Intelligent traffic dynamic path optimization method based on infinite graph structure

Abstract

The invention discloses an intelligent traffic dynamic path optimization method based on an infinite graph structure, which solves the problem of a unique solution of a p-Laplace Schrdinger equation on a dynamic traffic network by defining a pseudo-metric constraint and a weighted space of the traffic network, combining positive qualification of a potential function and designing a differential analysis process for a parameter range. And therefore, real-time path optimization is realized. According to the method, a traffic network is abstracted into an infinite weighted graph, nodes are intersections, side weights are real-time passing time, network geometric conditions and potential function constraints are verified, judgment branches are selected according to traffic state parameters, and road network flow steady-state distribution is determined through a unique solution. An energy inequality or a convex regularization test function is respectively constructed for congestion and non-congestion situations, uniqueness of a solution is proved in combination with a limit process, and a signal lamp period and a path recommendation strategy are dynamically adjusted, so that the problems of difficulty in congestion propagation modeling and low real-time path planning precision in a dynamic road network are solved.

Description

Technical Field

[0001] The present invention relates to a dynamic path optimization method, and in particular to an optimization method suitable for real-time traffic management and path planning in large-scale urban road networks. Background Art

[0002] In recent years, with the acceleration of urbanization and the rapid development of intelligent transportation systems, dynamic path optimization technology has become a core means of improving road network efficiency and alleviating traffic congestion. However, existing technologies still face significant challenges when dealing with large-scale, dynamically expanding traffic networks. Traditional path planning algorithms (such as Dijkstra and A* algorithms) typically rely on static graph models and fixed weights, making it difficult to respond in real time to dynamic fluctuations in travel times or sudden changes in road network topology, such as the addition of new roads or temporary area closures. These methods are all based on the assumption of a finite graph and cannot effectively adapt to complex, infinitely expanding road networks. This leads to the accumulation of prediction errors as the network scales, and local optimization strategies often lead to global imbalances. Although machine learning methods have made some progress in traffic prediction, their black-box nature means that the stability and uniqueness of the solutions lack rigorous mathematical verification. In particular, in congestion propagation modeling, the existence of multiple or chaotic solutions can mislead the traffic flow strategy and exacerbate the uncertainty of the system.

[0003] Dynamic traffic networks must handle the infinite expansion of nodes and edges in real time. Traditional methods, due to theoretical limitations, struggle to ensure solution stability, resulting in reduced real-time path planning accuracy and insufficient robustness of congestion control strategies. In this context, an innovative approach combining mathematical rigor with engineering practicality is needed to provide a reliable theoretical framework and efficient optimization tools for dynamic traffic systems, addressing the urgent need for high-precision, adaptive traffic management in smart cities. Summary of the Invention

[0004] Purpose of the invention: In view of the above-mentioned existing technologies, an intelligent traffic dynamic path optimization method is proposed to ensure that the congestion probability is effectively reduced and resource allocation is optimized in a dynamically expanding road network.

[0005] Technical solution: A method for intelligent traffic dynamic path optimization based on infinite graph structure, including:

[0006] Step 1: Obtain traffic network data and dynamic parameters;

[0007] Step 2: Verify the geometric conditions of the transportation network;

[0008] Step 3: Check traffic potential function constraints;

[0009] Step 4: Select a decision branch based on the real-time traffic status;

[0010] Step 5: Execute the unique solution determination of the congestion state of branch 1;

[0011] Step 6: Execute the unique solution determination of the non-congested state of branch 2;

[0012] Step 7: Generate a dynamic path optimization plan based on the unique solution.

[0013] Furthermore, the step 1 specifically includes:

[0014] Step 1.1: Input an infinitely weighted traffic graph (G, ω, μ), where G is a graph representing traffic paths, each node in the graph represents an intersection, ω is an edge weight function representing real-time travel time, and μ is a node measure representing intersection capacity.

