Edge computing unloading and transmitting power optimization method based on double-leader game

Abstract

The invention discloses an edge computing unloading and transmitting power optimization method based on a double-leader game, and belongs to the technical field of edge computing and wireless communication networks. A macro-micro heterogeneous three-layer network model is constructed, the model comprises a cloud computing layer, an edge layer and a user layer, the user layer is composed of a plurality of terminal user devices, the edge layer is composed of a plurality of micro base stations, a macro base station and a terminal user are connected through the micro base stations, and unloading of a computing task at the network edge by the terminal user is achieved. According to the method, a Stein Kolberg game model is constructed, a macro base station serves as a main leader, a micro base station serves as an auxiliary leader, and a user serves as a follower to participate in task unloading and power distribution decision making. According to the method, optimal allocation of computing resources and transmitting power can be realized under a game framework, so that the total energy consumption of the system is effectively reduced, and the network performance is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of edge computing and wireless communication networks, and specifically to an edge computing offloading and transmission power optimization method based on a dual-leader game. Background Art

[0002] With the rapid growth of Internet of Things (IoT) devices and the widespread adoption of 5G technology, Mobile Edge Computing (MEC), a key technology architecture, significantly reduces system processing latency and enhances computing efficiency by shifting computing resources from the cloud to the edge of the network. However, one of the main challenges facing MEC is the limited computing power of edge nodes. This makes it imperative to effectively allocate computing tasks and optimize resource utilization, especially when processing large numbers of tasks.

[0003] While current cloud computing architectures offer powerful computing capabilities, they can also lead to high latency and energy consumption when processing large volumes of tasks. These issues are particularly acute in time-critical applications. To address this, HetNets, a heterogeneous network structure combining macro base stations for widespread coverage with micro base stations for localized, high-density data processing, provide a more flexible infrastructure to support edge computing. However, in this network environment, efficiently offloading computing tasks and properly allocating transmit power directly impact the system's energy efficiency and performance.

[0004] Existing task offloading and power optimization methods mostly focus on a single aspect of the problem, failing to fully consider computing resource pricing, user offloading decisions, and the game interactions between multiple parties, resulting in inefficient resource utilization. Furthermore, resource competition and signal interference between users make it difficult for existing power optimization methods to achieve a global optimal solution, further hindering system performance. Therefore, we propose an edge computing offloading and transmit power optimization method based on a dual-leader game to address these issues. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, the present invention provides an edge computing offloading and transmission power optimization method based on dual-leader game, which solves the problems raised in the above background technology.

[0006] The edge computing offloading and transmission power optimization method based on dual-leader game of the present invention includes the following steps: S1: Build a macro-micro heterogeneous three-layer network model. This model includes a cloud computing layer, an edge layer, and a user layer. The user layer consists of multiple end-user devices, and the edge layer consists of multiple micro base stations. Micro base stations connect macro base stations to end users, enabling end users to offload computing tasks at the network edge. S2: Based on the macro-micro heterogeneous three-layer network model, a low-energy computing task offloading model is constructed. Users divide the task into three parts according to the computing task requirements and device performance: the first part of the task is calculated locally, the second part of the task is offloaded to the micro base station, and the third part of the task is offloaded to the macro base station. For these three computing modes, computing delay and energy consumption models are established, and a joint optimization problem of task offloading, computing resource allocation, and communication resource allocation is constructed. The optimization goal is to minimize the total energy consumption of the system while meeting the maximum delay constraint of the task. To reduce the complexity of the optimization problem, the block coordinate descent method is used to decompose the optimization problem into two sub-problems: Sub-problem 1: Optimize the task offloading strategy and computing resource allocation under given communication resources; Sub-problem 2: Optimize the transmission power resource allocation when the task offloading and computing resource allocation have been determined. S3: For sub-problem 1, we construct a task offloading and computing resource allocation strategy based on a dual-leader game. By building a Stan-Kohlberg game framework, the macro base station serves as the primary leader, the micro base station serves as the secondary leader, and the end user serves as the follower. The user determines the task offloading ratio and computing resource requirements based on the base station's pricing strategy. We achieve optimal resource allocation through Nash equilibrium and develop an optimal pricing algorithm to optimize resource utilization and computing offloading efficiency. S4: For sub-problem 2, a transmit power optimization model is constructed. While ensuring that the data transmission rate meets the maximum latency constraint of the task, each user's transmit power is optimized to minimize transmission energy consumption. The Lagrangian dual method and subgradient method are used to solve the problem, and a game-based optimal response algorithm is developed to obtain the optimal transmit power allocation plan for each user within a limited number of iterations. S5: Based on the optimization of computational offloading, the base station combines a dynamic optimal pricing mechanism to adjust the allocation scheme of computing resources and communication resources to adapt to changes in the network environment, further optimize system energy consumption and computational offloading efficiency, and obtain the optimal computational offloading decision and resource allocation strategy. Furthermore, in one embodiment of the present invention, the cloud computing layer in S1 includes a macro base station equipped with a cloud server, which is responsible for remote centralized processing of computing tasks; the edge layer is composed of multiple micro base stations, forming The micro base station is responsible for receiving, processing or forwarding user tasks, and is connected to the macro base station through high-speed optical fiber for efficient data transmission; the user layer includes Terminal user devices are sensors, smart phones, and other devices with computing needs. Users offload computing tasks through micro base stations or macro base stations. The first cell in the micro base station range A user is defined as ,in is a collection of micro base stations, For each cell user set.

