two-phase phases was calculated using the total cost formula. =3311-12281=-8970 yuan / h<0 yuan / h.
[0080] Table 17 Parameters of Mixed Vehicles in Four Import Lanes
[0081] Step 4: Using VISSIM simulation, the average delays of pedestrians and vehicles in different directions at each approach lane under the pedestrian early-opening phase signal control are obtained, with the early-opening phase for pedestrians defined as 5 seconds. The total equivalent expected pedestrian delay for the pedestrian early-opening phase is calculated to be 20645 s / eau, the total equivalent expected mixed vehicle delay is 663556 s / pcu, and the equivalent expected conflict quantity is 161883 / h. Finally, the total cost increment of the pedestrian-dedicated phase versus the pedestrian early-opening phase is calculated using the total cost formula. =3311-12423=-9112 yuan / h<0 yuan / h.
[0082] Based on the above, according to the method of the present invention, in order to ensure the safety of students and residents crossing the street around the intersection, it is recommended to replace the existing ordinary two-phase signal control scheme with a pedestrian-only phase signal control scheme, investigate the implementation effect after a period of time, and verify whether the setting of the pedestrian-only phase is reasonable based on actual delay data and traffic conflict data.
[0083] It should be noted that, in specific applications, this invention can also modify parameters such as intersection geometry design, traffic volume, signal cycle, pedestrian-only phase green light time, pedestrian early-opening phase early-opening time, proportion of different pedestrian types, proportion of electric bicycles, and vehicle turning ratio according to the actual situation of the intersection, and set applicable pedestrian protection phases.
[0084] The foregoing description and illustrations explain the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.
Claims
1. A method for setting a pedestrian protection phase of a signalized intersection, characterized in that Includes the following steps: S1: Using microscopic traffic simulation, within the preset range of equivalent pedestrian flow and equivalent mixed turning conflict parameters, the simulation operation data of each approach lane under three signal control schemes: ordinary two-phase, pedestrian early opening phase, and pedestrian dedicated phase are obtained. The simulation operation data includes at least the average delay of pedestrians and the average delay of mixed vehicles. S2: Calculate the equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict amount based on the equivalent pedestrian flow, equivalent mixed turning conflict amount, average pedestrian delay, and average mixed vehicle delay of each approach lane; S3: Calculate the unit time delay cost for pedestrians, the unit time delay cost for mixed vehicles, and the unit cost of pedestrian-vehicle conflicts; based on the equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict amount of each approach lane obtained in step S2, calculate the total intersection cost of the three signal control schemes: ordinary two-phase, pedestrian early opening phase, and pedestrian dedicated phase. S4: Based on the total cost of the three signal control schemes obtained in step S3, calculate the total cost increment of the pedestrian early-opening phase and the pedestrian-dedicated phase relative to the ordinary two-phase phase, and determine the decision on the setting of the ordinary two-phase phase, the pedestrian early-opening phase and the pedestrian-dedicated phase according to the total cost increment.
2. The method for setting pedestrian protection phases at signalized intersections according to claim 1, characterized in that, The micro-traffic simulation in step S1 is performed using the micro-traffic simulation software VISSIM.
3. The method for setting pedestrian protection phases at signalized intersections according to claim 1, characterized in that, The equivalent pedestrian flow in step S1 is calculated by converting different types of people into the pedestrian flow of a standard adult. The formula for calculating the equivalent pedestrian flow of a single entrance is as follows: , in, The equivalent pedestrian flow at entrance i is expressed in eau / h. The actual number of pedestrians at entrance i, in person / hour; , , , These are the equivalent conversion factors for children, the elderly, the disabled, and adults, respectively, converted to one standard adult. , b , c , d The pedestrian flow rates are categorized into children, the elderly, the disabled, and adults, and are expressed as a percentage. The equivalent mixed steering conflict amount for a single approach lane is the equivalent mixed traffic volume for that approach lane multiplied by the steering ratio. The formula for calculating the equivalent mixed traffic volume for a single approach lane is: , in, The equivalent mixed traffic flow rate for lane i is expressed in pcu / h. The number of mixed-use vehicles entering lane i, in vehicles / hour; , These are the equivalent conversion factors for converting motor vehicles and electric bicycles into one standard passenger car, respectively. m , e The figures represent the proportions of traffic flow for motor vehicles and electric bicycles, expressed as a percentage.
4. The method for setting pedestrian protection phases at signalized intersections according to claim 3, characterized in that, In step S2, the formula for calculating the equivalent expected pedestrian delay for a single approach lane is as follows: , in, Equivalent expected pedestrian delay for entrance lane i, in seconds per hour (s / eau). The average pedestrian delay in a certain direction at entrance i is expressed in seconds per person. The average delay for pedestrians in the opposite direction of entrance i is given in seconds per person; pedestrian flow is the same in both directions. The formula for calculating the equivalent expected mixed vehicle delay for a single import lane is as follows: , in, The equivalent expected mixed vehicle delay for lane i is expressed in seconds per cubic meter (pcu). , , The average delays for mixed vehicles traveling in the straight, left-turn, and right-turn directions at the i-entry lane are respectively, in seconds per vehicle. s , l , r These represent the percentages of vehicles going straight, turning left, and turning right in a mixed traffic system, expressed as a percentage.