[0015] Step 1.2: Input the path length pseudo-metric d:G×G→[0,+∞) representing the shortest travel time between intersections;

[0016] Step 1.3: Input the traffic potential function V(x) that reflects the regional traffic restriction policy or congestion cost;

[0017] Step 1.4: Input the vehicle density threshold p, the real-time vehicle density corresponding parameter q, and the exponential decay parameter γ.

[0018] Furthermore, the step 2 specifically includes:

[0019] Step 2.1: Verify the infinite scalability, global connectivity, and local finite capacity of the traffic network, that is, verify the infinity, connectivity, and local finiteness of the graph G;

[0020] Step 2.2: Define the jump size s of the pseudo-metric d and verify its finiteness: s = sup{d(x,y)|x~y}<+∞, where sup{·} represents the supremum.

[0021] Step 2.3: Verify the path length pseudo-metric d constraint based on the range of vehicle density threshold p:

[0022] If q≥2, for all x∈G, verify

[0023] If 1<q<2, for all x∈G, verify Where C0 and C1 are constants, x and y represent two intersections in the road network G, μ(x) is the node measure representing the capacity of intersection x, d(x,y) represents the distance between intersection x and intersection y, and ω(x,y) represents the edge weight function between intersection x and intersection y.

[0024] Furthermore, the step three specifically includes: verifying that the traffic potential function satisfies global positive definiteness: for all x∈G, V(x)≥c0>0, that is, the congestion cost is always higher than the preset lower limit c0; if not satisfied, readjusting the restricted area or dynamically correcting the potential function.

[0025] Furthermore, the step 4 specifically includes: selecting a decision branch based on the comparison between the real-time vehicle density and the threshold: if the vehicle density exceeds the threshold, executing branch 1 of step 5; otherwise executing branch 2 of step 6.

[0026] Furthermore, the step five specifically includes:

[0027] Step 5.1: Load the nonlinear diffusion model, define the steady-state function u(x), and satisfy the p-Laplace Equation Δ p u(x)-V(x)|u(x)| p-2 u(x)=0, where Δ p Represents the p-Laplace operator, which is defined as Among them, y~x means that intersection y is connected to intersection x, that is, there is a road between y and x;

[0028] Step 5.2: Dynamically verify the connectivity of the infinite graph to ensure that valid paths still exist at all intersections after adding new roads or temporarily closing areas. Update the maximum instantaneous capacity of intersections in real time. If the capacity of an intersection exceeds the limit, trigger a local flow control strategy. Monitor the fluctuations in travel time at adjacent intersections in real time. If the jump size of the path is too large, initiate a path reconstruction algorithm.

[0029] Step 5.3: Calculate the traffic flow gradient difference based on the edge weight ω(x,y), and use the node measure μ(x) to evaluate the energy accumulation intensity of the congested area. Then, calculate the traffic flow energy difference between adjacent intersections based on the energy conservation principle.

[0030] Step 5.4: Increase the corresponding parameter q according to the real-time congestion level to suppress the traffic energy in the congested area; increase the exponential decay parameter γ to weaken the influence of long-distance paths and give priority to alleviating local congestion; introduce the convex function The constant α>0 eliminates the singularity of the nonlinear operator, thereby ensuring the numerical stability of path allocation under non-congested conditions;

[0031] Step 5.5: If the model verifies that the steady-state solution to the road network flow is zero, that is, there is no stable traffic flow, the following strategies are triggered: extend the red light cycle in the congested area to reduce the input of new traffic flow; push alternative routes through the navigation system to avoid high-energy difference sections, and mark the real-time travel time of the detour route; if it is determined that there is a non-zero solution, re-optimize the parameters q and γ and start the secondary verification process.

