A method for calculating average queue length of road network based on three-dimensional macroscopic fundamental diagram

Abstract

The application provides a road network average queue length calculation method based on a three-dimensional macroscopic fundamental diagram, and specifically comprises the following steps: constructing a road network level traffic simulation model, drawing a three-dimensional macroscopic fundamental diagram according to a simulation running result, fitting the three-dimensional macroscopic fundamental diagram to obtain a dynamic vehicle conversion coefficient, calculating a road network average speed according to a traffic flow, a vehicle density and a vehicle speed according to a three-phase traffic flow theory, establishing an equation to solve under the premise that the road network average speed does not change, calculating the dynamic vehicle conversion coefficient, calculating an average number of people in a queue by using the dynamic vehicle conversion coefficient, counting a number of vehicles in a queue to calculate a road network average queue length. The application calculates the road network average queue length by using the dynamic vehicle conversion coefficient, dynamically adapts to an evolution law of traffic flow, and optimizes a road network average queue length estimation method.

Description

Technical Field

[0001] This invention relates to the field of transportation technology, and in particular to a method for calculating the average queue length of a road network based on a three-dimensional macroscopic basic map. Background Technology

[0002] In urban transportation systems, queue length is a key indicator for evaluating traffic operation status, effectively reflecting the degree of traffic congestion on the road network and the efficiency of intersections. With the acceleration of urbanization, urban traffic congestion has become increasingly prominent. Calculating the average queue length of the entire macro-road network has significant theoretical and practical implications, providing important guidance for alleviating traffic congestion, improving road network efficiency, and optimizing urban traffic management.

[0003] Mixed traffic flow is a typical characteristic of urban traffic in my country. The composition and driving characteristics of vehicles in mixed traffic environments significantly impact road network efficiency. To assess the impact of mixed traffic flow on road and intersection capacity, it is necessary to introduce vehicle conversion factors. This converts the mixed traffic volume, composed of different vehicle types such as private cars, buses, trains, and intelligent connected vehicles, into an equivalent of a uniform axle load, quantifying the degree of influence of different vehicle types. However, traffic flow has dynamic evolutionary characteristics; traditional static vehicle conversion factors can only reflect the traffic flow state at a certain moment and cannot reflect the dynamic changes in traffic flow.

[0004] The macroscopic basic map is a fundamental attribute of the road network, enabling a macroscopic assessment of overall regional traffic trends and playing a crucial role in studying the characteristics of mixed heterogeneous traffic flows. To adapt to the dynamic evolution of traffic flow and comprehensively reflect road network capacity, traffic demand, and supply relationships, a three-dimensional macroscopic basic map is introduced. This map characterizes the evolution of traffic congestion and the dynamic interactions between different types of vehicles at the network level, providing a new perspective for analyzing the average queue length of the road network and helping to more accurately and reasonably reflect traffic congestion conditions. Summary of the Invention

[0005] The technical problem to be solved by this invention is to overcome the defects of the existing technology. This invention proposes a method for calculating the average queue length of the road network based on a three-dimensional macroscopic basic map, realizing dynamic estimation of the vehicle conversion system, reflecting the uncontrolled resource occupation of the road under different traffic operation turnarounds, so as to adapt to the dynamic evolution of traffic flow.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for calculating the average queue length of a road network based on a three-dimensional macroscopic basic map, as detailed below: Construct a road network-level traffic simulation model, and draw a three-dimensional macroscopic basic map based on the simulation results. The dynamic vehicle conversion factor is obtained by combining the three-dimensional macroscopic basic graph obtained through function fitting with three-phase traffic flow theory. According to the three-phase traffic flow theory, the average speed of the road network is calculated based on traffic volume, vehicle density, and vehicle speed. Under the premise that the average speed of the road network remains unchanged, the dynamic vehicle conversion factor is obtained by solving a set of equations. The average number of people stranded is calculated using a dynamic vehicle conversion factor, and then the number of stranded vehicles is statistically analyzed to calculate the average queue length of the road network.