[0007] Furthermore, in one embodiment of the present invention, a low-energy offloading model is constructed in S2 based on the macro-micro network three-layer model. The total energy consumption of the system is minimized through task offloading decision-making, computing resource allocation, and transmission power allocation. The specific steps for modeling this problem are as follows: S2.1: Make fine-grained task offloading decisions and assign user computing tasks to It is divided into three parts; the first part is calculated on the local device; the second part is calculated in proportion Unload to the micro base station in the same cell for calculation; the third part is calculated by ratio Offload to macro base station for calculation; the proportion of unoffloaded tasks meets ; S2.2: Calculate local latency and energy consumption; Local computing latency Expressed as: ; in, The local computing power of the user's device, To calculate the number of CPU cycles required; Local computing energy consumption Expressed as: ; in, is the effective switch capacitance coefficient; S2.3: Calculate the latency and energy consumption of micro and macro base stations; Computational delay of task offloading to micro base stations Expressed as: ; in, The computing resources allocated to the tasks for the micro base station; the computing tasks are offloaded to the energy consumption of the micro base station ; Computational latency of task offloading to macro base stations Expressed as: ; in, Computing resources allocated to macro base stations; energy consumption of computing tasks offloaded to macro base stations ; S2.4: Computational latency based on task offloading to macro base stations and transmission energy consumption , calculate the total delay of task execution respectively Total energy consumption : ; ; in, is the maximum value; S2.5: Establish a system total energy consumption optimization problem model to minimize the system total energy consumption while ensuring network resource constraints and performance constraints; the task offloading ratio should be between 0 and 1, and the sum of the ratios of tasks offloaded to micro base stations and macro base stations should not be greater than 1; the computing resources allocated by the base station to the task are positive numbers, and the sum of the computing resources provided for all tasks does not exceed the maximum computing resources of the base station; the user transmission power does not exceed the maximum transmission power; the total delay of task execution shall not exceed the maximum tolerable delay .