[0032] Furthermore, the step six specifically includes:

[0033] Step 6.1: Load the nonlinear diffusion model, define the steady-state function u(x), and satisfy the p-Laplace Equation Δp u(x)-V(x)|u(x)| p-2 u(x)=0, where Δ p Represents the p-Laplace operator, which is defined as Among them, y~x means that intersection y is connected to intersection x, that is, there is a road between y and x;

[0034] Step 6.2: Dynamically verify the connectivity of the infinite graph to ensure that valid paths still exist at all intersections after adding new roads or temporarily closing areas. Update the maximum instantaneous capacity of intersections in real time. If the capacity of an intersection falls below a preset lower limit, trigger a local traffic replenishment strategy. Monitor the fluctuations in travel time at adjacent intersections in real time. If the jump size of the path is within a specified range, the road network is considered stable.

[0035] Step 6.3: Evaluate the balance of traffic flow distribution based on edge weights ω(x,y), verify the uniformity of path loads based on node measures μ(x), and then calculate the traffic flow energy difference between adjacent intersections based on the principle of energy conservation.

[0036] Step 6.4: Reduce the parameter q according to the real-time traffic density to enhance the balanced distribution of traffic flow; reduce the exponential decay parameter γ to increase the optimization weight of the long-range path; introduce the convex function Eliminating model singularities ensures the numerical stability of path assignment under congestion conditions;

[0037] Step 6.5: If the model verifies that a unique steady-state solution exists for the road network traffic flow, the following strategies are triggered: shorten the green light cycle in non-congested areas to improve traffic efficiency; simultaneously push three or more optimal routes through the navigation system, annotating the real-time travel time and load balancing index of each path; if a non-zero solution is determined to exist, re-optimize the parameters q and γ and initiate a secondary verification process.

[0038] Beneficial Effects: This invention overcomes the limitations of traditional finite graph models for dynamically expanding road networks by abstracting the urban road network into an infinite weighted graph (with real-time updates of node capacity and edge weights). It also introduces a traffic potential function to quantify congestion costs, and combines pseudo-metric constraints to precisely control path length fluctuations, effectively coordinating the infinite graph topology with the global behavior of the solution. To address the complexity and singularity of the nonlinear p-Laplace operator, this method establishes a priori estimates by introducing an exponentially decaying weighted space and partial integration techniques. This, combined with a convex regularized test function and a limit process to circumvent direct manipulation of nonsmooth terms, significantly simplifies the analytical process for nonlinear problems.

[0039] Furthermore, the unique solution determination mechanism designed for congested and non-congested situations can dynamically switch traffic light control and path navigation strategies, and realize congestion propagation suppression and balanced traffic flow distribution based on mathematical rigor. It breaks through the blindness of traditional empirical decision-making at the theoretical level, and improves global traffic efficiency and system robustness at the application level, providing an innovative solution for intelligent transportation systems that combines theoretical depth and engineering practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of the intelligent traffic dynamic path optimization method based on infinite graph structure of the present invention;

[0041] Figure 2 This is the real-time road network status simulation interface diagram of the present invention. DETAILED DESCRIPTION

[0042] The present invention will be further explained below with reference to the accompanying drawings.

[0043] An intelligent traffic dynamic path optimization method based on infinite graph structure, the specific steps are as follows:

[0044] Step 1: Obtain traffic network data and dynamic parameters;

[0045] Step 2: Verify the geometric conditions of the transportation network;

[0046] Step 3: Check traffic potential function constraints;

[0047] Step 4: Select a decision branch based on the real-time traffic status;

[0048] Step 5: Execute the unique solution determination of the congestion state of branch 1;

[0049] Step 6: Execute the unique solution determination of the non-congested state of branch 2;

[0050] Step 7: Generate a dynamic path optimization plan based on the unique solution.

[0051] Specifically, step one includes:

[0052] Step 1.1: Input an infinitely weighted traffic graph (G, ω, μ), where G represents the graph, ω:G×G→[0,+∞) is the edge weight function, and μ:G→(0,+∞) is the node (or vertex) measure. Define the graph as a traffic path; define the nodes as intersections; and define the edge weights as real-time travel time (in seconds), which is updated every 30 seconds by traffic sensors. For example, the travel time from intersection A to intersection B is w AB (t) = 120 seconds (off-peak period) or w AB(t) = 300 seconds (peak hours). The node measure is the intersection capacity, that is, the maximum instantaneous vehicle capacity (unit: vehicles / minute). For example, the capacity of main road intersection A is μ(A) = 500 vehicles / minute, and the capacity of secondary road intersection B is μ(B) = 200 vehicles / minute.

