A method for managing and optimizing merging of multiple vehicles merging into an empty lane based on Stackelberg game theory
By constructing a traffic system model using Stackelberg game theory and utilizing the game relationship between vacant lanes and adjacent lanes, the system optimizes the vehicle vacancy distance purchase strategy, solving the problem of multiple vehicles merging when vacant lanes are restricted, and improving the traffic efficiency and safety of the traffic system.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHANGSHU INSTITUTE OF TECHNOLOGY
- Filing Date
- 2026-05-09
- Publication Date
- 2026-06-26
Smart Images
Figure CN122290356A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to intelligent transportation vehicle merging methods, and more particularly to a method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane based on Stackelberg game theory. Background Technology
[0002] With continuous advancements in vehicle manufacturing technology, improved vehicle performance has made merging into empty lanes more flexible and safer for drivers. Simultaneously, the gradual rollout of intelligent transportation systems, such as traffic light control, traffic monitoring, and autonomous braking systems, provides more refined management tools for merging into empty lanes. In practical applications, empty lane merging technology typically combines traffic flow prediction, road condition analysis, and driving behavior research. By monitoring traffic flow and queue length in real time, precise vehicle control using traffic lights or intelligent guidance systems allows for the alternating release of vehicles by direction and lane. This method not only improves lane utilization and capacity but also effectively reduces the incidence of traffic accidents. This invention focuses on how to rationally allocate limited empty lanes among multiple vehicles in adjacent lanes, a critical issue that urgently needs to be addressed in intelligent transportation systems. Summary of the Invention
[0003] Purpose of the invention: Under the premise of limited vacant vehicle spacing in vacant lanes, this invention proposes a management and optimization method for multiple vehicles merging into vacant lanes from adjacent lanes, based on Stackelberg game theory.
[0004] Technical solution: A method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane based on Stackelberg game theory, including:
[0005] Construct a transportation system in which a lane has a length of Empty vehicle spacing, shared space between adjacent lanes A vehicle can merge into an empty lane by changing lanes. The set of vehicles that can merge into an empty lane from an adjacent lane is represented as follows: ;
[0006] Based on a traffic system model with limited empty lane spacing and multiple vehicles merging into the empty lane from adjacent lanes, a Stackelberg game model is constructed. In the Stackelberg game model, the empty lane acts as the leader of the game model, while vehicles from adjacent lanes that can merge into the empty lane act as followers competing for limited resources.
[0007] Each vehicle that can merge into an empty lane uses its own utility function as its objective function; for a vehicle that can merge into an empty lane, its own utility function is the difference between the revenue gained from purchasing empty lane space resources and the cost of purchasing empty lane space resources:
[0008]
[0009] In the formula, For set The Middle The length of the empty lane distance purchased by each vehicle; For set The Middle The current speed of each vehicle; The speed of the vehicle in front in the empty lane; This is the vehicle speed difference adjustment coefficient, which is a positive value. Its value represents the sensitivity of the vehicle or driver to changes in speed, and its dimension is the reciprocal of speed. For set The Middle The distance between a vehicle and the vehicle in front in its current lane is the value of the distance. The larger the value, the greater the distance between the vehicle and the vehicle in front in the current lane. In this case, the benefit of merging into an empty lane is lower, and vice versa. This indicates the price paid for the length of available lane space for a vehicle purchase unit.
[0010] In game theory, sets The Middle The more idle space a vehicle purchases, the greater its benefit in terms of traffic efficiency, but the greater the cost. This applies to a set of vehicles. The Middle The game optimization problem of individual vehicles is modeled as follows:
[0011]
[0012] st
[0013] In the formula, For set The Middle The minimum available parking space required for a vehicle is related to the length of the vehicle; the longer the vehicle, the more available parking space it needs to purchase. The larger the setting, the smaller it is;
[0014] For the leader in the game, with the total cost incurred by all participating vehicles in purchasing the available lane as its objective function, the leader's game optimization problem is modeled as maximizing the total cost incurred by all participating vehicles in purchasing the available lane:
[0015]
[0016] st
[0017] in, This represents the distance between available vehicles in an empty lane; the constraint is that the distance between available vehicles in an empty lane that can be sold should not exceed its maximum distance between available vehicles.