[0007] Furthermore, the relationship between traffic flow, vehicle density, and vehicle speed is shown in the following formula: ; In the formula, Q is the traffic flow, K is the traffic flow density, V is the traffic flow speed, l is the road segment length, and n is the number of vehicles on the road segment.

[0008] Furthermore, the equation is as follows: ; Substituting the average passenger number, the dynamic vehicle conversion factor is obtained as follows: ; In the formula, n c To accumulate traffic for the private car road network, n b For other types of vehicles, P c For the average passenger capacity of private vehicles, P b This represents the average passenger capacity of other types of vehicles.

[0009] Furthermore, the queue length is calculated using the following formula: ; In the formula, Let n be the average queue length of the road network at time t. cqi For road section The number of private vehicles queuing, n bqi For road section Queue numbers for other types of vehicles, BBCU is the equivalent conversion factor for the passenger capacity of other types of vehicles, T qi For road section The delay time.

[0010] Furthermore, in the function fitting process, the fitting of the three-dimensional macroscopic basic graph function is transformed into a nonlinear least squares problem, and the fitting function is obtained by solving the Gauss-Newton method.

[0011] Furthermore, the three-dimensional macroscopic basic map is fitted with an exponential function, in which the accumulated amount of private cars and other types of vehicles in the road network is the independent variable, and the road network passenger flow is the dependent variable. The function has the following form: In the formula, Q c Q represents private car traffic volume. b P represents other types of traffic flow. c This indicates the average passenger capacity of private vehicles, P b This indicates the average passenger capacity of other types of vehicles. , , , , , , All of these are parameters to be determined.

[0012] Furthermore, the function, after processing, is as follows: In the formula, Z represents the loss function. This represents the passenger flow value obtained from simulation data. It is the residual function; The parameters to be determined were then solved using the Gauss-Newton method.

[0013] Furthermore, the statistical process is completed according to the following approximation rules: (1) If there are vehicles with a speed of zero on the detected road section, they are included in the road section queue; (2) If there are at least two vehicles with non-zero speed after the vehicle with zero speed in the detected road section, or if there are no vehicles, the detection queue is considered to be over.

[0014] Compared with the prior art, the beneficial effects of the present invention include: By using a three-dimensional macroscopic basic map to analyze the characteristics of mixed traffic flow, two different types of vehicles are respectively used as the X-axis and Y-axis, and the passenger flow carried by the road network is used as the Z-axis. This can form a macroscopic basic map that reflects the dynamic evolution relationship between different vehicle flows and road network passenger flow, which is beneficial for studying mixed heterogeneous traffic flow. By using Gaussian Newton short hair to solve the functional form of the three-dimensional macroscopic fundamental graph, the complex nonlinear function of the three-dimensional macroscopic fundamental graph is transformed into a nonlinear least squares problem, which enables fast and accurate fitting of the functional form of the three-dimensional macroscopic fundamental graph; By using dynamic vehicle conversion factors to calculate the average queue length of the road network, the method of estimating the average queue length of the road network is dynamically adapted to the evolution of traffic flow. Attached Figure Description

[0015] The disclosure of this invention is illustrated with reference to the accompanying drawings. It should be understood that the drawings are for illustrative purposes only and are not intended to limit the scope of protection of this invention. In the drawings, the same reference numerals are used to refer to the same parts. Wherein: Figure 1 This is a flowchart of the method for calculating the average queue length of a road network based on a three-dimensional macroscopic basic map, as described in this invention. Figure 2 A flowchart for drawing a three-dimensional macroscopic basic diagram to build a road network-level traffic flow simulation model based on SUMO and obtain simulation results; Figure 3 This is a schematic diagram of a road network according to a specific embodiment of the present invention; Figure 4 A three-dimensional macroscopic basic diagram of road network passenger flow; Figure 5 A three-dimensional macroscopic basic diagram of the average speed of the road network; Figure 6 The graph of the dynamic vehicle conversion factor BBCU; Figure 7 The average queue length of the road network under different mixed traffic flow optimization strategies. Detailed Implementation

[0016] It is readily understood that, based on the technical solution of this invention, those skilled in the art can propose various interchangeable structural methods and implementations without altering the essential spirit of the invention. Therefore, the following detailed embodiments and accompanying drawings are merely illustrative examples of the technical solution of this invention and should not be considered as the entirety of the invention or as limitations or restrictions on the technical solution of this invention.

