A method for managing and optimizing release time of each driving direction at an intersection based on Stackelberg game theory

Abstract

This invention discloses a method for managing and optimizing the passage time for each traffic direction at intersections based on Stackelberg game theory. In this invention, the total passage time of a traffic light cycle at an intersection is finite and fixed. However, considering that the statistical average number of waiting vehicles and the number of lanes can change, adaptive management of the passage time for each traffic direction at intersections in smart cities is a critical problem that urgently needs to be solved. To address this problem, this invention proposes a method for managing and optimizing the passage time for each traffic direction at intersections based on Stackelberg game theory, which integrates the limited passage time for each traffic direction into a game model. This invention aims to provide a unique solution that physically conforms to real-world application scenarios and can be effectively applied to engineering practice.

Description

Technical Field

[0001] This invention relates to the field of intelligent traffic control technology, and in particular to a method for managing and optimizing the release time of each driving direction at an intersection based on Stackelberg game theory. Background Technology

[0002] With rapid urbanization and a surge in traffic volume, traditional fixed-time traffic management models are struggling to adapt to dynamically changing traffic conditions, leading to frequent problems such as intersection congestion and low traffic efficiency. Against this backdrop, the concept of intelligent transportation has emerged, emphasizing the dynamic optimization and management of traffic flow through technological means. By installing sensors at intersections to collect traffic information such as vehicle and pedestrian data, and then analyzing and processing this information through algorithms, adaptive control of traffic lights can be achieved. This control method can flexibly adjust parameters such as green and red light times based on real-time traffic flow and vehicle speed information to optimize road traffic efficiency. The implementation of intelligent traffic light timing control technology relies on various advanced technologies, such as the Internet of Things (IoT), artificial intelligence (AI), and big data. The application of these technologies enables traffic lights to respond more accurately to traffic changes, improving road traffic efficiency and safety. Furthermore, this technology can be combined with information platform sharing technologies such as electronic police systems, smart light poles, and satellite navigation to achieve intelligent and interconnected traffic command and dispatch, further enhancing the level of urban traffic management. Therefore, designing a method for allocating travel time in different directions at intersections to automatically allocate travel time among these directions under various traffic conditions is a critical problem that urgently needs to be solved in the scenario studied in this invention. This invention proposes a method for managing and optimizing travel time in different directions at intersections based on Stackelberg game theory, modeling the aforementioned problem of optimizing travel time allocation in different directions at intersections into a game theory model. This invention aims to provide a unique solution that physically conforms to real-world application scenarios and can be effectively applied to engineering practice. Summary of the Invention

[0003] Purpose of the invention: Under the premise of limited total travel time at intersections, this invention addresses the problem of allocating travel time for each direction of traffic under different parameters such as the number of lanes, the number of waiting vehicles, and traffic efficiency. It provides a method for managing and optimizing the release time of each direction of traffic at intersections based on Stackelberg game theory.

[0004] Technical solution: The present invention provides a method for managing and optimizing the traffic flow time for each direction at an intersection based on Stackelberg game theory, comprising:

[0005] Construct a traffic model for intelligent intersections, in which an intersection has Let the set of intersections be _ . Each intersection contains one or more directions of traffic, and each direction of traffic has its own number of lanes; there are a total of [number missing] lanes at the intersection. The set of car directions controlled by each traffic light individually is represented as: If opposing lanes can be opened and stopped simultaneously, they can be considered as being controlled by the same traffic light timing; if they cannot be opened and stopped simultaneously, they can be considered as different traffic light timings controlling the direction of vehicle travel.

[0006] Based on the traffic model of the intelligent intersection, a Stackelberg game model is constructed. In the Stackelberg game model, the intersection acts as the leader of the game model, while each direction of vehicle travel acts as the follower.