[0053] Step 1.2: Input the path length pseudo-metric, defined as the shortest travel time between intersections. d: G×G→[0,+∞). For example, the shortest path from intersection A to intersection D is A→C→D, so the total travel time is d(A,D)=w AC +w CD =180 seconds.

[0054] Step 1.3: Input the traffic potential function V(x) = 0.6L(x) + 0.4C(x), which reflects the regional restriction policy or congestion cost; where L(x) is the restriction policy coefficient, L(x) = 1.5 in restricted areas and L(x) = 1.0 in non-restricted areas; C(x) is the real-time congestion index. When C(x)≥80, it is judged as congestion;

[0055] Step 1.4: Enter the vehicle density threshold p>1, the real-time vehicle density parameter q>1, and the exponential decay parameter γ>0. Select p=3>1. Set the vehicle density threshold to 85 vehicles / km. If the threshold is exceeded, the congestion determination branch is triggered, and select q=3>1; if the threshold is not exceeded, the non-congestion determination branch is triggered, and select q=0.5<1. Select γ=0.05>1 for the distance decay function in the weighted space. Among them, x0 is a fixed vertex that controls the influence weight of the remote path on the local decision.

[0056] Step 2 specifically includes:

[0057] Step 2.1: Verify the infinite scalability, global connectivity, and local finite capacity of the traffic network, that is, verify the infinity, connectivity, and local finiteness of the graph G;

[0058] Step 2.2: Define the jump size s of the pseudo-metric d and verify its finiteness: s = sup{d(x,y)|x~y}<+∞, ensuring that it satisfies the real-time traffic fluctuation constraint. Here, d(x,y) represents the distance between points x and y, i.e., the distance between two intersections. sup{·} represents the supremum, which ensures that it satisfies the real-time traffic fluctuation constraint.

[0059] Step 2.3: Verify the path length pseudo-metric d constraint based on the range of vehicle density threshold p:

[0060] If p≥2, verify Where C0 is a constant;

[0061] If 1<p<2, verify Where C1 is a constant. μ(x) represents the capacity of intersection x; ω(x,y) represents the edge weight connecting points x and y, that is, the degree of congestion on the road between the two intersections.

[0062] Step three specifically includes:

[0063] Verify that the traffic potential function satisfies the global positive definiteness: V(x)≥c0>0 (for all x∈G), that is, the regional restriction policy or congestion cost is always higher than the preset lower limit c0; if not, readjust the restricted area or dynamically modify the potential function.

[0064] Step 4 specifically includes:

[0065] Based on the comparison between the real-time vehicle density and the threshold, a decision branch is selected: if the vehicle density exceeds the threshold, execute branch 1 of step five; otherwise, execute branch 2 of step six.

[0066] Step 5 specifically includes:

[0067] Step 5.1: Define the steady-state function u(x) of the road network flow as p-Laplace Equation Δ p u(x)-V(x)|u(x)| p-2 The solution of u(x)=0, where Δ p represents the p-Laplace operator, which is defined as: Among them, y~x means that intersection y is connected to intersection x, that is, there is a road between y and x; μ(y) represents the capacity of intersection y.

[0068] Constructing convex functions The constant α is greater than 0 to ensure the numerical stability of path allocation under non-congested conditions.

