Urban traffic bottleneck edge global identification method under travel demand uncertain scene

Abstract

The invention discloses an urban traffic bottleneck edge global identification method in a travel demand uncertain scene, and relates to the technical field of intelligent traffic management. The method comprises the following steps: 1, constructing a bottleneck edge index and an identification framework based on traffic sensitivity; 2, defining a traffic network and flow parameters in an uncertain demand scene; 3, establishing a linear programming model for road flow distribution optimization under the worst condition in the uncertain demand scene; 4, factors such as traffic demand, traffic balance and travel uncertainty are planned as a whole, and linear programming model constraints are constructed; 5, solving the model to obtain an optimal flow distribution result; and step 6, bottleneck edge indexes are calculated according to a flow distribution result, and key bottleneck edges are obtained through sorting. According to the method, the key bottleneck road sections in the urban traffic network can be accurately identified, the influence caused by the uncertainty of travel demands can be effectively handled, the method can be widely applied to the fields of urban traffic planning, congestion management and road network optimization, and scientific decision support is provided for traffic management departments.

Description

Technical Field

[0001] The present invention provides a linear programming method for global identification of urban traffic bottleneck edges under a scenario of uncertain travel demand. The present invention relates to the field of urban traffic planning and management technology, and specifically to a method for global identification of urban traffic bottleneck edges under a scenario of uncertain travel demand. The method achieves accurate identification of key bottleneck sections in the urban traffic network by combining traffic network modeling, travel demand uncertainty analysis, and worst-case traffic distribution optimization. The present invention is applicable to the fields of intelligent transportation systems, traffic congestion management, road network optimization design, etc., providing scientific decision-making basis for urban traffic management departments, helping to optimize road network resource allocation, and alleviate traffic congestion problems. The technology can be widely used in traffic planning, emergency traffic management, and smart city construction in large and medium-sized cities, and has important theoretical value and practical significance. Background Art

[0002] With the acceleration of urbanization, traffic congestion has become increasingly severe, becoming a major bottleneck affecting urban efficiency and residents' quality of life. Traditional traffic bottleneck identification methods are often based on static traffic flow models or deterministic travel demand assumptions, failing to fully account for the uncertainty and dynamic nature of travel demand, resulting in discrepancies between identification results and actual traffic conditions. For example, existing technologies often employ fixed travel demand data or simple probabilistic models, making it difficult to capture the complex impact of factors such as peak hours, emergencies, and seasonal variations on traffic flow. Furthermore, traditional methods often ignore worst-case traffic loads when calculating flow distribution, leading to underestimation of critical bottleneck sections. While recent research has attempted to address uncertainty by introducing stochastic programming or robust optimization methods, these methods are computationally complex and difficult to apply to large-scale road networks. Furthermore, existing technologies lack a comprehensive assessment of flow distribution and travel time sensitivity, making it difficult to accurately identify critical sections where even slight changes in flow lead to significant increases in travel time. Therefore, a bottleneck identification method that can effectively handle travel demand uncertainty, comprehensively consider worst-case flow distribution, and scientifically quantify section sensitivity is urgently needed to provide more precise technical support for urban traffic management. Summary of the Invention

[0003] (1) Objects of the present invention:

[0004] The purpose of the present invention is to provide a global identification method for urban traffic bottleneck edges under a scenario of uncertain travel demand, so as to solve the problem of inaccurate bottleneck identification caused by ignoring the uncertainty of travel demand in the existing technology. Specifically, the present invention constructs a scientific bottleneck edge index, and by defining a bottleneck edge index based on flow sensitivity, quantifies the impact of increased road flow on travel time, thereby accurately identifying key bottleneck sections. At the same time, the present invention can handle the uncertainty of travel demand. By establishing a linear programming model under an uncertain travel scenario, the flow demand and its occurrence probability of different travel scenarios are comprehensively considered, the flow distribution in the worst case is obtained, and the robustness of the identification results is enhanced. Finally, by optimizing the model design and solution algorithm, the computational complexity is reduced while ensuring accuracy, making it suitable for real-time or near real-time analysis of large-scale urban traffic networks. The present invention not only provides a reliable bottleneck identification tool for traffic management departments, but also lays a theoretical foundation for subsequent road network optimization and congestion management.