[0007] For each follower car's direction of travel in the game, each car aims to increase its own travel time to improve traffic conditions, maximizing its own utility function as its objective function. Its utility function is the difference between the traffic improvement gained from purchasing intersection travel time resources and the cost incurred in purchasing those resources. The mathematical model is as follows:

[0008]

[0009] in, The unit travel time is used to ensure that the logarithmic independent variable is dimensionless; The benefit function for traffic improvement; To purchase time resources The price paid; Represents a set The Middle The extra travel time gained by a game of strategy for a car whose direction of travel requires traffic lights; Represents a set The Middle The basic travel time for a vehicle's direction of travel that requires traffic lights; a set of intersections. The Middle There are several directions of car travel. The statistical average number of cars waiting in each lane and in the direction of travel over a period of time is: , Represents a set The Middle The average number of cars waiting in each lane in the direction of travel that requires traffic lights; Represents a set The Middle The efficiency of vehicle passage in the direction of travel that requires traffic lights; Price indicates the unit of travel time;

[0010] For the leader intersection in the game, the objective function is to maximize the total cost incurred by all cars traveling in each direction that requires traffic light control in purchasing their respective passage time.

[0011]

[0012] st

[0013] in, This indicates the total green time for traffic lights at an intersection in one cycle. This indicates the total base travel time allocated to the direction of travel of vehicles requiring traffic light control. This represents the total travel time resources that the game leader can allocate.

[0014] During the game, each direction of vehicle travel determines the size of the intersection clearance time to be purchased based on the optimal price of the game leader's unit passage time.

[0015] Furthermore, in the aforementioned game, the total green time of one cycle of the traffic lights at the intersection is used as a limited resource in the Stackelberg game to play the game among the various directions of vehicle travel that require traffic light control, while the directions of vehicle travel that do not require traffic light control do not participate in the game.

[0016] Furthermore, in the aforementioned game, if opposing lanes can be opened and stopped simultaneously, they can be considered as being controlled by the same traffic light timing and participating in the game as the same follower; if they cannot be opened and stopped simultaneously, they can be considered as cars traveling in different directions controlled by different traffic light timings and participating in the game as different followers.

[0017] Furthermore, the payoff function for traffic improvement adopted by the follower in this game is:

[0018]

[0019] in, Represents a set The Middle A set of actual vehicle travel directions that require light control. The Middle A set of actual vehicle travel directions that require light control. The Middle The number of lanes, the number of waiting cars, and the throughput efficiency for each actual driving direction are expressed as follows: , and .

[0020] Furthermore, regarding the direction of travel of the follower car in the game, maximizing its own utility function is used as its objective function. Its utility function is the difference between the traffic improvement benefit gained from purchasing intersection passage time resources and the cost incurred in purchasing those time resources.

[0021]

[0022] in, For set The Middle The traffic improvement benefit function for a traffic direction that requires traffic light control is such that as the travel time for a certain traffic direction increases, more vehicles will pass through. At the same time, in order to ensure relative fairness among the traffic directions, the growth rate of the benefit for each traffic direction decreases as the travel time increases. This indicates that as the efficiency of car passage increases, the set The Middle The reduced return on time resources for a car whose direction of travel requires lighting control is achieved through game theory. Represents a set The Middle The average number of cars waiting in each lane in the direction of travel requiring traffic lights, as... Increasing the travel time required by followers in this game increases their travel time, while decreasing it decreases their travel time.

[0023] Furthermore, if the opposing lanes can be opened and stopped simultaneously, they can be considered as separate controls operating under the same traffic light timing and participating in the game as a single follower. The optimization problem can then be modeled as follows:

[0024]

[0025] in, Represents a set The Middle A set of actual vehicle travel directions that require light control. The Middle A set of actual vehicle travel directions that require light control. The Middle The number of lanes, the number of waiting cars, and the throughput efficiency for each actual driving direction are expressed as follows: , and .

[0026] Furthermore, the leader intersection in the game takes maximizing the total cost incurred by all vehicles requiring traffic light control in purchasing their respective travel time as its objective function, i.e. .

[0027] Furthermore, the constraints of the objective function for the leader intersection in the game theory problem include: the total travel time that needs to be allocated for traffic lights in each direction of vehicle travel should be less than or equal to the total travel time that the leader can allocate, expressed as: .

[0028] Beneficial Effects: This invention discloses a method for managing and optimizing the passage time of each traffic direction at an intersection based on Stackelberg game theory. It integrates the aforementioned problem of limited passage time for each traffic direction into a game model. Compared with existing technologies, this invention applies a competitive mechanism to the problem of allocating passage time resources at intelligent traffic intersections, establishing a Stackelberg-based resource game mechanism among the traffic directions requiring traffic light control. This invention aims to provide a unique solution that physically conforms to real-world application scenarios and can be effectively applied to engineering practice. Attached Figure Description

[0029] Figure 1 This is a schematic diagram illustrating a scenario for a method for managing and optimizing the release time of traffic in each direction at an intersection based on Stackelberg game theory, as proposed in this invention. Detailed Implementation

[0030] Now combined with the appendix Figure 1 The technical solutions of the present invention are further illustrated by the embodiments.