[0069] Step 5.2: Define the test function ξ(x) = -α[d(x,x0)-δR] + , δ is a weight parameter satisfying 0<δ<1, R is an intermediate variable satisfying R>0; define the test function

[0070] Use π α (u(x))η p (x)e ξ(x) μ(x) multiplied by Δ p π α (u(x)), and sum x∈G, and denote the resulting formula as I:

[0071] Step 5.3: Use Green's formula to calculate the energy conservation at the intersection. The specific Green's formula is:

[0072]

[0073] Where f, g are any two functions, Ω is a finite subset of G, Ω c is the complement of Ω, represents the difference operator, which is defined as Therefore, I can be simplified as:

[0074]

[0075] Step 5.4: Use the definition of the gradient to perform integration by parts and use the inequality to estimate I. The three resulting terms are denoted as J1, J2, and J3.

[0076]

[0077] Step 5.5: According to inequality a p-1 b≤εa p +ε 1-p b p (p-1) p-1 p -p , where ε is the weight parameter, a and b are constants, and the condition [η p (y)-η p (x)][e ξ(y) -e ξ(x) ]≥0, estimate J2 and J3 respectively, and get:

[0078]

[0079] Among them, ε1 and ε2 are weight parameters.

[0080] Step 5.6: Take This ensures that the coefficients satisfy Thus we get the inequality.

[0081] Step 5.7: According to the definition of p-Laplace operator, we have Δ p ψ(u(x))≥|ψ′(u(x))| p-2 ψ′(u(x))Δ p u(x), where is a convex function, ψ′ represents the derivative of ψ. Combined with p-Laplace Equation, and let the parameter α→0 + , and obtain the prior estimate under congestion conditions:

[0082]

[0083] Step 5.8: Based on the definition of the test function ξ(x), the jump size is defined as s = sup{d(x,y)|x~y} and the condition We get the inequality:

[0084]

[0085] in

[0086] Step 5.9: According to the definition of the test function η(x), combined with the condition Get the gradient estimate of η

[0087]

[0088] Among them, χ is the characteristic function of the set, that is, It means that when the distance is between (1-δ)R-2s≤d(x,x0)≤R, it takes 1, and if the distance is not in this range, it takes 0.

[0089] Step 5.10: Select the parameter α so that 2 2p-3 (p-1) p-1 p -p C0α p e psα <q p-1 c0, select make Combined conditions is a weighted space that controls the rate of change of the steady-state function u(x) of the road network flow, that is, (for any R>1), where B r (x0)={x∈Gs.td(x,x0)<r}, that is, the distance between adjacent intersections is controlled within r, and we get:

[0090]

[0091] in, represents the distance decay function that depends on the parameter β, B R (x0) represents the range of the circle with x0 as the center and R as the radius, B r (x0) represents the range of a circle with x0 as the center and r as the radius, and C represents a constant.

[0092] Step 5.11: Let R→∞, and we get because Therefore, u(x)≡0, that is, the steady-state solution of the road network flow is zero, thus triggering the emergency diversion strategy.

[0093] Step 5.12: Dynamically adjust the traffic light cycle and the path recommendation weight γ to reduce the global congestion probability.

[0094] Step six specifically includes:

[0095] Step 6.1: Define the steady-state function u(x) of the road network flow as p-Laplace Equation Δ p u(x)-V(x)|u(x)| p-2 The solution of u(x)=0, where

[0096]

[0097] Define the convex regularization test function under non-congested conditions Ensure the numerical stability of path assignment under congestion conditions.

[0098] Step 6.2: According to the symmetry of x and y, we have

[0099]

[0100] Where v(x) is a non-negative test function.

[0101] Step 6.3: Using the property of convex function φ α (u(y))-φ α (u(x))≥φ α ′(u(x))(u(y)-u(x)), combined with p-Laplace Equation, and let α→0 + , and obtain the prior estimate

[0102]

[0103] Step 6.4: Define the test function Then define the test function v(x) = η(x)ζ(x), and calculate the gradient to get

[0104]

[0105] Step 6.5: Using the inequality |e a -1|≤|a|e |a| , according to the definition of jump size s=sup{d(x,y):x,y∈G,ω(x,y)>0} and the condition Get the inequality

[0106] in

[0107] Step 6.6: Combine the inequalities obtained in step 6.4 and step 6.5 to obtain

[0108] in

[0109]

[0110] Step 6.7: Based on the conditions and an estimate of the gradient η have to

[0111] Step 6.8: Based on the conditions and an estimate of the gradient η have to

[0112] Step 6.9: Combine conditions Right now And let R→∞, we get

[0113] Step 6.10: Combining steps 6.6 and 6.9, we can obtain u(x)≡0, thus generating a multi-path balanced allocation solution.