[0005] (2) Technical Solution: Based on the above theories and ideas, the present invention provides a global identification method for urban traffic bottleneck edges under uncertain travel demand, namely a method based on linear programming. The specific implementation steps are as follows:

[0006] Step 1: Definition of bottleneck edge indicators and construction of identification framework;

[0007] Specifically, the worst-case traffic distribution on the road network is calculated based on the traffic network and travel demand. Different traffic distribution results are comprehensively evaluated, bottleneck edge indicators are defined, and a bottleneck edge identification framework is established. First, based on a common road resistance function (BPR function is used as an example in this invention), the degree to which the increase in traffic on each road causes the travel time to slow down is determined, that is, the road resistance function is derived with respect to the traffic flow. The BPR function expression is as follows:

[0008] t=t0[1+α(f / c) β ] (1)

[0009] Taking the derivative of the impedance function with respect to the flow rate, we obtain:

[0010] dt / df=(αβt0 / c β )f β-1 (2)

[0011] Then, based on the given road network structure and travel demand, we determine the worst-case flow distribution f* for each road. Substituting f* into (2) yields the following indicator for identifying bottleneck edges, which we denote by p. If the value of this indicator for a road section is large, an increase in traffic volume on that section will lead to a significant increase in travel time.

[0012]

[0013] Step 2: Define the urban traffic network and flow parameter representation under the travel demand uncertainty scenario;

[0014] Specifically, the traffic network is mathematically abstracted into a connected graph G = (V, E), where i, j ∈ V is the serial number of the road node, i, j = 1, 2, ..., |V| (|*| represents the total number of elements in the set), and the nodes correspond to intersections and key locations with traffic demand in the traffic network, such as schools, factories, hospitals, banks, office buildings, and residential areas. Each edge (i, j) ∈ E in the graph represents a road in the traffic network, d ij represents the length of edge (i, j) (i.e. the distance from point i to point j on this path); t 0ij represents the free flow travel time of this edge, that is, the shortest time to pass this edge; c ij represents the capacity of edge (i, j), that is, the maximum number of vehicles that can pass through this road within a period of time (usually one day). K represents the set of travel demands, k∈K, k=1,2,…,|K|. (s k ,t k ) represent the starting point and end point of the k-th travel demand, s k ,t k ∈V. Parameter N k Represents the set of travel scenarios corresponding to the kth travel demand, n∈N k ,n=1,2,…,|N k |. Different travel scenarios correspond to different demand flows and occurrence probabilities. Parameter q kn represents the flow required for the nth travel scenario of the kth travel demand, r kn This demand (q kn ) is the probability of occurrence of the travel scenario corresponding to it.

[0015] Step 3: Establish a linear programming model for optimizing road flow distribution in the worst case under uncertain demand scenarios, using the flow rate on each road segment as the decision variable and minimizing the total travel distance to meet all flow demands as the optimization objective;

[0016] Specifically, people typically choose the shortest or second-shortest route when traveling, and will not take long detours unless the shortcut is completely blocked. Therefore, minimizing the total distance as the optimization objective will result in a worst-case traffic distribution, which will lead to higher traffic on certain critical paths, significantly increasing travel time on these sections. In this problem, since uncertain travel scenarios are considered, the impact of this uncertainty on the objective function must also be addressed when building the model.

[0017] Define the decision variables for optimizing traffic network flow distribution under uncertain travel scenarios;

[0018] x ijkn : a non-negative continuous variable, representing the flow of the k-th pair of travel demands on road segment (i, j) under the n-th travel scenario;

[0019] y ijk : a non-negative continuous variable representing the expected flow of the k-th pair of travel demands on road segment (i, j) for all travel scenarios;

[0020] f ij : a non-negative continuous variable, representing the total expected flow on the road segment (i, j);

[0021] Establish the objective function for optimizing traffic network flow distribution under uncertain travel scenarios;

[0022]

[0023] Among them, D is the established objective function.

[0024] Step 4: Coordinate factors such as traffic demand, traffic balance, and travel uncertainty to constrain the linear programming model. Steps 2 and 3 determined the parameters, variables, and optimization objectives of the linear programming model, respectively. This step imposes multi-dimensional constraints on the linear programming model.

[0025] Step 4.1: Establish travel demand constraints;

[0026]

[0027]

[0028] in, The kth pair of travel demands from starting point s under the nth travel scenario k Outflow flow, The kth pair of travel demand flows into the starting point s under the nth travel scenario k The first equation in constraint (5) indicates the flow rate from the starting point s k The sum of the outflow flows should be equal to the flow q required for the nth travel scenario of the kth travel demand kn , the second formula represents the flow into the starting point s k The total flow should be 0. Similarly, the first equation in constraint (6) represents the flow into the terminal t k The sum of the total flows should be equal to the flow q required for the nth travel scenario of the kth travel demand kn , the second formula represents the outflow end point t k The total flow should be 0.