[0008] Furthermore, in one embodiment of the present invention, the specific steps of S3 are as follows: S3.1: Construct a dual-leader game model. The macro base station acts as the primary leader, determining the pricing strategy for computing resources and influencing the resource allocation strategy of the micro base station. The micro base station acts as the secondary leader, setting the pricing of its own computing resources based on the macro base station's pricing strategy. The end user acts as a follower, determining the task offloading ratio based on the base station's pricing strategy, calculating the resource requirements, and calculating the task execution cost, including the costs of local computing, micro base station computing, and macro base station computing. S3.2: Establish a utility function model for all parties involved in the game, minimize the total cost of task calculation and transmission, and establish a user utility function: ; in, and The unit price of computing resources for micro and macro base stations, respectively, The amount of data for the calculation task, is the user's transmission power and the data transmission rate between the user and the micro base station for: ; in, is the bandwidth, is the transmit power, is the channel gain between the user and the micro base station, is the power spectral density of Gaussian white noise, For the community except the Other users of users, For the exception of other micro base stations of micro base stations, For the In the community The transmission power of each user, For the In the community User and The channel gain between micro base stations, and Similarly, the main considerations are the signal interference from other users in the same cell and the signal interference from users in other cells; Based on macro base station pricing, micro base stations optimize their own computing resource pricing strategy and maximize utility: ; As the main leader, the macro base station has the following functions: ; ; S3.3: Constructing a Stan-Kohlberg game model with two leaders and multiple followers , The user's uninstall policy set, Pricing strategy and computing resource allocation set for micro base stations, Calculate resource prices for micro base stations, The computing resources allocated to the tasks for the micro base station, is the pricing strategy and computing resource allocation set for the macro base station, Calculate resource prices for macro base stations, Allocate computing resources to tasks for macro base stations; solve task offloading and computing resource allocation strategies based on Nash equilibrium; solve the game equilibrium through backward induction, splitting the game problem into multi-follower subgames and dual-leader subgames; prove that the game model satisfies strict potential game conditions and that the strategy space belongs to a bounded closed set in Euclidean space, ensuring the existence of a unique Nash equilibrium point for the game; use backward induction to gradually obtain the optimal solution to the game; users, micro base stations, and macro base stations all choose the optimal strategy within their respective strategy spaces, achieving system stability, and no player can improve their utility by changing their strategy; Prove that the utility functions of the primary leader and the secondary leader satisfy the properties of concave functions; the strategy space of the two-leader subgame belongs to a bounded closed set in Euclidean space; when the leader adopts the only optimal strategy set When , the two-leader subgame reaches the Nash equilibrium state; The unloading strategy in the multi-follower subgame is uniquely determined, that is, the optimal unloading strategy ; Two-leader and multiple-follower Stan-Kohlberg game There is a unique Nash equilibrium point; and when the game Adopting the optimal strategy set When , Nash equilibrium is reached; S3.4: Game optimization iterative solution: macro base stations and micro base stations optimize pricing parameters based on system revenue, adjust computing resource prices, and formulate the best pricing algorithm for iterative optimization so that the computing resource allocation plan meets the optimization goal; micro base stations and macro base stations adjust computing resource prices through dynamic pricing to maximize revenue; users continuously adjust the offloading ratio during the base station pricing change process to minimize computing and transmission costs; based on the game equilibrium solution, a stable resource pricing strategy is finally determined, and an optimized task offloading and computing resource allocation plan is formed.

[0009] Furthermore, in one embodiment of the present invention, the specific steps of S4 are as follows: S4.1: Construct a transmission power optimization model based on the transmission power of each user. Perform fine-grained optimization analysis to ensure that the data transmission rate meets the maximum delay constraint and minimizes the transmission energy consumption. Since all power resources in the macro and micro networks are independent and do not conflict with each other, the optimization problem is decomposed into Independent power resource subproblems are solved one by one using the Dinkelbach method; transmission energy consumption is reduced while meeting data transmission rate and maximum delay constraints; the model considers the proportion of user offload tasks and further optimizes transmission energy consumption by adjusting the transmit power; S4.2: Based on the system model, construct transmission delay and energy consumption constraints; enable user tasks to be completed within the maximum tolerable delay Completed within: ; Among them, the transmission energy consumption is calculated as: ; S4.3: Multiple user devices in the system will offload tasks at the same time. The power optimization problem needs to be solved using the Lagrange dual method and the subgradient method to control the computational complexity and formulate the optimal power allocation plan. is a non-negative parameter. By solving the Karosh-Kuhn-Tucker condition, the optimal transmit power allocation is obtained: ; in, and are different Lagrange multipliers respectively; S4.4: Develop a game-based optimal response algorithm, and gradually adjust the power allocation strategy under the energy consumption feedback mechanism until the system energy consumption converges to the optimal level while meeting the data transmission rate and delay constraints.