[0017] like Figure 1 As shown, a method for calculating the average queue length of a road network based on a three-dimensional macroscopic basic map is implemented through the following steps: S1. Utilize the collected information on road networks and mixed traffic flows to build a road network-level traffic simulation model, and draw a three-dimensional macroscopic basic map based on the simulation results (e.g., Figure 2 (As shown).

[0018] A simulation model was built using a mixed traffic flow consisting of private cars and regular buses as an example. The test road network consisted of three horizontal road segments and three vertical road segments (e.g., Figure 3 (As shown). Basic road network information includes the geometric alignment and channelization methods of each road segment, the cross-sectional structure of each segment, bus routes and bus departure frequencies, private car traffic volume, intersection types, and signal control schemes. Multiple simulation experiments were set up based on different proportions of private vehicles and regular buses in the mixed traffic flow, with each simulation lasting 3600 seconds. Scatter plots of the three-dimensional macroscopic basic map were extracted from the simulation data and plotted using MATLAB.

[0019] S2. Based on the simulation results and the average passenger capacity of different types of vehicles, the Gauss-Newton method is used to fit the three-dimensional macroscopic basic graph to clarify the specific function form and image.

[0020] As a preferred example, S2 specifically includes the following steps: S201, introducing the average passenger capacity of private vehicles and the average passenger capacity of regular buses, corresponds to the following formula: Equation (1) Equation (2) In the formula Q c Q represents private car traffic (pcu / h). b P represents the regular bus traffic flow (pcu / h). c This indicates the average passenger capacity (people) of a regular bus.

[0021] Based on this, and according to the scatter plot form of the three-dimensional macroscopic basic map, an exponential function is used as the fitting function for the three-dimensional macroscopic basic map. In this embodiment, the accumulated volume of private vehicles and the accumulated volume of regular buses on the road network are selected as the independent variables of the function, and the passenger flow of the road network is selected as the dependent variable. Considering that the number of passengers carried by regular buses is much greater than the number of passengers carried by private vehicles, a parameter g (>1) is introduced, and the specific function form is as follows: Equation (3) In the formula, a, b, c, d, e, f, and g are parameters to be determined.

[0022] S202. By fitting the three-dimensional macroscopic fundamental graph function, the problem is transformed into a nonlinear least squares problem, which is then solved using the Gauss-Newton method.

[0023] Specifically, the function in equation (3) is processed as follows: Equation (4) In the formula, Z represents the loss function, and P ' This represents the passenger flow value (per / h) obtained from the simulation data. This is the residual function.

[0024] The solution to equation (4) is obtained using the Gauss-Newton method. The specific algorithm flow is as follows: Step 1: Given initial values Set threshold , place ; Step 2: Perform iterations, until the iteration reaches the... Next, calculate the Jacobian matrix for the current value. and residual value ; Step 3: Solve the incremental equation ; Step 4: If threshold Stop iteration and output the optimal solution; otherwise, let... Continue iterating.

[0025] The optimal parameter solution was obtained by compiling the Gauss-Newton method using MATLAB software: a=308, b=-4e-8, c=-6.3e-5, d=-1e-6, e=1.721e-3, f=-1.23e-4, g=4.6. Substituting these values ​​into equation (3), the specific functional form of the three-dimensional macroscopic basic graph was obtained. Simultaneously, the fitting plot of the three-dimensional macroscopic basic graph was drawn using MATLAB software (see [link to relevant documentation]). Figure 4 ).

