A long-distance arterial multi-path collaborative green wave optimization method

Abstract

The present invention discloses a long-distance arterial multi-path collaborative green wave optimization method, and the method includes: S1. Obtaining the long-distance arterial road network structure, intersection signal timing parameters, and vehicle trajectory data; S2. Selecting key traffic flow paths in the long-distance arterial according to the vehicle trajectory data; S3. Establishing a green wave constraint equation for the key traffic flow paths with intersections as segmentation points; S4. Establishing a multi-path collaborative green wave optimization model with the maximization of the key traffic flow path bandwidth and the minimization of the stop waiting time as the optimization objectives; S5. Solving the multi-path collaborative green wave optimization model and outputting the best coordinated control timing plan. The present invention comprehensively considers the sub-region division of the long-distance arterial and the synchronous green wave passing requirements of multiple traffic flows, and can significantly improve the overall operation efficiency of the long-distance arterial under short cycles and low saturations, and reduce the stop delay time of the driving vehicles at intersections.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic signal coordinated control, and particularly relates to a multi-path collaborative green wave optimization method for long-distance arterial roads. Background Art

[0002] Long-distance arterial roads have become the main road network structure of cities, and are characterized by complex section structures, high traffic demands, strong asymmetry, unbalanced carrying capacities, and great difficulties in coordinated control, which also pose higher requirements for the optimization methods of arterial road coordinated control.

[0003] Existing arterial coordinated control schemes only provide two-way green waves for two-way straight single-lane traffic flows and cannot meet the green wave demand of other traffic flows. However, with the increase in the number of arterial intersections, the traffic flow on long-distance arterials is distributed on multiple paths, and the traffic volume on some paths is much higher than that on other paths. There is an interaction between different paths. The traditional signal coordination control method targeting single-lane traffic flows cannot meet the bandwidth requirements of multi-lane traffic flows on long arterials. Therefore, in order to better control arterial traffic flows and ensure smoother and more efficient driving paths for arterial vehicles, scholars at home and abroad have conducted some research to meet the bandwidth requirements of multi-conflicting traffic flows and improve the overall bandwidth efficiency. Arsava et al. analyzed the impact of multi-branch arterials on bandwidth and proposed a coordinated control method considering the entry or exit of branch traffic flows (Chen C, Che X, Huang W, et al. A two-way progression model for arterial signal coordination considering side-street turning traffic[J]. Transportmetrica B: Transport Dynamics, 2019, 7(1): 1627-1650.); Yan et al. extracted the key paths of the network from vehicle trajectory data and used a heuristic algorithm to solve the coordination scheme for each path (Yan H, He F, Lin X, et al. Network-level multiband signal coordination scheme based on vehicle trajectory data[J]. Transportation Research Part C: Emerging Technologies, 2019, 107: 266-286.); Hai et al. proposed a heuristic method for multi-path signal coordination control and used a distributed traffic scenario to solve the uncertainty problem of arterial traffic flow fluctuations (Hai T, Ren G, Chen W, et al. A Heuristic Approach for Multi-Path Signal Progression Considering Traffic Flow Uncertainty[J]. Mathematics, 2023, 11(2): 377.). However, none of these studies considered the problem of sub-region division and synchronous solution of green wave coordination.

[0004] Studies have shown that when the number of arterial intersections exceeds 16, the two-way coordination bandwidth can hardly be guaranteed. Therefore, it is necessary to further refine the concept of control sub-areas. The traditional arterial section coordination method only divides sub-areas based on intersection correlation, and the sub-area division and the step-by-step optimization strategy of green wave coordination control do not consider the impact of sub-area division on coordination control. In contrast, the synchronous optimization strategy of arterial sub-area division and signal coordination control can improve the overall optimization level of the arterial. However, the current automatic division only optimizes the coordination of a single traffic flow at a fixed speed and does not consider the bandwidth requirements of multiple heterogeneous conflicting traffic flows on the arterial. Summary of the Invention

[0005] To solve the problems existing in the prior art, the present invention provides a multi-path collaborative green wave optimization method for long-distance arterials, which comprehensively considers the sub-area division of long-distance arterials and the synchronous green wave passing requirements of multiple traffic flows, significantly improves the overall operation efficiency of long-distance arterials under short cycle and low saturation, and reduces the parking delay time of vehicles at intersections.

[0006] The present invention is achieved by at least one of the following technical solutions.