[0114] Step 6.11: Optimize real-time navigation recommendations to avoid local congestion.

[0115] The present invention abstracts the dynamic traffic network into an infinite weighted graph structure (nodes are intersections, and edge weights are real-time travel times), and combines p-Laplace By combining the nonlinear theory of equations with weighted spatial constraints, a highly adaptive path optimization system is constructed. Based on the dynamic selection of the parameter q, a unique solution determination process is designed for each scenario. Pseudo-metric constraints are used to control path fluctuations, and potential functions are used to quantify congestion costs, enabling dynamic coordinated regulation of traffic light cycles and navigation strategies. This invention overcomes the limitations of traditional finite graph models and provides a mathematically provable and scenario-generalizable solution for smart city traffic management, significantly improving road network stability and resource utilization efficiency.

[0116] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. An intelligent traffic dynamic path optimization method based on infinite graph structure, characterized in that: include: Step 1: Obtain traffic network data and dynamic parameters; Step 2: Verify the geometric conditions of the transportation network; Step 3: Check traffic potential function constraints; Step 4: Select a decision branch based on the real-time traffic status; Step 5: Execute the unique solution determination of the congestion state of branch 1; Step 6: Execute branch 2 to determine the only solution for the non-congested state; Step 7: Generate a dynamic path optimization plan based on the unique solution.

2. The intelligent traffic dynamic path optimization method based on infinite graph structure according to claim 1 is characterized in that: The step 1 specifically includes: Step 1.1: Input an infinitely weighted traffic graph (G, ω, μ), where G is a graph representing traffic paths, each node in the graph represents an intersection, ω is an edge weight function representing real-time travel time, and μ is a node measure representing intersection capacity. Step 1.2: Input the path length pseudo-metric d:G×G→[0,+∞) representing the shortest travel time between intersections; Step 1.3: Input the traffic potential function V(x) that reflects the regional traffic restriction policy or congestion cost; Step 1.4: Input the vehicle density threshold p, the real-time vehicle density corresponding parameter q, and the exponential decay parameter γ.

3. The intelligent traffic dynamic path optimization method based on infinite graph structure according to claim 2 is characterized in that: The second step specifically includes: Step 2.1: Verify the infinite scalability, global connectivity, and local finite capacity of the traffic network, that is, verify the infinity, connectivity, and local finiteness of the graph G; Step 2.2: Define the jump size s of the pseudo-metric d and verify its finiteness: s = sup{d(x,y)|x~y}<+∞, where sup{·} represents the supremum. Step 2.3: Verify the path length pseudo-metric d constraint based on the range of vehicle density threshold p: If q≥2, for all x∈G, verify If 1<q<2, for all x∈G, verify Where C0 and C1 are constants, x and y represent two intersections in the road network G, μ(x) is the node measure representing the capacity of intersection x, d(x,y) represents the distance between intersection x and intersection y, and ω(x,y) represents the edge weight function between intersection x and intersection y.

4. The intelligent traffic dynamic path optimization method based on infinite graph structure according to claim 3 is characterized in that: The step three specifically includes: verifying that the traffic potential function satisfies global positive definiteness: for all x∈G, V(x)≥c0>0, that is, the congestion cost is always higher than the preset lower limit c0; if not satisfied, readjusting the restricted area or dynamically correcting the potential function.