[0010] Furthermore, in one embodiment of the present invention, the specific steps of S5 are as follows: S5.1: Dynamically adjust computing resource pricing. Within the Stan-Kohlberg game framework, macro and micro base stations, as computing resource providers, dynamically adjust their pricing strategies based on the computing resource demands of user devices. Based on the optimal pricing algorithm, macro and micro base stations adjust prices, influencing user task offloading decisions and adjusting the task offloading ratio. S5.2: Dynamic iteration is performed in conjunction with transmit power optimization. After base station pricing is adjusted, users adjust their task offload ratios based on the latest pricing strategy and optimize computing resource allocation. A game-based best response algorithm is used to dynamically optimize computing resource pricing, optimal task offload ratios, and optimal transmit power. S5.3: Iterate optimization until the system energy consumption converges to the optimal value, and set the maximum number of iterations In each round of iteration, the computing resource pricing is updated, the optimal task offloading strategy is calculated, the transmission power is optimized according to the task offloading strategy, the current total energy consumption of the system is calculated, and it is judged whether convergence is achieved; if the convergence conditions are met, the final optimal strategy is output, otherwise the iteration continues until the minimum total energy consumption is achieved. Compared with the existing technology, the present invention provides an edge computing offloading and transmission power optimization method based on dual-leader game, which has the following beneficial effects: The present invention implements a low-energy, efficient resource allocation strategy by constructing a macro-micro heterogeneous three-layer network model consisting of macro base stations, micro base stations, and end users. First, the game theory method and block coordinate descent method are used to decompose the complex optimization problem into two sub-problems: task offloading, computing resource allocation, and transmit power optimization. The optimal solution is gradually solved to minimize the total energy consumption of the system. Secondly, by constructing a transmit power optimization model and introducing the subgradient method and Lagrange dual method, the data transmission rate is ensured to meet the maximum latency requirements, achieving low latency and stable computing of user computing tasks. At the same time, by combining the base station pricing strategy with the game response algorithm, the base station can dynamically adjust prices based on energy consumption, encourage users to reasonably offload tasks, and effectively improve resource utilization efficiency. The strategy proposed in the present invention supports multi-user and dynamic task demand changes, and is particularly suitable for heterogeneous network environments. It realizes resource collaborative optimization through the game model, has strong adaptability, effectively reduces the energy consumption of the edge computing network, improves network performance, and has broad application prospects in edge computing. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 A flowchart of the edge computing offloading and transmission power optimization method based on dual-leader game provided by the present invention; Figure 2 A schematic diagram of the structure of the edge computing offloading system for establishing a macro-micro heterogeneous three-layer network provided by the present invention; Figure 3 Schematic diagram of the dual-leader Stan-Kohlberg game framework structure provided by the present invention. DETAILED DESCRIPTION

[0012] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0013] Example like Figure 1-3 As shown, an edge computing offloading and transmission power optimization method based on dual-leader game proposed in one embodiment of the present invention includes the following steps: S1: Construct a macro-micro heterogeneous three-layer network model. The macro-micro heterogeneous three-layer network model includes a cloud computing layer, an edge layer, and a user layer. The user layer is composed of multiple end-user devices, and the edge layer is composed of multiple micro base stations. The macro base stations are connected to the end users through the micro base stations, enabling the end users to offload computing tasks at the edge of the network.

[0014] The cloud computing layer includes macro base stations equipped with cloud servers, which are responsible for remote centralized processing of computing tasks; the edge layer is composed of multiple micro base stations, forming a The micro base station is responsible for receiving, processing or forwarding user tasks, and is connected to the macro base station through high-speed optical fiber for efficient data transmission; the user layer includes Terminal user devices are sensors, smart phones, and other devices with computing needs. Users offload computing tasks through micro base stations or macro base stations. The first cell in the micro base station range A user is defined as ,in is a collection of micro base stations, For each cell user set.

[0015] Each microcell service coverage area has End users with computing needs, including but not limited to sensors, smartphones, and other devices, are connected to micro base stations in the edge layer via high-speed optical fiber. This ensures optimized data transmission paths, reduces energy consumption, and improves resource utilization. Due to the hardware limitations of edge devices, micro base stations have limited computing resources. In contrast, macro base stations are equipped with more abundant computing resources to meet a wider range of data processing needs.

[0016] The user's computing tasks can be offloaded to micro base stations and macro base stations for processing. The tasks in , For computing tasks The number of CPU cycles required, For users Computational tasks The amount of data, To calculate the number of CPU cycles required for each bit of data, The maximum tolerable delay for task execution.

[0017] S2: Based on the macro-micro heterogeneous three-layer network model, a low-energy computing task offloading model is constructed.