[0007] A multi-path collaborative green wave optimization method for long-distance arterials, comprising the following steps:

[0008] S1. Obtain the road network structure of the long-distance arterial, intersection signal timing parameters, and vehicle trajectory data;

[0009] S2. Select the key traffic flow paths in the long-distance arterial according to the vehicle trajectory data;

[0010] S3. Establish green wave constraint equations for the key traffic flow paths with intersections as segmentation points;

[0011] S4. Establish a multi-path collaborative green wave optimization model with the maximization of the key traffic flow path bandwidth and the minimization of the parking waiting time as the optimization objectives;

[0012] S5. Solve the multi-path collaborative green wave optimization model and output the optimal coordinated control timing scheme.

[0013] Furthermore, the road network structure of the long-distance arterial described in step S1 includes the lane information of the sections and intersections on the arterial and the distances between intersections; the intersection signal timing parameters include the initial sub-area division, signal cycle, phase sequence, and green ratio; the vehicle trajectory data is the driving trajectory data of all vehicles entering and leaving each intersection on the long-distance arterial.

[0014] Further, the step S2 of selecting the key traffic flow paths in the long-distance arterial roads according to the vehicle trajectory data includes: traversing the vehicle trajectory data to obtain the driving paths of each vehicle on the long-distance arterial roads; defining the trajectories with the same origin and destination as one traffic flow path, classifying the trajectories with the same origin and destination into one category and counting the quantity, classifying and counting the driving paths of all vehicles to form multiple optional traffic flow path sets; sorting the path quantities of the optional traffic flow path sets to obtain the key traffic flow paths in the long-distance arterial roads.

[0015] Further, the step S3 of establishing the green wave constraint formula for the key traffic flow paths with the intersection as the segmentation point includes the following steps:

[0016] Define i as the key traffic flow path number, I as the number of key traffic flow paths, i = 1, 2,..., I; k as the arterial road intersection number, K as the number of long-distance arterial road intersections, k = 1, 2,..., K.

[0017] 1) Signal cycle constraint

[0018] The reciprocal z of the signal cycle at intersection k k , the constraint expression is

[0019]

[0020] -Mp k+1 ≤z k+1 -z k ≤MP k+1 (2)

[0021] In the formula, C max represents the maximum value of the signal cycle; C min represents the minimum value of the signal cycle, z k represents the reciprocal of the signal cycle at intersection k; M is an integer of positive infinity; p k+1 is a 0-1 variable. When p k+1 = 0, it means that intersection k + 1 is not a segmentation point, and the intersections in the same sub-region use the same signal cycle; when p k+1 = 1, it means that intersection k + 1 is a segmentation point and the constraint fails.

[0022] 2) Phase constraint

[0023] To achieve the effectiveness of the bandwidth, the bandwidth should always be within the green light time of intersection k, and the constraint expression is

[0024]

[0025] In the formula, b i,k represents the bandwidth in the upstream direction of path i at intersection k; Denote the bandwidth of the downstream direction of path i at intersection k; ω i,k Denote the offset from the center of the green wave bandwidth of the upstream direction of path i at intersection k to the left edge of the green light; Denote the offset from the center of the green wave bandwidth of the downstream direction of path i at intersection k to the left edge of the green light; r i,k Denote the red light of the upstream direction of path i at intersection k.

[0026] To ensure the bandwidth continuity of the same sub - area, the bandwidth should be constrained within the green light time of intersection i + 1, expressed as

[0027]

[0028] In the formula, μ i,k+1 Denote the bandwidth b i,k+1 and the offset of the center line of bandwidth b i,k ; Denote the bandwidth and the bandwidth The offset of the center line; when intersection k + 1 is a splitting point, p k+1 = 1, the signal cycles of intersection k and intersection k + 1 are different, and the constraint fails; otherwise, the constraint holds.

[0029] To make the bandwidth size match the traffic demand in different directions, taking the ratio of upstream and downstream traffic as a coefficient, introduce the constraint

[0030]

[0031] In the formula, ρ k Denote the ratio of the traffic flow in the downstream and upstream directions of intersection k.

[0032] 3) Path selection constraints

[0033] Paths in the same sub - area at intersection i should obtain effective bandwidths simultaneously, and the constraint is expressed as

[0034]

[0035] In the formula, y i,k , y i,k+1 are 0 - 1 variables. When p k+1 = 0, intersection k + 1 is not a splitting point, and intersections k and k + 1 should either obtain effective bandwidths simultaneously or not obtain them, that is, y i,k = y i,k+1 ; otherwise, the states of intersections obtaining effective bandwidths are different.

[0036] The bandwidth obtained by each path at the intersection should be greater than the minimum bandwidth, and the constraint is expressed as

[0037]

[0038] In the formula, be represents the minimum bandwidth sufficient for vehicle passage. When path i can obtain the effective bandwidth at intersection k, y i,k = 1, and the bandwidth is greater than the minimum bandwidth to satisfy vehicle passage; otherwise, when path i cannot obtain the effective bandwidth at intersection k, y i,k = 0, and the bandwidth is equal to 0.