[0018] The optimization problems of followers and leaders together constitute the Stackelberg game. The two players, acting according to certain rules, can reach the final Stackelberg equilibrium: First, the optimal pricing per unit length of empty lane is obtained. Then, each vehicle is priced according to the optimal value per unit of available space. Determine the optimal vehicle distance for purchase.
[0019] Furthermore, for the empty lane, the objective function is to maximize the total cost incurred by all participating vehicles in purchasing empty lanes, expressed as:
[0020]
[0021] In the formula, For set The Middle The length of the empty lane distance purchased by each vehicle; This indicates the price for purchasing the length of empty lane space for a vehicle.
[0022] Furthermore, the constraints on the objective function of the vacant lane in the game problem include:
[0023] The total distance between vehicles that can merge into an empty lane should be less than or equal to the distance between vehicles in the empty lane. , is represented as:
[0024]
[0025] In the formula, For set The Middle The length of the empty lane distance purchased by each vehicle; This indicates the distance between empty vehicles in an empty lane.
[0026] Furthermore, the available vehicle spacing in the available lanes is used as a limited resource in the Stackelberg game to play among multiple vehicles that can merge into the available lanes.
[0027] Furthermore, for vehicles that can merge into an empty lane, maximizing their own utility function as their objective function is expressed as:
[0028]
[0029] In the formula, For set The Middle The length of the empty lane distance purchased by each vehicle; For set The Middle The current speed of each vehicle; The speed of the vehicle in front in the empty lane; The vehicle speed difference adjustment coefficient is a positive value, which represents the sensitivity of the vehicle or driver to changes in speed, and its dimension is the reciprocal of speed; For set The Middle The distance between a vehicle and the vehicle in front in its current lane. The larger the value, the greater the distance between the vehicle and the vehicle in front in its current lane, and the lower the benefit of merging into an empty lane. Conversely, the smaller the value, the higher the benefit. This indicates the price for purchasing the length of empty lane space for a vehicle.
[0030] Furthermore, This is a speed difference adjustment factor, reflecting the dynamic impact of speed differences on traffic efficiency benefits: when When, it indicates that the current lane is faster. Leading to the The benefit of a vehicle merging into an empty lane is lower; conversely, when When, it indicates that the current lane is slow and This led to the first The benefits of a vehicle merging into an empty lane are higher; Indicates the distance to the vehicle in front in the current lane. Smaller vehicles have a higher purchase clearance distance. The higher the gains, the stronger the willingness to change lanes through competitive game; conversely, the lower the gains, the weaker the willingness.
[0031] Furthermore, the constraints of the vehicle optimization problem incorporated into the game theory problem include:
[0032] Each vehicle merging into an empty lane must purchase a minimum distance between its lane and the available lane, expressed as:
[0033]
[0034] In the formula, For set The Middle The length of the empty lane distance purchased by each vehicle; For set The Middle The minimum available parking space that a vehicle needs to purchase.
[0035] The beneficial effects of this invention are as follows: This invention discloses a method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane based on Stackelberg game theory. Since traffic flow is not perfectly uniform, vehicles experience fluctuations during driving due to acceleration, deceleration, or lane changes, leading to temporary empty lanes in certain road sections or lanes. Furthermore, some drivers tend to maintain a large safety distance from the vehicle in front, or their slow reaction time or distracted driving may also result in excessively large distances, creating empty lanes between vehicles. Given a limited empty lane length, multiple vehicles from adjacent lanes attempt to merge into adjacent empty lanes through lane changes. Therefore, how to allocate the limited empty lane is a critical problem that urgently needs to be solved in intelligent transportation systems' lane-changing decision-making. To address this problem, a method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane based on Stackelberg game theory is presented. This method considers parameters such as current vehicle speed, distance to the vehicle in front, speed of the vehicle in the merging lane, and minimum safe distance for merging into an empty lane, aiming to provide a unique and efficient solution. It physically conforms to real-world application scenarios and can be effectively applied in engineering practice. Attached Figure Description
[0036] Figure 1 This is a scenario diagram illustrating a method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane, based on Stackelberg game theory, as proposed in this invention. Detailed Implementation
[0037] Now combined with the appendix Figure 1 The technical solutions of the present invention are further illustrated by the embodiments.