[0031] This embodiment proposes a method for managing and optimizing the traffic release time for each direction at an intersection based on Stackelberg game theory, which mainly includes the following steps:

[0032] Step 1: First, construct a traffic model for the intelligent intersection, such as... Figure 1 As shown, in this traffic model, an intersection has Let the set of intersections be _ . Each intersection contains one or more directions of traffic, and each direction of traffic has its own number of lanes. Therefore, there are a total of [number] lanes at an intersection. The set of car directions controlled by each traffic light individually is represented as: If opposing lanes can be opened and stopped simultaneously, they can be considered as being controlled by the same traffic light timing. If they cannot be opened and stopped simultaneously, they can be considered as different traffic light timings controlling the direction of vehicle travel.

[0033] Set of intersections The Middle There are several directions of car travel. The statistical average number of cars waiting in each lane and in the direction of travel over a period of time is: Specifically, the number of lanes in each direction of vehicle travel. The statistical average number of cars waiting can be changed through reversible lanes. It can also change due to phenomena such as tides. Furthermore, different directions of vehicle travel result in different vehicle throughput efficiencies. (For example, going straight is more efficient than turning left or making a U-turn), which represents the collection time per unit of time. The Middle The number of cars passing in each direction of travel.

[0034] In this example, the total green time of a traffic light cycle at an intersection, that is, the total time from the start of the green light for one direction of traffic to the next green light for that direction of traffic, is: Since the total green light time of a traffic light cycle at an intersection is limited and fixed, and considering that the statistical average number of waiting vehicles and the number of lanes may also change, how to adaptively manage the passage time for each direction of vehicle travel at intersections in smart cities is a critical issue that urgently needs to be addressed.

[0035] Step 2: Then, mathematical modeling is performed to allocate travel time among different directions of vehicle travel for the limited travel time at the intersection.

[0036] Resource games typically refer to interactive processes among multiple participants concerning the allocation, acquisition, utilization, or competition for limited resources. They are characterized by the finiteness and scarcity of resources, conflicting interests among the players, and information asymmetry. The Stackelberg game is a hierarchical, non-cooperative game where the core characteristic lies in the unequal decision-making order and power positions of the participants: a leader acts first, and the followers make their optimal responses after observing the leader's decision. In this embodiment, since the intersection controls the travel time resource, it is considered the leader in the game model, while the various directions of vehicle travel that need to compete for resources act as followers. Therefore, the travel time allocation problem for each direction of vehicle travel can be modeled as follows:

[0037] Each direction of vehicle travel desires to increase its travel time in order to achieve better commuting quality and efficiency. Therefore, in this example, the set of intersections... The Middle The optimization problem of considering the direction of travel of a car requiring traffic lights as a follower in a game is modeled as follows:

[0038]

[0039] in, The unit travel time is used to ensure that the logarithmic independent variable is dimensionless; Represents a set The Middle The extra travel time gained by a game of strategy for a car whose direction of travel requires traffic lights; Represents a set The Middle The basic passage time for a vehicle traveling in a direction that requires traffic lights; Represents a set The Middle The average number of cars waiting in each lane in the direction of travel requiring traffic lights. and They are all pure numbers and do not introduce any additional dimensions; Price indicates the unit of travel time.