[0039] 4) Arterial road segmentation constraint

[0040] Restrict that the number of intersections in a sub - area is greater than or equal to 2. The constraint expression is

[0041] p k + p k+1 <= 1 (8)

[0042] To unify the modeling methods of the segmentation point and the non - segmentation point, introduce the offset μ of the center line of the green - wave bandwidth i,k , and the constraint is expressed as

[0043]

[0044] In the formula, μ i,k represents the offset of the center lines of bandwidth b i,k-1 and bandwidth b i,k . ε is a positive number close to zero. Relax the constraint according to whether the intersection is a segmentation point. When p k = 1, intersection k is a segmentation point, and there is an offset between the bandwidths of adjacent intersections, μ i,k ≥ 0; otherwise, when p k = 0, there is no offset between the bandwidths of adjacent intersections, μ i,k = 0.

[0045] 5) Loop shaping constraint

[0046] Introduce y i,k+1 to represent whether path i can obtain the effective bandwidth at intersection k + 1. Then the loop shaping constraint expression for the upstream direction of the arterial road is

[0047]

[0048] In the formula, θ k represents the coordinated phase difference of intersection k, represents the time difference between the start of the green light of path i in the upstream direction at intersection k and the start time of the first phase, t k represents the travel time of the vehicle in the upstream direction between intersection k and intersection k + 1, n i,k+1 represents an integer multiple of the signal cycle. When path i can obtain the bandwidth at intersection k + 1, y i,k+1= 1, the adjacent intersections satisfy the coordination process, and the constraint holds; conversely, when the effective bandwidth cannot be obtained, the constraint fails.

[0049] Similarly, the loop shaping constraint expression for the downstream direction of the arterial road is

[0050]

[0051] In the formula, represents the red light in the downstream direction of intersection k for path i; represents the time difference between the start of the green light and the start of the first phase in the downstream direction of intersection k for path i, represents the travel time in the downstream direction between intersection k and intersection k + 1 for the vehicle, represents an integer multiple of the signal cycle.

[0052] 6) Travel time constraint

[0053] Similar to the Multiband model, the arterial road travel time constraint is expressed as

[0054]

[0055] In the formula, d k represents the distance between intersection k and intersection k + 1, v max,k represents the upper speed limit in the upstream direction of intersection k, v min,k represents the lower speed limit in the upstream direction of intersection k, represents the upper speed limit in the downstream direction of intersection k, represents the lower speed limit in the downstream direction of intersection k.

[0056] The speed fluctuation change constraint is expressed as

[0057]

[0058] In the formula, Δv max,k represents the maximum value of the speed change of the car on the upstream section of intersection k, Δv min,k represents the minimum value of the speed change of the car on the upstream section of intersection k, represents the maximum value of the speed change of the car on the downstream section of intersection k, represents the minimum value of the speed change of the car on the downstream section of intersection k.

[0059] Furthermore, taking the maximization of the bandwidth of the key traffic flow path and the minimization of the stop-and-wait time as the optimization objectives in step S4, the multi-path collaborative green wave optimization model is established as:

[0060] maxmize w1D1 - w2D2 (14)

[0061] In the formula, D1 represents the sum of the bandwidths of the key traffic flows, D2 represents the sum of the parking waiting times of the key traffic flows at the intersection splitting points, w1 represents the weight coefficient of the sum of the bandwidths of the key traffic flows, and w2 represents the weight coefficient of the sum of the waiting times.

[0062] The sum of the bandwidths of the key traffic flows D1 has the expression

[0063]

[0064] In the formula, e i,k represents the ratio of the upstream traffic flow to the downstream traffic flow of path i at intersection k.

[0065] The waiting time of path i in the upstream direction at the intersection splitting point k is The waiting time of path i in the downstream direction at the intersection splitting point k is The sum of the parking waiting times D2 of the key traffic flows at the intersection splitting points has the expression

[0066]

[0067] Furthermore, for the solution of the multi-path coordinated green wave optimization model described in step S5, Python is used to call Cplex to solve the multi-path coordinated green wave optimization model, and the intersection splitting points of the long-distance arterial road and the optimal coordinated control timing scheme are output.

[0068] Compared with the prior art, the present invention can at least achieve the following beneficial effects:

[0069] 1. The present invention proposes a synchronous optimization method for sub-region division and green wave coordinated control, which considers the relevance of the key traffic flow paths and the influence of the splitting point positions on the coordinated control, and realizes the global optimum.

[0070] 2. The present invention proposes a multi-path coordinated green wave optimization model, which provides effective bandwidths for the vehicles on different key traffic flow paths, meets the bandwidth requirements of multiple traffic flow paths on the long arterial road, and realizes the synchronous optimization of the multi-path green wave.