[0038] This embodiment proposes a method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane based on Stackelberg game theory, including:
[0039] Construct a transportation system in which a lane of the system has a length of Empty vehicle spacing, shared space between adjacent lanes Every vehicle can merge into an empty lane by changing lanes. The set of adjacent vehicles that can merge into an empty lane is defined as follows: ,like Figure 1 As shown.
[0040] It is worth noting that there are other vehicles in the adjacent lanes, but they cannot participate in the lane change operation due to insufficient space, such as not meeting the safe distance requirement for changing lanes from vehicles behind or in front of the empty lane. Additionally, because the empty lane has a limited clearance, it may not be possible for all vehicles to participate in the lane change. Each vehicle can merge into an empty lane, therefore Vehicles compete for the limited available lane spacing within an empty lane. Based on the above analysis, the key problem this invention aims to solve is how to effectively manage, model, and optimize the merging of vehicles from adjacent lanes into empty lanes.
[0041] Considering that vehicles in adjacent lanes that can merge into an empty lane all hope to improve their traffic efficiency by merging, a competitive relationship exists between multiple vehicles in adjacent lanes with different speeds merging into an empty lane, given the limited distance between empty lanes. The Steinberg game is a pure-strategy, non-cooperative sequential game model in economics. Based on the priority of actions and the completeness of information possessed, the participants can be divided into leaders and followers. Followers possess only partial information and act first; while leaders possess all the information of followers and act subsequently. When setting their game strategy, leaders need to consider the optimal responses of followers, while followers determine their optimal resource purchase amounts based on the leader's optimal decision. In this embodiment, since the empty lane possesses the game resources, it is considered the leader in the game model, while vehicles in adjacent lanes that can merge into the empty lane act as followers competing for limited resources.
[0042] In this example, each follower in the game mechanism purchases available lane space resources to improve the traffic efficiency of their vehicles. Therefore, the utility function of vehicles in adjacent lanes that can merge into available lanes for a follower consists of two parts: a payoff function and a cost function. The traffic efficiency gained from purchasing available lane space resources is expressed as the payoff function as follows:
[0043]
[0044] in, For set The Middle The length of the empty lane distance purchased by each vehicle; For set The Middle The current speed of each vehicle; The speed of the vehicle in front in the empty lane; The vehicle speed difference adjustment coefficient is a positive value, which represents the sensitivity of the vehicle or driver to changes in speed. Its dimension is the reciprocal of speed, and its value can be obtained through statistical characteristics of driving behavior. For set The Middle The distance between a vehicle and the vehicle in front in its current lane. The larger the value, the greater the distance between the vehicle and the vehicle in front in its current lane, and the lower the benefit of changing lanes. Conversely, the smaller the value, the higher the benefit. This represents the utility value of the payoff function.
[0045] therefore, This is a speed difference adjustment factor, reflecting the dynamic impact of speed differences on traffic efficiency benefits: when When, it indicates that the current lane is faster, thus This led to the first The benefits of a vehicle changing lanes are lower; conversely, when When, it indicates that the current lane is slow and Thus the first The benefits of changing lanes for individual vehicles are higher.
[0046] If the current lane is already very congested, that is It's very small, even if you only buy a small amount of available parking space. This ratio will also be larger, meaning that merging into an empty lane has a more significant improvement in traffic efficiency; conversely, if the current lane is already very spacious, i.e. It's very large, so even if you buy a larger one... The ratio is also not large, indicating that merging into an empty lane has little improvement on traffic efficiency. Therefore, vehicles with smaller following distances are more sensitive to additional empty lanes, and thus have a stronger willingness to change lanes through competitive play.