[0029] Step 4.2: Establish traffic balance constraints for each node in the network;

[0030]

[0031] This constraint means that for every node in the network, for every travel scenario of every travel demand, the flow into the node should be equal to the flow out of the node. This constraint ensures that the flow in the network will not suddenly disappear.

[0032] Step 4.3: Establish the expected flow constraints for each travel demand;

[0033]

[0034] Among them, r nk represents the demand (i.e. q nk ) is the probability of occurrence of the travel scenario corresponding to it.

[0035] Step 4.4: Establish the total flow constraint for each edge in the network;

[0036]

[0037] Among them, f ij is the total expected flow on the road section (i, j), y ijk is the expected flow of the kth pair of travel demands on road segment (i, j) for all travel scenarios.

[0038] Step 5: Model Solving – Solve the proposed linear programming model for optimizing the worst-case road flow distribution under uncertain demand scenarios, aiming to efficiently obtain the optimal flow distribution that meets the constraints.

[0039] This step relies on high-performance commercial solvers (such as CPLEX, Gurobi, etc.) to perform global optimization and solve the model. The linear programming model proposed in this invention also has high solving efficiency for large-scale data.

[0040] Step 6: The solution f obtained by the above model ij Substituting the bottleneck edge index p defined in formula (3), the larger the value obtained, the more likely the road section is to become a bottleneck edge.

[0041] (3) Advantages and effects:

[0042] This invention can construct a linear programming model that balances computational efficiency and sensitivity analysis for large-scale, complex urban road networks and the complex and diverse travel demands on such networks, achieving accurate identification of bottleneck edges. Compared with existing technologies, this invention has the following advantages:

[0043] ① Accurately identify key bottleneck sections: By defining bottleneck edge indicators based on flow sensitivity, we can scientifically quantify the impact of road flow changes on travel time, thereby accurately identifying key sections where a slight increase in flow leads to a significant increase in travel time, providing clear goals for traffic management.

[0044] ② Strong robustness: By establishing a linear programming model under uncertain travel scenarios, comprehensively considering different travel demands and their occurrence probabilities, and obtaining the worst-case traffic distribution, the recognition results are made more robust and can cope with dynamic changes and emergencies in actual traffic.

[0045] ③ Efficient and practical: The model design takes into account both computational efficiency and accuracy, and is suitable for real-time analysis of large-scale urban traffic networks. It provides fast and scientific decision-making support for traffic management departments and facilitates the construction of smart cities. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flow chart of the global identification method for urban traffic bottleneck edges under the travel demand uncertainty scenario described in the present invention.

[0047] Figure 2 It is a road network structure diagram used in describing the specific implementation methods of the present invention.

[0048] Figure 3 It is a schematic diagram of the impact of the bottleneck edge identified by the present invention and the bottleneck edge identified by the comparison method on the total travel time of the road network. DETAILED DESCRIPTION

[0049] (1) Project background

[0050] This implementation takes a large-scale road network in Beijing's urban area as the research object, selects two travel scenarios, weekdays and holidays, simulates travel demand, obtains corresponding parameter values, tests the above models and methods, and obtains the most likely bottleneck edges.

[0051] The research example is a very dense traffic network in the urban area of ​​Beijing. It has a high population density and many important nodes such as hospitals, schools, large shopping malls, banks, office buildings and residential areas. The traffic demand is complex and diverse and varies at different times. Congestion is very likely to occur during peak traffic periods. Therefore, it is of great practical significance to analyze the traffic distribution in this area and identify bottleneck edges. There are 4933 nodes, 6632 bidirectional edges, and 7918 pairs of traffic demands in this area. Each pair of traffic demands has two travel scenarios: holidays and weekdays. The road network structure of this area is shown in the attached figure. Figure 2 .

[0052] (2) Basic information

[0053] Some specific data of the network structure are shown in Table 1 below, and some specific data of the traffic demand are shown in Table 2 below: Table 1 Specific data of network structure Table 2 Specific data of flow requirements Serial number starting point end Travel scenarios Traffic demand / vehicle Probability of occurrence / % 1 18 13 working day 4021 70 1 18 13 Holidays 2033 30 2 28 125 working day 257 70 2 28 125 Holidays 187 30 3 30 116 working day 282 70 3 30 116 Holidays 150 30 …… …… …… …… …… …… 7916 3472 191 working day 8 70 7916 3472 191 Holidays 200 30 7917 1754 1009 working day 25 70 7917 1754 1009 Holidays 370 30 7918 1635 3278 working day 25 70 7918 1635 3278 Holidays 400 30

[0054] (3) Optimize calculation results

[0055] The solution of the model and the top 20 most likely bottleneck edges obtained by calculating the proposed indicators and sorting them from large to small are shown in Table 3 below: Table 3 Bottleneck edge results obtained by optimization calculation

[0056] Table 3 shows the 20 road sections most likely to become bottlenecks, identified by calculating and ranking the traffic distribution calculated by the optimization model using the bottleneck edge index proposed in this invention. As can be seen, the traffic distribution on these sections far exceeds the section capacity, and the traffic values ​​generally follow the defined bottleneck edge index from high to low, but do not completely follow a decreasing pattern. This method helps identify sections that appear less congested but could significantly improve network efficiency if expanded or restricted.