[0071] 3. The method proposed by the present invention is superior to the Multiband model in terms of the expected bandwidth, average delay, average number of stops, average queue length, etc., solves the problem of difficult coordination of urban long-distance arterial roads, and effectively improves the overall operation efficiency of the arterial road. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 is a flow chart of a method for optimizing multi-path coordinated green waves on a long-distance arterial road provided by an embodiment of the present invention.

[0073] Figure 2 is a spatio-temporal operation trajectory diagram of vehicles provided by an embodiment of the present invention.

[0074] Figure 3 This is the key vehicle flow path and flow diagram in the embodiments of the present invention.

[0075] Figure 4 This is the schematic diagram of the bandwidth of the key vehicle flow path in the embodiments of the present invention. Specific embodiments

[0076] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts are within the scope of protection of the present invention.

[0077] The present invention provides a long arterial distance sub - area division and green wave coordination method suitable for multi - path collaborative optimization, constructs a synchronous coordination control model for the mixed multi - stream vehicle flow on the arterial road, realizes the synchronous optimization of the multi - path green wave, and improves the robustness of the long - distance arterial coordination scheme.

[0078] Please refer to Figure 1 , a long - distance arterial multi - path collaborative green wave optimization method provided by the present invention includes the following steps:

[0079] S1. Obtain the long - distance arterial road network structure, intersection signal timing parameters, and vehicle trajectory data.

[0080] The long - distance arterial road network structure includes lane information of sections and intersections on the arterial road and the distance between intersections; the intersection signal timing parameters include initial sub - area division, signal cycle, phase sequence, and green ratio; the vehicle trajectory data includes the driving trajectory data of all vehicles entering and leaving each intersection on the long - distance arterial road.

[0081] In some embodiments of the present invention, taking the section from Yue Lai South Road to Hao Dong Road on Zhongshan Road in Zhongshan City as the analysis object, the road cross - section adopts a three - lane form, including 12 signal - controlled intersections and 1 pedestrian crossing signal control. Taking the off - line signal timing as the optimization object, the minimum effective bandwidth be is set to 8s, and the arterial road and intersection signal timings are shown in Table 1.

[0082] Table 1 Arterial road distance and intersection signal timing

[0083]

[0084] S2. Select the key vehicle flow paths in the long - distance arterial road according to the vehicle trajectory data.

[0085] Selecting key vehicle flow paths on long-distance arterial roads according to vehicle trajectory data includes: traversing vehicle trajectory data to obtain the driving paths of each vehicle on long-distance arterial roads; defining trajectories with the same origin and destination as one vehicle flow path, classifying trajectories with the same origin and destination into one category and counting the quantity, classifying and counting the driving paths of all vehicles to form multiple optional vehicle flow path sets; sorting the path quantities of the optional vehicle flow path sets to obtain the key vehicle flow paths on long-distance arterial roads.

[0086] In some embodiments of the present invention, as Figure 3 shown, 6 key vehicle flow paths and their flows are determined according to trajectory data, where paths 1, 2, and 3 are upward vehicle flows, and paths 4, 5, and 6 are downward vehicle flows.

[0087] S3. Taking intersections as segmentation points, establishing green wave constraints for key vehicle flow paths.

[0088] Define i as the key vehicle flow path number, I as the number of key vehicle flow paths, i = 1, 2,..., I; k as the arterial road intersection number, K as the number of intersections on long-distance arterial roads, k = 1, 2,..., K.

[0089] 1) Signal cycle constraint

[0090] The reciprocal z of the signal cycle at intersection k k , the constraint expression is

[0091]

[0092] -Mp k+1 ≤z k+1 -z k ≤MP k+1 (2)

[0093] In the formula, C max represents the maximum value of the signal cycle; C min represents the minimum value of the signal cycle, z k represents the reciprocal of the signal cycle at intersection k; M is an infinitely large positive integer; p k+1 is a 0-1 variable. When p k+1 = 0, it means that intersection k + 1 is not a segmentation point, and intersections in the same sub-region use the same signal cycle; when p k+1 = 1, it means that intersection k + 1 is a segmentation point and the constraint fails.

[0094] 2) Phase constraint

[0095] To achieve the effectiveness of the bandwidth, the bandwidth should always be within the green light time at intersection k, and the constraint expression is

[0096]

[0097] In the formula, b i,k represents the upstream bandwidth of path i at intersection k; represents the downstream bandwidth of path i at intersection k; ω i,k represents the offset from the center of the upstream green wave bandwidth of path i at intersection k to the left edge of the green light; represents the offset from the center of the downstream green wave bandwidth of path i at intersection k to the left edge of the green light; r i,k represents the upstream red light of path i at intersection k.