[0047] Based on the above analysis Represents a set The Middle Vacancy distance of vacant lanes purchased by individual vehicles The revenue function is chosen to be a logarithmic function, primarily due to diminishing marginal returns. This means that as the length of available parking spaces increases, the revenue generated by the vehicle gradually decreases. The logarithmic function... exist Since the time value is negative, the conventional method to ensure that the payoffs constructed by the players in a game are all positive is to add the number 1 to the variable, i.e., At this time, as long as , Hengzheng.
[0048] At the same time, the set The Middle The cost of purchasing available lane spacing resources for each vehicle is expressed as a cost function, as follows:
[0049]
[0050] in, This indicates the price for purchasing the length of empty lane space for a vehicle.
[0051] gather The Middle The game utility function for each vehicle is the difference between the payoff function and the cost function, expressed as:
[0052]
[0053] Therefore, in game theory, sets The Middle The more idle space a vehicle purchases, the greater its benefit in terms of traffic efficiency, but the greater the cost. This applies to sets... The Middle The game optimization problem of individual vehicles is modeled as follows:
[0054]
[0055] st
[0056] in, For set The Middle The minimum available vehicle distance for a vehicle purchase is related to the length of the vehicle; the longer the vehicle, the greater the available space. The larger the setting, the smaller it is. It's worth noting that... Should be greater than the set The Middle The length of each vehicle is designed to ensure a safe driving distance between the front and rear of the vehicle after it merges.
[0057] In the game theory, the leader, represented by the empty lane, improves its traffic efficiency by selling limited empty lane space to multiple competing vehicles. Therefore, its objective function is defined as the total cost incurred by all participating vehicles in purchasing empty lane space. Thus, the optimization problem for the leader in the game is modeled as follows:
[0058]
[0059] st
[0060] in, The empty lane represents the distance between empty vehicles; the objective function is the total revenue obtained from the empty lane game; the constraint is that the length of the empty lane that can be sold should not exceed the maximum value of its total empty vehicle distance.
[0061] The objective functions of both the follower and the leader constitute the Stackelberg game. By following certain rules and engaging in game action, the two sides can reach the final Stackelberg equilibrium, which represents the optimal pricing per unit length of empty lane space. Then, each vehicle is priced according to the optimal value per unit of available space. Determine the distance between the purchased vehicle and the available lane. If the distance is greater than the length of the vehicle itself, it can merge into the available lane; otherwise, it cannot merge into the available lane.
Claims
1. A method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane based on Stackelberg game theory, characterized in that, include: Construct a transportation system in which a lane has a length of Empty vehicle spacing, shared space between adjacent lanes A vehicle can merge into an empty lane by changing lanes. The set of vehicles that can merge into an empty lane from an adjacent lane is represented as follows: ; Based on a traffic system model with limited empty lane spacing and multiple vehicles merging into the empty lane from adjacent lanes, a Stackelberg game model is constructed. In the Stackelberg game model, the empty lane acts as the leader of the game model, while vehicles from adjacent lanes that can merge into the empty lane act as followers competing for limited resources. Each vehicle that can merge into an empty lane uses its own utility function as its objective function; for a vehicle that can merge into an empty lane, its own utility function is the difference between the revenue gained from purchasing empty lane space resources and the cost of purchasing empty lane space resources, i.e. In the formula, For set The Middle The length of the empty lane distance purchased by each vehicle; For set The Middle The current speed of each vehicle; The speed of the vehicle in front in the empty lane; This is the vehicle speed difference adjustment coefficient, which is a positive value. Its value represents the sensitivity of the vehicle or driver to changes in speed, and its dimension is the reciprocal of speed. For set The Middle The distance between a vehicle and the vehicle in front in its current lane is the value of the distance. The larger the value, the greater the distance between the vehicle and the vehicle in front in the current lane. In this case, the benefit of merging into an empty lane is lower, and vice versa. This indicates the price paid for the length of available lane space for a vehicle purchase unit. In game theory, sets The Middle The more idle space a vehicle purchases, the greater its benefit in terms of traffic efficiency, but the greater the cost. This applies to a set of vehicles. The Middle The game optimization problem involving individual vehicles is modeled as follows: s.t. In the formula, For set The Middle The minimum available parking space required for each vehicle; the longer the car, the more... The larger the setting, the smaller it is; For the leader in the game, with the total cost incurred by all participating vehicles in purchasing empty lanes as its objective function, the leader's game optimization problem is modeled as maximizing the total cost incurred by all participating vehicles in purchasing empty lanes. s.t. in, Indicates the distance between empty lanes; The constraint is that the distance between vehicles that can be sold in an empty lane should not exceed the maximum value of its empty vehicle distance; The optimization problems of followers and leaders together constitute the Stackelberg game. The two players, acting according to certain rules, can reach the final Stackelberg equilibrium: First, the optimal pricing per unit length of empty lane space is obtained. Then, each vehicle is priced according to the optimal value per unit of available space. Determine the optimal vehicle distance for purchase.