[0057] (4) Comparative effect analysis

[0058] To verify the superiority of the present invention, a comparative analysis was conducted with the "flow-to-capacity ratio ranking" method. As the name suggests, "flow-to-capacity ratio ranking" calculates the ratio of flow to capacity for each road section. The larger this ratio, the greater the degree to which flow exceeds capacity on each road section, and the more likely that section will be congested. However, this method has the following limitations in practical application: first, it ignores the extent to which increased flow leads to increased travel time, and second, it ignores the mutual influence between road sections. Expanding the bottleneck edge thus obtained may actually cause even more severe congestion on adjacent sections.

[0059] Table 4 lists the results of the “flow rate to capacity ratio ranking” method that conforms to intuitive logic: Table 4 Results of the “flow rate to capacity ratio ranking” method

[0060] The bottleneck edges identified by the two methods are compared, and the total travel time index (travel time is calculated by the road resistance function (1)) obtained by expanding the capacity of these bottleneck edges one by one (uniformly expanding them to 1.2 times the original value) is analyzed. The impact of the proposed method and the "flow and capacity ratio ranking" method on the travel time of the entire road network is calculated, as shown in Table 5 below: Table 5 Comparison of method results

[0061] It can be observed that the method proposed in this invention has a good effect in identifying bottleneck edges, especially on the first edge, which can lead to a significant reduction in the total travel time. As more and more edges are expanded, the difference in the results obtained by the two methods gradually decreases. Therefore, especially under the condition of limited resources, the method proposed in this invention will greatly improve the traffic efficiency of the road network. The results of the impact of these two methods on the traffic efficiency of the road network are shown in the attached figure. Figure 3 .

[0062] In summary, the present invention proposes a global identification method for urban traffic bottleneck edges under scenarios with uncertain travel demand, which effectively solves the problem of inaccurate bottleneck identification caused by traditional technologies ignoring the dynamic nature of travel demand. This method establishes a scientific bottleneck edge indicator system and combines it with a linear programming model under uncertain travel scenarios to achieve accurate identification of key bottleneck sections in urban traffic networks. The present invention can comprehensively consider different travel demands and their probability of occurrence, obtain the worst-case traffic flow distribution, and significantly improve the reliability of the identification results. This technology provides a scientific basis for urban traffic congestion management and road network optimization, and has important theoretical value and practical significance.

[0063] This invention significantly improves the scientificity and efficiency of bottleneck edge identification in large-scale and complex urban road networks through the following core innovations:

[0064] ① Scientific Definition of the Bottleneck Edge Index: This paper innovatively proposes a bottleneck edge index based on flow sensitivity. By taking the derivative of the road resistance function with respect to flow, it quantifies the impact of increased flow on travel time. This index accurately reflects the sensitivity and potential congestion risk of a road section, providing an objective basis for bottleneck identification.

[0065] ② Traffic Distribution Optimization Model for Uncertain Demand Scenarios: To address the uncertainty of travel demand, this paper constructs a linear programming model with the goal of minimizing total travel distance. This model comprehensively considers the traffic demand and probability of occurrence in different travel scenarios, and obtains the worst-case traffic distribution by applying expected flow constraints and node flow balance constraints. This model not only addresses the flaw of traditional methods that ignore uncertainty but also significantly improves the reliability of identification results.

[0066] ③ Efficient Solution and Global Identification Framework: This invention achieves efficient analysis of large-scale transportation networks by optimizing model design and solution algorithms. Furthermore, by combining model solution results with bottleneck edge indicators, a comprehensive global identification framework is formed. This framework can quickly and accurately locate key bottleneck sections in transportation networks, providing strong technical support for urban transportation planning and management.

[0067] Through practical application, this method demonstrates significant superiority in identifying bottleneck edges in large-scale urban road networks, boasting high computational efficiency and significantly improving overall network efficiency. Compared to straightforward methods that identify bottleneck edges by sorting traffic flow relative to capacity, this method is particularly effective when network expansion resources are limited. It provides a scientific and efficient decision-making support tool for traffic planning, emergency traffic management, and smart city development in large and medium-sized cities.