[0098] To ensure the bandwidth continuity of the same sub - area, the bandwidth should be constrained within the green light time of intersection i + 1, and the constraint expression is

[0099]

[0100] In the formula, μ i,k+1 represents the offset of bandwidth b i,k+1 and bandwidth b i,k from the center line; represents the offset of bandwidth and bandwidth from the center line; when intersection k + 1 is a segmentation point, p k+1 = 1, the signal cycles of intersection k and intersection k + 1 are different, and the constraint fails; otherwise, the constraint holds.

[0101] To make the bandwidth size match the traffic demand in different directions, taking the ratio of upstream and downstream traffic as a coefficient, the constraint

[0102]

[0103] In the formula, ρ k represents the ratio of downstream and upstream traffic volumes at intersection k.

[0104] 3) Path selection constraint

[0105] Paths in the same sub - area of path i should obtain effective bandwidths at intersections simultaneously, and the constraint expression is

[0106]

[0107] In the formula, y i,k , y i,k+1 are both 0 - 1 variables. When p k+1 = 0, intersection k + 1 is not a segmentation point, and intersections k and k + 1 should either obtain effective bandwidths simultaneously or not obtain them, that is, y i,k = y i,k+1 ; otherwise, the states of intersections obtaining effective bandwidths are different.

[0108] The bandwidth obtained by each path at the intersection should be greater than the minimum bandwidth, and the constraint is expressed as

[0109]

[0110] In the formula, be represents the minimum bandwidth for sufficient vehicle passage. When path i can obtain the effective bandwidth at intersection k, y i,k = 1, and the bandwidth is greater than the minimum bandwidth to satisfy vehicle passage; otherwise, when path i cannot obtain the effective bandwidth at intersection k, y i,k = 0, and the bandwidth is equal to 0.

[0111] 4) Main road segmentation constraint

[0112] Restrict that the number of intersections in a sub - area is greater than or equal to 2, and the constraint is expressed as

[0113] p k +p k+1 <= 1 (8)

[0114] To unify the modeling methods of the segmentation point and the non - segmentation point, introduce the offset μ of the center line of the green - wave bandwidth i,k , and the constraint is expressed as

[0115]

[0116] In the formula, μ i,k represents the offset of the center lines of bandwidth b i,k-1 and bandwidth b i,k . ε is a positive number close to zero. Relax the constraint according to whether the intersection is a segmentation point. When p k = 1, intersection k is a segmentation point, and there is an offset between the bandwidths of adjacent intersections, μ i,k ≥0; otherwise, when p k = 0, there is no offset between the bandwidths of adjacent intersections, μ i,k = 0.

[0117] 5) Loop - shaping constraint

[0118] Introduce y i,k+1 to represent whether path i can obtain the effective bandwidth at intersection k + 1. Then the loop - shaping constraint expression for the upstream direction of the main road is

[0119]

[0120] In the formula, θ k represents the coordination phase difference of intersection k, represents the time difference between the start of the green light of path i in the upstream direction at intersection k and the start time of the first phase, t k represents the travel time of vehicles in the upstream direction between intersection k and intersection k + 1, ni,k+1 represents an integer multiple of the signal cycle. When path i can obtain bandwidth at intersection k + 1, y i,k+1 = 1, the adjacent intersections satisfy the coordination process, and the constraint holds; conversely, when the effective bandwidth cannot be obtained, the constraint fails.

[0121] Similarly, the cycle shaping constraint expression for the downstream direction of the arterial road is

[0122]

[0123] In the formula, represents the red light of path i in the downstream direction at intersection k; represents the time difference between the start of the green light of path i in the downstream direction at intersection k and the start of the first phase, represents the travel time of the vehicle in the downstream direction between intersection k and intersection k + 1, represents an integer multiple of the signal cycle.

[0124] 6) Travel time constraint

[0125] Similar to the Multiband model, the arterial road travel time constraint is expressed as

[0126]

[0127] In the formula, d k represents the distance between intersection k and intersection k + 1, v max,k represents the upper speed limit in the upstream direction of intersection k, v min,k represents the lower speed limit in the upstream direction of intersection k, represents the upper speed limit in the downstream direction of intersection k, represents the lower speed limit in the downstream direction of intersection k.

[0128] The speed fluctuation change constraint is expressed as

[0129]

[0130] In the formula, Δv max,k represents the maximum value of the speed change of cars on the upstream section of intersection k, Δv min,k represents the minimum value of the speed change of cars on the upstream section of intersection k, represents the maximum value of the speed change of cars on the downstream section of intersection k, represents the minimum value of the speed change of cars on the downstream section of intersection k.