[0040] In this example, the follower (in the direction of vehicle travel) in the game mechanism purchases travel time resources with the aim of improving traffic conditions based on parameters such as the number of waiting vehicles, the number of lanes, and traffic efficiency. Therefore, the utility function of the follower's vehicle travel direction consists of two parts: a traffic improvement benefit function and a cost function. The traffic improvement gained from purchasing travel time resources is the traffic improvement benefit function, while the time cost of purchasing them is the cost function. Therefore, the follower's utility function in the game is the difference between the traffic improvement benefit function and the cost function. For set The Middle A traffic improvement benefit function for a vehicle's direction of travel that requires traffic light control, using... Function follows This property increases with the increase in travel time. This is because as the travel time gained in a certain direction of vehicle travel increases, more vehicles will pass through, thus increasing their travel time gain. However, it should be noted that in order to ensure relative fairness among different directions of vehicle travel, the rate of increase in travel time gain for each direction of vehicle travel decreases as the travel time increases. This indicates that as the efficiency of car passage increases, the set The Middle The reduced return on time resources for a car whose direction of travel requires traffic light control is achieved through game theory. Meanwhile, Represents a set The Middle The average number of cars waiting in each lane in the direction of travel requiring traffic lights can be determined in a real-world scenario. The larger the value, the greater the travel time required by the followers in this game; conversely, the smaller the value, the less travel time required. Represents a set The Middle The direction of travel for vehicles requiring traffic lights to obtain passage time. And the price paid.

[0041] It should be noted that the logarithmic function in the formula implicitly involves dimensional normalization in physics. For example, it can be understood as... ,in The unit travel time is used (e.g., 1 second) to ensure that the logarithmic independent variable is dimensionless.

[0042] With the set The Middle As the time a car traveling in a traffic light-controlled direction purchases to travel increases, its gains also increase, but so does its cost function. For each participant in the game model, the goal is to obtain higher gains with lower costs in the game's activities.

[0043] Specifically, if opposing lanes can be opened and stopped simultaneously, they can be considered as separate controls operating under the same traffic light timing and participating in the game as a single follower. The payoff function for traffic improvement adopted by this follower is...

[0044]

[0045] in, Represents a set The Middle A set of actual vehicle travel directions that require light control. The Middle A set of actual vehicle travel directions that require light control. The Middle The number of lanes in each vehicle's actual driving direction, the number of waiting vehicles, and the vehicle throughput efficiency are respectively expressed as follows: , and .

[0046] Therefore, considering the multiple actual driving directions of the aforementioned cars participating in the game as the same follower, the optimization problem is modeled as follows:

[0047]

[0048] In a game theory scenario, an intersection sells limited travel time to multiple competing directions of traffic. Therefore, the objective function in this game is defined as the total cost incurred by each direction of traffic in purchasing its respective travel time.

[0049]

[0050] Furthermore, since the total permitted time at an intersection is finite, there are constraints in the game theory relationship as follows:

[0051]

[0052] Therefore, in the game theory relationship, the leader has an optimization problem.

[0053]

[0054] st

[0055] The optimization problems of resource buyers and sellers together constitute the Stackelberg game. By having the two sides act according to certain rules, the final game equilibrium can be obtained. That is, the optimal unit resource price is obtained by maximizing the utility functions representing the interests of the leader intersection and the directions of travel of cars with mutual competition. Then, each vehicle's direction of travel is priced according to the optimal resource allocation at the leader intersection. This determines how much of the passage time they can purchase.

Claims

1. A method for managing and optimizing the release time of each traffic direction at an intersection based on Stackelberg game theory, characterized in that, include: Construct a traffic model for intelligent intersections, in which an intersection has Let the set of intersections be _ . Each intersection contains one or more directions of traffic, and each direction of traffic has its own number of lanes; there are a total of [number missing] lanes at the intersection. The set of car directions controlled by each traffic light individually is represented as: If opposing lanes can be opened and stopped simultaneously, they can be considered as being controlled by the same traffic light timing; if they cannot be opened and stopped simultaneously, they can be considered as different traffic light timings controlling the direction of vehicle travel. Based on the traffic model of the intelligent intersection, a Stackelberg game model is constructed. In the Stackelberg game model, the intersection acts as the leader of the game model, while each direction of vehicle travel acts as the follower. For each follower car's direction of travel in the game, each car aims to increase its own travel time to improve traffic conditions, maximizing its own utility function as its objective function. Its utility function is the difference between the traffic improvement gained from purchasing intersection travel time resources and the cost incurred in purchasing those resources. The mathematical model is as follows: in, The unit travel time is used to ensure that the logarithmic independent variable is dimensionless; The benefit function for traffic improvement; To purchase time resources The price paid; Represents a set The Middle The extra travel time gained by a game of strategy for a car whose direction of travel requires traffic lights; Represents a set The Middle The basic travel time for a vehicle's direction of travel that requires traffic lights; a set of intersections. The Middle There are several directions of car travel. The statistical average number of cars waiting in each lane and in the direction of travel over a period of time is: , Represents a set The Middle The average number of cars waiting in each lane in the direction of travel that requires traffic lights; Represents a set The Middle The efficiency of vehicle passage in the direction of travel that requires traffic lights; Price indicates the unit of travel time; For the leader intersection in the game, the objective function is to maximize the total cost incurred by all cars traveling in each direction that requires traffic light control in purchasing their respective passage time. s.t. in, This indicates the total green time for traffic lights at an intersection in one cycle. This indicates the total base travel time allocated to the direction of travel of vehicles requiring traffic light control. This represents the total travel time resources that the game leader can allocate. During the game, each direction of vehicle travel determines the size of the intersection clearance time to be purchased based on the optimal price of the game leader's unit passage time.