[0026] S3. Based on the three-dimensional macroscopic basic graph function form and combined with the three-phase traffic flow theory, calculate the dynamic vehicle conversion factor.

[0027] As a preferred example, S3 specifically includes the following steps: S301: In the road network, both regular buses and private vehicles have their own speeds, and different conversion factors should be applied at different speeds. According to the three-phase traffic flow theory and equations (3) and (2), the traffic flow Q, traffic flow density K, and traffic flow speed V have the following relationships: Equation (5) Equation (6) Based on the obtained three-dimensional macroscopic basic diagram, the parameters are substituted to obtain the average speed planar diagram of the road network (see [link]). Figure 5 ).

[0028] S302: Based on the physical meaning of the conversion factor, it is determined that the impact on the road network after converting regular buses into an equivalent number of private vehicles is the same as before, that is, it satisfies the following equation: Equation (7) Equation (8) Solving equations (7) and (8) simultaneously yields: Equation (9) In this embodiment, the average passenger number is incorporated into the model as the public transport priority intensity coefficient, thereby obtaining the dynamic vehicle conversion factor based on public transport priority: Equation (10) The function graph of the dynamic vehicle discount factor BBCU based on public transport priority is as follows: Figure 6 As shown.

[0029] S4. By using a dynamic vehicle conversion factor to adapt to the dynamic changes in traffic flow, the average queue length of the road network is calculated. Considering that traditional queue length statistics are difficult to accurately reflect queue length, this invention adopts the following two approximation principles: The nth vehicle on the inspected road segment has a speed of zero at time t and is added to the road segment's queue. If the speed of the nth vehicle in the detected road segment is not zero, and the speed of the (n-1)th vehicle is zero, then the speed of the (n+1)th vehicle is checked. If the speeds of the nth and (n+1)th vehicles are not zero, the detection queue is considered to be over; otherwise, the detection of subsequent vehicles continues until there are no vehicles left or the speed of two vehicles is not zero in two consecutive tests.

[0030] The above rules can be used to approximate the queue length of vehicles. By recording the number of regular buses and private vehicles in the queue, the average queue length of the road network can be calculated using the following formula: In the formula, This represents the average queue length of the road network at time t. Indicates road segment The number of private vehicles queuing (vehicles). Indicates road segment The number of regular buses queuing (vehicles). Indicates road segment The delay time.

[0031] Traditional calculations of intersection queue length typically only consider the physical distance from the end of the queue to the stop line of the approach lane, failing to reflect the impact of different vehicle types on traffic efficiency in mixed traffic flows. Existing methods for calculating average queue length on road networks mainly employ inherent static vehicle conversion factors (as shown in Equation 11), which are insufficient to accurately describe the dynamic impact between different types of vehicles during the evolution of mixed traffic flow states.

[0032] Equation (11) In the formula, This represents the equivalent conversion factor for other types of vehicles. The average length of a private vehicle (m).

[0033] Compared with existing queue length calculation methods, this invention comprehensively considers factors such as changes in the macro-traffic status of the road network, different vehicle types, and passenger capacity. It can adapt to dynamic traffic evolution and provide stronger support and basis for road network traffic status assessment, intensive transportation services, and traffic planning and management.

[0034] This invention verifies the effectiveness and practicality of the proposed method for calculating the average queue length of the road network based on a three-dimensional macroscopic basic map, based on simulation experiments and benefit analysis of public transport optimization strategies in mixed traffic environments. Option 1: Do not implement any public transport priority technology; Option 2: Bus signal priority technology based on traditional queue length calculation; Option 3: Bus signal priority technology based on queue length calculation proposed in this invention; Simulation experiments showed that the average queue length of the road network under the three schemes was as follows: Figure 7 As shown, the average queue length of the road network is significantly reduced under Scheme 3, indicating that the average queue length calculation scheme based on the three-dimensional macroscopic basic map can effectively adapt to the dynamic evolution of traffic flow and reasonably quantify the impact of different types of vehicles on road traffic efficiency.