[0131] S4. Taking the maximization of the bandwidth of the key traffic flow paths and the minimization of the stop-and-wait time as the optimization objectives, a multi-path collaborative green wave optimization model is established.

[0132] Taking the maximization of the bandwidth of the key traffic flow path and the minimization of the parking waiting time as the optimization objectives, the multi-path collaborative green wave optimization model is established as follows:

[0133] maxmize w1D1 - w2D2(14)

[0134] In the formula, D1 represents the sum of the bandwidths of the key traffic flows, D2 represents the sum of the parking waiting times of the key traffic flows at the intersection splitting points, w1 represents the weight coefficient of the sum of the bandwidths of the key traffic flows, and w2 represents the weight coefficient of the sum of the parking waiting times.

[0135] The expression for the sum of the bandwidths of the key traffic flows D1 is

[0136]

[0137] In the formula, e i,k represents the ratio of the upstream traffic flow to the downstream traffic flow of path i at intersection k.

[0138] The waiting time of path i in the upstream direction at the intersection splitting point k is The waiting time of path i in the downstream direction at the intersection splitting point k is The sum of the parking waiting times D2 of the key traffic flows at the intersection splitting points, the expression is

[0139]

[0140] S5. Solve the multi-path collaborative green wave optimization model and output the optimal coordinated control timing plan.

[0141] For the solution of the multi-path collaborative green wave optimization model mentioned above, in some embodiments of the present invention, Python is used to call Cplex to solve the multi-path collaborative green wave optimization model, and the long-distance arterial intersection splitting points and the optimal coordinated control timing plan are output.

[0142] In some embodiments of the present invention, in a computer operating environment of 64-bit Win 10 operating system, AMD R7-5800H processor, 16G running memory, and 3.2GHz main frequency, the model weight values w1 and w2 are respectively taken as 0.5 and 0.5. Python is used to construct the multi-path collaborative green wave optimization model and Cplex is called for solution, which takes 1.75s. The arterial sub-region division and intersection phase difference are solved, and it is calculated that 13 intersections are divided into 4 sub-regions, namely intersections S1 - S5, intersections S6 - S7, intersections S8 - S9, intersections S10 - S13. The traffic flow paths are disconnected at the splitting points, and the intersections within the same sub-region are coordinated and controlled. The bandwidths of 6 key traffic flow paths are as Figure 4 shown.

[0143] The model provides average bandwidths of 30s, 23s, and 33s for the upstream paths 1 - 3 respectively, and average bandwidths of 34s, 37s, and 34s for the downstream paths 4 - 6 respectively. Since paths 1 and 2 are both straight from intersection S1 to intersection S5, the model classifies them as the same traffic flow and assigns the same bandwidth; however, path 2 turns left and exits at intersection S7, and obtains smaller bandwidths at intersections S6 and S7. Path 4 is the traffic flow path from intersection S13 to intersection S1. Due to the influence of distance, green signal ratio, and other traffic flows, it cannot obtain bandwidth from intersection S9 to intersection S7, indicating that the model can automatically select whether a path can obtain bandwidth in a sub - area. Path 5 turns left and exits at intersection S8, and the model can also provide a personalized bandwidth design.

[0144] In some embodiments of the present invention, to verify the effectiveness of the model, the model of the present invention is compared and analyzed with Multiband, MSband, MPband, and three other models. The bandwidths of the key traffic flow paths of each model are shown in Table 2. MSband provides larger bandwidths for the straight paths 2 and 4 in both the upstream and downstream directions than Mutliband and MPband. The straight - through bandwidth of MPband is slightly smaller than that of Multiband, but the overall bandwidth increases, indicating that by designing a unique coordination model for each path, the automatic trade - off of bandwidth is achieved, thus ensuring the overall optimality of the arterial road. Although MPband designs the bandwidth for each path individually, the sum of its bandwidths is less than that of MSband, indicating that the position of the splitting point has a great impact on the overall coordination effect of the arterial road. Although the model of the present invention cannot provide the largest bandwidth for the straight - through direction, the sum of the bandwidths is still greater than the other three schemes, indicating that modeling the arterial road segmentation and the green wave synchronization of mixed traffic flows can provide a larger bandwidth for the system.

[0145] Table 2 Bandwidths of Key Traffic Flow Paths of Each Model

[0146]

[0147] Table 3 shows the Vissim simulation results of the 6 key traffic flow paths under four models. The simulation results of MSband are contrary to the bandwidth. It obtains a smaller bandwidth but less delay in the upstream direction, and a larger bandwidth but greater delay in the downstream direction, indicating that the bandwidth cannot guarantee the actual operation effect of the arterial road vehicles. MPband can reduce the average delay, average stop time, and number of stops of each path, indicating the necessity of providing independent bandwidths for traffic flow paths. The model of the present invention performs best among the four models, and can reduce the average delay, average stop time, and average number of stops of paths 1, 2, and 5 by about 20%, thus improving the overall operation efficiency.