Claims

1. A global identification method for urban traffic bottlenecks under uncertain travel demand scenarios, including the following steps: (1) Definition of bottleneck edge indicators and construction of an identification framework: Based on the traffic network and travel demand, the worst-case flow distribution on the road network is calculated. Different flow distribution results are comprehensively evaluated to define bottleneck edge indicators and establish a bottleneck edge identification framework. First, based on a common road resistance function (using the BPR function as an example in this paper), the degree to which increased flow on each road causes travel time to slow down is determined. In other words, the road resistance function is derived with respect to flow. (1.1) First, the road resistance function expression used in the present invention is given as follows: t=t0[1+α(f / c) β ] (1.2) Then, the impedance function is differentiated with respect to the flow rate to obtain: dt / df=(αβt0 / c β )f β-1 (1.3) Then, based on the given road network structure and travel demand, we determine the worst-case flow distribution f* for each road. We substitute f* into the following metric for identifying bottleneck edges, which we denote by p. If the value of this metric for a particular road segment is large, an increase in traffic volume on that segment will result in a significant increase in travel time. p=dt / df| f＝f* =(αβt0 / c β )(f*) β-1 (2) Definition of urban traffic network and flow parameters under uncertain travel demand scenarios The traffic network is mathematically abstracted into a connected graph G = (V, E), where i, j ∈ V, is the serial number of the road node, i, j = 1, 2, ..., |V| (|*| represents the total number of elements in the set), and the nodes correspond to intersections and key locations with traffic demand in the traffic network, such as schools, factories, hospitals, banks, office buildings, and residential areas. Each edge (i, j) ∈ E in the graph represents a road in the traffic network, d ij represents the length of edge (i, j) (i.e. the distance from point i to point j on this path); t 0ij represents the free flow travel time of this edge, that is, the shortest time to pass this edge; c ij represents the capacity of edge (i, j), that is, the maximum number of vehicles that can pass through this road within a period of time (usually one day). K represents the set of travel demands, k∈K, k=1,2,…,|K|. (s k ,t k ) represent the starting point and end point of the k-th travel demand, s k ,t k ∈V. Parameter N k Represents the set of travel scenarios corresponding to the kth travel demand, n∈N k ,n=1,2,…,|N k |. Different travel scenarios correspond to different demand flows and occurrence probabilities. Parameter q kn represents the flow required for the nth travel scenario of the kth travel demand, r kn This demand (q kn ) is the probability of occurrence of the travel scenario corresponding to it. (3) Establish a linear programming model for optimizing road flow distribution in the worst case under uncertain demand scenarios, using the flow on each road segment as the decision variable and minimizing the total travel distance to meet all flow demands as the optimization objective; Since people typically choose the shortest or second-shortest route when traveling, and will not take long detours unless the shortcut is completely blocked, minimizing the total distance traveled will result in a worst-case traffic distribution. This will lead to higher traffic on certain critical paths, significantly increasing travel time on these sections. In this problem, since uncertain travel scenarios are considered, the impact of this uncertainty on the objective function must also be addressed when building the model. Define the decision variables for optimizing traffic network flow distribution under uncertain travel scenarios; x ijkn : a non-negative continuous variable, representing the flow of the k-th pair of travel demands on road segment (i, j) under the n-th travel scenario; y ijk : a non-negative continuous variable representing the expected flow of the k-th pair of travel demands on road segment (i, j) for all travel scenarios; f ij : a non-negative continuous variable, representing the total expected flow on the road segment (i, j); (3.1) Establish the objective function for optimizing traffic network flow distribution under uncertain travel scenarios; in, d ij represents the length of edge (i, j) (i.e. the distance from point i to point j on this path), f ij represents the total expected flow on the road segment (i, j), and D is the total travel distance of all travel demands on the road network. (4) Coordinate factors such as flow demand, flow balance, and travel uncertainty to constrain the linear programming model; (4.1) Establish travel demand constraints; (4.2) Establish traffic balance constraints for each node in the network; (4.3) Establishing the expected flow constraints for each travel demand; (4.4) Establish the total flow constraint for each edge in the network; (5) Model solution: Solve the linear programming model for optimizing the road flow distribution in the worst case under the proposed uncertain demand scenario, aiming to efficiently obtain the optimal flow distribution result that meets the constraints. (6) Bottleneck edge identification The solution f obtained by the above model ij Substitute the bottleneck edge index p defined in the present invention and sort the index. The larger the obtained value, the more likely the road section is to become a bottleneck edge.

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