2. The method for managing and optimizing the traffic flow time for each direction at an intersection based on Stackelberg game theory, as described in claim 1, is characterized in that: In the aforementioned game, the total green time of one cycle of the traffic lights at the intersection is used as a limited resource in the Stackelberg game to play the game between the directions of vehicle travel that require traffic light control, while the directions of vehicle travel that do not require traffic light control do not participate in the game.

3. The method for managing and optimizing the traffic flow time for each direction at an intersection based on Stackelberg game theory, as described in claim 1, is characterized in that: In the aforementioned game, if opposing lanes can be opened and stopped simultaneously, they can be considered as being controlled by the same traffic light timing and participating in the game as the same follower; if they cannot be opened and stopped simultaneously, they can be considered as cars traveling in different directions controlled by different traffic light timings and participating in the game as different followers.

4. The method for managing and optimizing the traffic flow time for each direction at an intersection based on Stackelberg game theory, as described in claim 1, is characterized in that: The payoff function for improved traffic conditions adopted by the followers in this game is: in, Represents a set The Middle A set of actual vehicle travel directions that require light control. The Middle A set of actual vehicle travel directions that require light control. The Middle The number of lanes, the number of waiting cars, and the throughput efficiency for each actual driving direction are expressed as follows: , and .

5. The method for managing and optimizing the traffic flow time for each direction at an intersection based on Stackelberg game theory, as described in claim 1, is characterized in that: The aforementioned strategy for the follower's car's direction of travel in the game aims to maximize its own utility function as its objective function. This utility function is the difference between the traffic improvement gained from purchasing intersection passage time resources and the cost incurred in purchasing those resources. in, For set The Middle The traffic improvement benefit function for a traffic direction that requires traffic light control is such that as the travel time for a certain traffic direction increases, more vehicles will pass through. At the same time, in order to ensure relative fairness among the traffic directions, the growth rate of the benefit for each traffic direction decreases as the travel time increases. This indicates that as the efficiency of car passage increases, the set The Middle The reduced return on time resources for a car whose direction of travel requires lighting control is achieved through game theory. Represents a set The Middle The average number of cars waiting in each lane in the direction of travel requiring traffic lights, as... Increasing the travel time required by followers in this game increases their travel time, while decreasing it decreases their travel time.

6. The method for managing and optimizing the traffic flow time for each direction at an intersection based on Stackelberg game theory, as described in claim 1, is characterized in that: If opposing lanes can be opened and stopped simultaneously, they can be considered as separate controls operating under the same traffic light timing, participating in the game as a single follower. The optimization problem is modeled as follows: in, Represents a set The Middle A set of actual vehicle travel directions that require light control. The Middle A set of actual vehicle travel directions that require light control. The Middle The number of lanes, the number of waiting cars, and the throughput efficiency for each actual driving direction are expressed as follows: , and .

7. The method for managing and optimizing the traffic flow time for each direction at an intersection based on Stackelberg game theory, as described in claim 1, is characterized in that: The leader intersection in the game uses maximizing the total cost incurred by all cars requiring traffic lights in their respective directions of travel to purchase their respective passage time as its objective function, i.e. .

8. The method for managing and optimizing the traffic flow time for each direction at an intersection based on Stackelberg game theory, as described in claim 1, is characterized in that: In the game theory problem, the constraints of the objective function at the leader's intersection include: the total travel time allocated for traffic lights in each direction of vehicle travel should be less than or equal to the total travel time allocated to the leader, expressed as: .

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