[0148] Table 3 Simulation Comparison of Different Models

[0149]

[0150] The foregoing description of the disclosed embodiments enables those skilled in the art to practice or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-path collaborative green wave optimization method for long-distance arterial roads, characterized in that, It includes the following steps: S1. Obtain the long-distance arterial road network structure, intersection signal timing parameters, and vehicle trajectory data; S2. Select the key traffic flow paths in the long-distance arterial roads according to the vehicle trajectory data; S3. Taking intersections as segmentation points, establish the green wave constraint equations for key traffic flow paths; S4. Taking the maximization of the bandwidth of key traffic flow paths and the minimization of the stop-and-wait time as the optimization objectives, establish a multi-path collaborative green wave optimization model; S5. Solve the multi-path collaborative green wave optimization model and output the optimal coordinated control timing plan; Among them, the step of taking intersections as segmentation points in step S3 to establish the green wave constraint equations for key traffic flow paths includes the following steps: Define i as the key traffic flow path number, I as the number of key traffic flow paths, i = 1, 2,..., I; k as the arterial intersection number, K as the number of long-distance arterial intersections, k = 1, 2,..., K; 1) Signal cycle constraint The reciprocal z of the signal cycle of intersection k k , the constraint expression is -Mp k+1 ≤z k+1 -z k ≤MP k+1 (2) Wherein, C max represents the maximum value of the signal cycle; C min represents the minimum value of the signal cycle, z k represents the reciprocal of the signal cycle of intersection k; M is an integer of positive infinity; p k+1 is a 0-1 variable. When p k+1 = 0, it means that intersection k+1 is not a dividing point, and intersections in the same sub-area use the same signal cycle; when p k+1 = 1, it means that intersection k+1 is a dividing point and the constraint fails; 2) Phase constraint To ensure the effectiveness of the bandwidth, it should be ensured that the bandwidth is always within the green light time of intersection k, and the constraint expression is where b i,k represents the upstream bandwidth of path i at intersection k; represents the downstream bandwidth of path i at intersection k; ω i,k represents the offset from the center of the upstream green wave bandwidth of path i at intersection k to the left edge of the green light; represents the offset from the center of the downstream green wave bandwidth of path i at intersection k to the left edge of the green light; r i,k represents the upstream red light of path i at intersection k; To ensure the continuity of the bandwidth in the same sub-region, the bandwidth should be within the green light time of intersection i + 1, and the constraint expression is where μ i,k+1 represents the bandwidth b i,k+1 and the offset of the center line of the bandwidth b i,k ; represents the bandwidth and the bandwidth the offset of the center line; when the intersection k + 1 is the dividing point, p k+1 = 1, the signal cycles of intersections k and k + 1 are different, and the constraint fails; otherwise, the constraint holds; To make the bandwidth size match the traffic flow demands in different directions, taking the ratio of the upstream and downstream traffic flows as a coefficient, introduce the constraint where ρ k represents the traffic flow ratio in the downstream and upstream directions of intersection k; 3) Path selection constraint Path i should obtain an effective bandwidth simultaneously at intersections in the same sub-region, and the constraint expression is where y i,k , y i,k+1 are 0-1 variables. When p k+1 = 0, intersection k + 1 is not a splitting point, and intersections k and k + 1 should either both obtain or both not obtain the available bandwidth, that is, y i,k = y i,k+1 ; otherwise, the states of the intersections obtaining the available bandwidth are different. The bandwidth obtained by each path at the intersection should be greater than the minimum bandwidth, and the constraint expression is wherein, be represents the minimum bandwidth sufficient for vehicle passage. When the path i can obtain the effective bandwidth at the intersection k, y i,k = 1, and the bandwidth is greater than the minimum bandwidth required to satisfy vehicle passage; conversely, when the path i cannot obtain the effective bandwidth at the intersection k, y i,k = 0, and the bandwidth is equal to 0; 4) Arterial road segmentation constraint Restrict that the number of intersections in a sub-region is greater than or equal to 2, and the constraint expression is p k +p k+1 <= 1 (8) To unify the modeling methods of splitting points and non-splitting points, the offset μ of the center line of the green wave bandwidth is introduced i,k , and the constraint is expressed as where μ i,k represents the bandwidth b i,k-1 and the offset of the center line of the bandwidth b i,k ε is a positive number close to zero, and the constraint is relaxed according to whether the intersection is a splitting point. When p k = 1, the intersection k is a splitting point, and there is an offset between the bandwidths of adjacent intersections, μ i,k ≥ 0; otherwise, when p k = 0, there is no offset between the bandwidths of adjacent intersections, μ i,k = 0; 5) Loop shaping constraint Introduce y i,k+1 Indicating whether path i can obtain effective bandwidth at intersection k + 1, the loop shaping constraint expression for the upstream direction of the arterial road is where θ k represents the coordinated phase difference of intersection k, represents the time difference between the start of the green light in the upstream direction of path i at intersection k and the start time of the first phase, t k represents the travel time of the vehicle in the upstream direction between intersection k and intersection k + 1, n i,k+1 represents an integer multiple of the signal cycle; when path i can obtain bandwidth at intersection k + 1, y i,k+1 = 1, the adjacent intersections satisfy the coordination process, and the constraint holds; otherwise, when the effective bandwidth cannot be obtained, the constraint fails; Similarly, the loop shaping constraint expression for the downstream direction of the arterial road is In the formula, indicates that the red light is on in the downstream direction of path i at intersection k; represents the time difference between the start of the green light in the downstream direction of path i at intersection k and the start time of the first phase, represents the travel time of the vehicle in the downstream direction between intersection k and intersection k + 1, represents an integer multiple of the signal cycle; 6) Travel time constraint The arterial road travel time constraint expression is where d k represents the distance between intersection k and intersection k + 1, v max,k represents the upper speed limit in the upstream direction of intersection k, v min,k represents the lower speed limit in the upstream direction of intersection k, represents the upper speed limit in the downstream direction of intersection k, represents the lower speed limit in the downstream direction of intersection k; The speed fluctuation change constraint expression is where, Δv max,k represents the maximum value of the speed change of cars on the upstream section of intersection k, and Δv min,k represents the minimum value of the speed change of cars on the upstream section of intersection k, represents the maximum value of the speed change of cars on the downstream section of intersection k, represents the minimum value of the speed change of cars on the downstream section of intersection k.