5. The intelligent traffic dynamic path optimization method based on infinite graph structure according to claim 4 is characterized in that: The step 4 specifically includes: selecting a decision branch based on the comparison between the real-time vehicle density and the threshold: if the vehicle density exceeds the threshold, executing branch 1 of step 5; otherwise executing branch 2 of step 6.

6. The intelligent traffic dynamic path optimization method based on infinite graph structure according to claim 5 is characterized in that: The step five specifically includes: Step 5.1: Load the nonlinear diffusion model, define the steady-state function u(x), and satisfy the p-Laplace Equation Δ p u(x)-V(x)|u(x)| p-2 u(x)=0, where Δ p Represents the p-Laplace operator, which is defined as Among them, y~x means that intersection y is connected to intersection x, that is, there is a road between y and x; Step 5.2: Dynamically verify the connectivity of the infinite graph to ensure that valid paths still exist at all intersections after adding new roads or temporarily closing areas. Update the maximum instantaneous capacity of intersections in real time. If the capacity of an intersection exceeds the limit, trigger a local flow control strategy. Monitor the fluctuations in travel time at adjacent intersections in real time. If the jump size of the path is too large, initiate a path reconstruction algorithm. Step 5.3: Calculate the traffic flow gradient difference based on the edge weight ω(x,y), and use the node measure μ(x) to evaluate the energy accumulation intensity of the congested area. Then, calculate the traffic flow energy difference between adjacent intersections based on the energy conservation principle. Step 5.4: Increase the corresponding parameter q according to the real-time congestion level to suppress the traffic energy in the congested area; increase the exponential decay parameter γ to weaken the influence of long-distance paths and give priority to alleviating local congestion; introduce the convex function The constant α>0 eliminates the singularity of the nonlinear operator, thereby ensuring the numerical stability of path allocation under non-congested conditions; Step 5.5: If the model verifies that the steady-state solution to the road network flow is zero, that is, there is no stable traffic flow, the following strategies are triggered: extend the red light cycle in the congested area to reduce the input of new traffic flow; push alternative routes through the navigation system to avoid high-energy difference sections, and mark the real-time travel time of the detour route; if it is determined that there is a non-zero solution, re-optimize the parameters q and γ and start the secondary verification process.

7. The intelligent traffic dynamic path optimization method based on infinite graph structure according to claim 5 is characterized in that: The step six specifically includes: Step 6.1: Load the nonlinear diffusion model, define the steady-state function u(x), and satisfy the p-Laplace Equation Δ p u(x)-V(x)|u(x)| p-2 u(x)=0, where Δ p Represents the p-Laplace operator, which is defined as Among them, y~x means that intersection y is connected to intersection x, that is, there is a road between y and x; Step 6.2: Dynamically verify the connectivity of the infinite graph to ensure that valid paths still exist at all intersections after adding new roads or temporarily closing areas. Update the maximum instantaneous capacity of intersections in real time. If the capacity of an intersection falls below a preset lower limit, trigger a local traffic replenishment strategy. Monitor the fluctuations in travel time at adjacent intersections in real time. If the jump size of the path is within a specified range, the road network is considered stable. Step 6.3: Evaluate the balance of traffic flow distribution based on edge weights ω(x,y), verify the uniformity of path loads based on node measures μ(x), and then calculate the traffic flow energy difference between adjacent intersections based on the principle of energy conservation. Step 6.4: Reduce the parameter q according to the real-time traffic density to enhance the balanced distribution of traffic flow; reduce the exponential decay parameter γ to increase the optimization weight of the long-range path; introduce the convex function Eliminating model singularities ensures the numerical stability of path assignment under congestion conditions; Step 6.5: If the model verifies that a unique steady-state solution exists for the road network traffic flow, the following strategies are triggered: shorten the green light cycle in non-congested areas to improve traffic efficiency; simultaneously push three or more optimal routes through the navigation system, annotating the real-time travel time and load balancing index of each path; if a non-zero solution is determined to exist, re-optimize the parameters q and γ and initiate a secondary verification process.

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