[0035] The technical scope of this invention is not limited to the content described above. Those skilled in the art can make various modifications and variations to the above embodiments without departing from the technical concept of this invention, and all such modifications and variations should fall within the protection scope of this invention.

Claims

1. A method for calculating the average queue length of a road network based on a three-dimensional macroscopic basic map, characterized in that, Specifically as follows: Construct a road network-level traffic simulation model, and draw a three-dimensional macroscopic basic map based on the simulation results. The dynamic vehicle conversion factor is obtained by combining the three-dimensional macroscopic basic graph obtained through function fitting with three-phase traffic flow theory. According to the three-phase traffic flow theory, the average speed of the road network is calculated based on traffic volume, vehicle density, and vehicle speed. Under the premise that the average speed of the road network remains unchanged, the dynamic vehicle conversion factor is obtained by solving a set of equations. The average number of people stranded is calculated using a dynamic vehicle conversion factor, and then the number of stranded vehicles is counted to calculate the average queue length of the road network. The dynamic vehicle conversion factor BBCU is obtained through the following steps: A scatter plot of the three-dimensional macroscopic basic map was obtained by extracting simulation data; Based on the scatter plot form of the three-dimensional macro basic map, an exponential function is used as the fitting function for the three-dimensional macro basic map. The accumulated amount of private vehicles and regular buses in the road network are selected as the independent variables of the function, and the passenger flow of the road network is selected as the dependent variable. The fitting function is in the form of equation (3): Equation (3) P c This indicates the average passenger capacity of private vehicles, P b This indicates the average passenger capacity of other types of vehicles. , , , , , , All of these are parameters to be determined; The function in equation (3) is processed as follows: Equation (4) Z represents the loss function. This represents the passenger flow value obtained from simulation data. It is the residual function; Equation (4) is solved using the Gauss-Newton method to obtain the parameters to be determined. , , , , , , The optimal solution; The relationship between traffic flow, vehicle density, and vehicle speed is shown in the following formula: Equation (5) Equation (6) In the formula, Q is the traffic flow, K is the traffic flow density, V is the traffic flow speed, l is the road segment length, and n is the number of vehicles on the road segment; Based on the physical meaning of the conversion factor, it is determined that the impact on the road network after converting regular buses into an equivalent number of private vehicles is the same as before, specifically satisfying the following conditions: Equation (7) Equation (8) Solving equations (7) and (8) simultaneously, we get: Equation (9) Introducing the average passenger number into the model as the public transport priority intensity coefficient, the dynamic vehicle conversion factor is obtained as follows: Equation (10) In the formula, n c n represents the number of private vehicles queuing. b For the number of other types of vehicles queuing, P c For the average passenger capacity of private vehicles, P b This represents the average passenger capacity of other vehicle types. Queue length is calculated using the following formula: ； In the formula, Let n be the average queue length of the road network at time t. cqi For road section The number of private vehicles queuing, n bqi For road section Queue numbers for other types of vehicles, BBCU is the equivalent conversion factor for the passenger capacity of other types of vehicles, T qi For road section The delay time.

2. The method for calculating the average queue length of a road network based on a three-dimensional macroscopic basic map according to claim 1, characterized in that, The three-dimensional macroscopic basic map is fitted with an exponential function, in which the accumulated amount of private cars and other types of vehicles in the road network is the independent variable, and the road network passenger flow is the dependent variable. The function has the following form: In the formula, Q c Q represents private car traffic volume. b This indicates other types of traffic flow.

3. The method for calculating the average queue length of a road network based on a three-dimensional macroscopic basic map according to claim 1, characterized in that, Complete the statistical process according to the following approximation rules: (1) If there are vehicles with a speed of zero on the detected road section, they are included in the road section queue; (2) If there are at least two vehicles with non-zero speed after the vehicle with zero speed in the detected road section, or if there are no vehicles, the detection queue is considered to be over.

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