5. The method for setting pedestrian protection phases at signalized intersections according to claim 1, characterized in that, In step S2, the equivalent expected conflict amount is calculated based on the pedestrian spacing theory. The equivalent expected conflict amount of the pedestrian early opening phase is the same as that of the ordinary two-phase phase, and the equivalent expected conflict amount of the pedestrian-dedicated phase is zero.
6. The method for setting pedestrian protection phases at signalized intersections according to claim 1, characterized in that, In step S3, the pedestrian unit time delay cost is calculated based on the per capita disposable wage income of residents; the mixed vehicle unit time delay cost is calculated by combining the motor vehicle unit time delay cost and the electric bicycle unit time delay cost, which is based on the pedestrian unit time delay cost and combined with the average number of occupants of motor vehicles and electric bicycles; the unit cost of pedestrian-vehicle conflict is calculated based on the average direct economic loss of road traffic accidents and the conversion relationship between conflict and accident.
7. The method for setting pedestrian protection phases at signalized intersections according to claim 6, characterized in that, The formula for calculating the total cost of the intersection in step S3 is as follows: , in, C The total cost of the four approach lanes at the intersection is expressed in yuan / hour. D v The total estimated delay for mixed vehicles is expressed in seconds per unit of cash. D p Equivalent expected total pedestrian delay, in seconds per hour (s / eau). P c The equivalent expected total number of conflicts is expressed in units per hour. S d The unit of time delay cost for mixed vehicles is: yuan / (vehicle / s); S p The cost of pedestrian delay per unit time is expressed in yuan per person per second. S c The unit cost of human-vehicle conflict is expressed in yuan per conflict.
8. The method for setting pedestrian protection phases at signalized intersections according to claim 1, characterized in that, In step S4, the decision to determine the settings of the ordinary two-phase, pedestrian early-opening phase, and pedestrian-dedicated phase based on the total cost increment is made by comparing the magnitude of the total cost increment with zero.
9. The method for setting pedestrian protection phases at signalized intersections according to claim 8, characterized in that, In step S4, the specific method for determining the settings of the ordinary two-phase, pedestrian early-opening phase, and pedestrian-dedicated phase based on the total cost increment is as follows: When the equivalent pedestrian flow is less than the first threshold, select normal two-phase; When the equivalent pedestrian flow is not less than the first threshold and less than the second threshold, and the total cost increment of the early pedestrian phase relative to the ordinary two-phase phase is less than zero, the early pedestrian phase is selected. When the equivalent pedestrian flow is not less than the second threshold, and the total cost increment of the pedestrian-dedicated phase relative to the ordinary two-phase phase is less than zero, and the total cost increment of the pedestrian-dedicated phase relative to the pedestrian early-opening phase is less than zero, the pedestrian-dedicated phase is selected.
10. The method for setting pedestrian protection phases at signalized intersections according to claim 9, characterized in that, The first threshold is 700 eau / h; the second threshold is 900 eau / h; the setting range for the early pedestrian phase is: 800≤P<900 and 280≤V<480; the setting range for the dedicated pedestrian phase is: P=1000 and 40≤V<560, where P is the equivalent pedestrian flow rate in eau / h; and V is the equivalent mixed turning conflict rate in pcu / h.
11. A signal control device for a road intersection, characterized in that, include: Data acquisition module: configured to acquire simulation operation data of each approach lane under three signal control schemes: ordinary two-phase, pedestrian early opening phase, and pedestrian dedicated phase, within the preset range of equivalent pedestrian flow and equivalent mixed turning conflict parameters through micro traffic simulation. The simulation operation data includes at least the average delay of pedestrians and the average delay of mixed vehicles. Data calculation module: configured to calculate equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict amount based on the equivalent pedestrian flow, equivalent mixed turning conflict amount, average pedestrian delay, and average mixed vehicle delay of each approach lane; Cost Analysis Module: Configured to calculate the unit time delay cost of pedestrians, the unit time delay cost of mixed vehicles, and the unit cost of pedestrian-vehicle conflicts; based on the equivalent expected pedestrian delay, equivalent expected mixed vehicle delay, and equivalent expected conflict amount of each approach lane, calculate the total intersection cost of three signal control schemes: ordinary two-phase, pedestrian early-opening phase, and pedestrian-dedicated phase. Decision module: Configured to calculate the total cost of the intersection based on three signal control schemes, calculate the total cost increment of the pedestrian early-opening phase and the pedestrian-dedicated phase relative to the ordinary two-phase phase, and determine the decision of setting the ordinary two-phase phase, the pedestrian early-opening phase and the pedestrian-dedicated phase based on the total cost increment.
12. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports a processor in executing the method of any one of claims 1-10, the processor being configured to execute the program stored in the memory.
13. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program is executed by the processor to perform the method described in any one of claims 1-10.
Citation Information
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