2. The method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane based on Stackelberg game theory, as described in claim 1, is characterized in that: For the leader of the game, the objective function is to maximize the total cost incurred by all participating vehicles in purchasing the available lane space, expressed as: In the formula, For set The Middle The length of the empty lane distance purchased by each vehicle; This indicates the price for purchasing the length of empty lane space for a vehicle.
3. The method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane based on Stackelberg game theory, as described in claim 1, is characterized in that: The constraints on the objective function of the empty lane in the game theory problem include: The total distance between vehicles that can merge into an empty lane should be less than or equal to the distance between vehicles in the empty lane. , represented as: In the formula, For set The Middle The length of the empty lane distance purchased by each vehicle; This indicates the distance between empty lanes.
4. The method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane based on Stackelberg game theory, as described in claim 1, is characterized in that: The available space between vehicles in an empty lane is used as a limited resource in a Stackelberg game to play among multiple vehicles that can merge into an empty lane.
5. The method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane based on Stackelberg game theory, as described in claim 1, is characterized in that: The objective function for vehicles that can merge into an empty lane is to maximize their own utility function, expressed as: In the formula, For set The Middle The length of the empty lane distance purchased by each vehicle; For set The Middle The current speed of each vehicle; The speed of the vehicle in front in the empty lane; The vehicle speed difference adjustment coefficient is a positive value, which represents the sensitivity of the vehicle or driver to changes in speed, and its dimension is the reciprocal of speed. For set The Middle The distance between a vehicle and the vehicle in front in its current lane. The larger the value, the greater the distance between the vehicle and the vehicle in front in its current lane, and the lower the benefit of merging into an empty lane. Conversely, the smaller the value, the higher the benefit. This indicates the price for purchasing the length of empty lane space for a vehicle.
6. The method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane based on Stackelberg game theory, as described in claim 5, is characterized in that: This is a speed difference adjustment factor, reflecting the dynamic impact of speed differences on traffic efficiency benefits: when When, it indicates that the current lane is faster. Leading to the The benefit of a vehicle merging into an empty lane is lower; conversely, when When, it indicates that the current lane is slow and This led to the first The benefits of a vehicle merging into an empty lane are higher; Indicates the distance to the vehicle in front in the current lane. Smaller vehicles have a higher purchase clearance distance. The higher the gains, the stronger the willingness to change lanes through competitive game; conversely, the lower the gains, the weaker the willingness.
7. The method for managing and optimizing the merging of multiple vehicles from adjacent lanes into an empty lane based on Stackelberg game theory, as described in claim 1, is characterized in that: The constraints of the optimization problem involving vehicles in a game theory problem include: Each vehicle merging into an empty lane must purchase a minimum clearance length that is less than the minimum clearance required for its vehicle, expressed as: In the formula, For set The Middle The length of the empty lane distance purchased by each vehicle; For set The Middle The minimum available parking space that a vehicle needs to purchase.