2. The multi-path collaborative green wave optimization method for long-distance arterial roads according to claim 1, wherein The long-distance arterial road network structure described in step S1 includes the lane information of sections and intersections on the arterial road and the distances between intersections.

3. A long-distance arterial multi-path collaborative green wave optimization method according to claim 1, characterized in that The intersection signal timing parameters include the initial sub-region division, signal cycle, phase sequence, and green signal ratio.

4. A long-distance arterial multi-path collaborative green wave optimization method according to claim 1, characterized in that The vehicle trajectory data includes the driving trajectory data of all vehicles entering and leaving each intersection on the long-distance arterial road.

5. A long-distance arterial multi-path collaborative green wave optimization method according to claim 1, characterized in that, The step of selecting the key traffic flow paths in the long-distance arterial roads according to the vehicle trajectory data described in step S2 includes: Traverse the vehicle trajectory data to obtain the driving paths of each vehicle on the long-distance arterial road; Define the trajectories with the same origin and destination as one traffic flow path, classify the trajectories with the same origin and destination into one category and count the quantity, classify and count the quantities of all vehicle driving paths to form a set of multiple optional traffic flow paths; Sort the number of paths in the set of optional traffic flow paths to obtain the key traffic flow paths in the long-distance arterial road.

6. The long-distance arterial multi-path collaborative green wave optimization method according to claim 1, characterized in that, The multi-path collaborative green wave optimization model established in step S4 with the maximization of the bandwidth of key traffic flow paths and the minimization of the stop-and-wait time as the optimization objectives is: maxmize w1D1 - w2D2 (Equation 14) where D1 represents the sum of the bandwidths of key traffic flows, D2 represents the sum of the stop-and-wait times of key traffic flows at the intersection segmentation points, w1 represents the weight coefficient of the sum of the bandwidths of key traffic flows, and w2 represents the weight coefficient of the sum of the stop-and-wait times.

7. A long-distance arterial multi-path collaborative green wave optimization method according to claim 6, characterized in that The sum of the bandwidths of key traffic flows D1, the expression is where, e i,k represents the ratio of the upstream flow to the downstream flow of path i at intersection k.

8. A long-distance arterial multi-path collaborative green wave optimization method according to claim 6, characterized in that The waiting time of path i in the upstream direction at the intersection splitting point k is The waiting time of path i in the downstream direction at the intersection splitting point k is The sum D2 of the stop-and-wait times of the key vehicle flows at the intersection splitting point, and the expression is 9. A long-distance arterial multi-path collaborative green wave optimization method according to any one of claims 1-8, characterized in that Solve the multi-path collaborative green wave optimization model described in step S5, use Python to call Cplex to solve the multi-path collaborative green wave optimization model, and output the segmentation points of long-distance arterial intersections and the optimal coordinated control timing plan.

Images