[0018] S2.1: Make fine-grained task offloading decisions and assign user computing tasks to It is divided into three parts; the first part is calculated on the local device; the second part is calculated in proportion Unload to the micro base station in the same cell for calculation; the third part is calculated by ratio Offload to macro base station for calculation; the proportion of unoffloaded tasks meets ; S2.2: Calculate local latency and energy consumption; Local computing latency Expressed as: ; in, The local computing power of the user's device, To calculate the number of CPU cycles required; Local computing energy consumption Expressed as: ; in, is the effective switch capacitance coefficient; S2.3: Calculate the latency and energy consumption of micro and macro base stations; Computational delay of task offloading to micro base stations Expressed as: ; in, The computing resources allocated to the tasks for the micro base station; the computing tasks are offloaded to the energy consumption of the micro base station ; Accordingly, the computing task is offloaded to the micro base station energy consumption It can be expressed as: ; Computational latency of task offloading to macro base stations Expressed as: ; in, Computing resources allocated to macro base stations; energy consumption of computing tasks offloaded to macro base stations ; Accordingly, the energy consumption of offloading computing tasks to macro base stations It can be expressed as: ; In a macro-micro network environment, consider the data transmission rate between users and micro base stations , which can be expressed as: ; in, is the bandwidth, is the transmit power, is the channel gain between the user and the micro base station, is the power spectral density of Gaussian white noise, For the community except the Other users of users, For the exception of other micro base stations of micro base stations, For the In the community The transmission power of each user, For the In the community User and The channel gain between micro base stations, and Similarly, the main considerations are the signal interference from other users in the same cell and the signal interference from users in other cells; Considering that the micro base station and the macro base station are connected by high-speed optical cables, their transmission delay and energy consumption are relatively low, and their impact on the offloading decision is small and can be ignored. and transmission energy consumption Can be expressed as: ; ; S2.4: Computational latency based on task offloading to macro base stations and transmission energy consumption , calculate the total delay of task execution respectively Total energy consumption : ; ; in, is the maximum value; S2.5: The ultimate goal of the optimization problem is to minimize the total energy consumption of the system while considering the resource limitations and performance constraints in the network. It can be specifically expressed as: ; in, is the minimum value, optimization problem Constraints in to Indicates that the task offloading ratio should be between 0 and 1, and the sum of the ratios of tasks offloaded to micro base stations and macro base stations should not be greater than 1, ensuring that the task offloading ratio is within a reasonable range. to Ensure that the computing resources allocated by the base station to the task are positive, and the total computing resources provided for all tasks does not exceed the maximum computing resources of the base station. Ensure that the user's transmit power does not exceed the maximum transmit power. Indicates that the total task execution delay must not exceed the maximum tolerated delay.

[0019] Given the optimization problem There are nonlinear coupling relationships between multiple variables in the problem, and direct solution has certain complexity. To simplify the problem, the block coordinate descent method is used to decompose the original optimization problem into two more tractable sub-problems: ; Subproblems It is to optimize the task offloading strategy and computing resource allocation under the condition of fixed user transmission power, and mainly focuses on how to efficiently coordinate computing resources and offloading decisions under the conditions of given communication resources.

[0020] ; Subproblems When the task offloading strategy and computing resource allocation have been determined, we focus on optimizing the transmission power and explore how to efficiently allocate communication resources under a fixed computing offloading framework.

[0021] S3: For sub-problem 1, a task offloading and computing resource allocation strategy based on a dual-leader game is constructed. By constructing a Stan-Kohlberg game framework, the macro base station serves as the primary leader, the micro base station serves as the secondary leader, and the end user serves as the follower. The user determines the task offloading ratio and computing resource demand based on the base station's pricing strategy. The optimal resource allocation is achieved through Nash equilibrium, and an optimal pricing algorithm is developed to optimize resource utilization and computing offloading efficiency. The specific steps are as follows: S3.1: Construct a dual-leader game model, a multi-follower Stan-Kohlberg game model with a macro base station as the primary leader and a micro base station as the secondary leader. Users act as followers, deciding their task offloading strategy based on the base station's pricing policy and paying the corresponding fees. The key challenge of this model lies in how to maximize the utility of each player, which relies on players making positive strategic adjustments based on each other's strategic feedback.

[0022] S3.2: Establish a utility function model for all parties involved in the game, minimize the total cost of task calculation and transmission, and establish a user utility function: ; in, and The unit price set for computing resources of micro and macro base stations respectively; Based on macro base station pricing, micro base stations optimize their own computing resource pricing strategy and maximize utility: ; As the main leader, the macro base station has the following functions: ; ; S3.3: Constructing a Stan-Kohlberg game model with two leaders and multiple followers , The user's uninstall policy set, Pricing strategy and computing resource allocation set for micro base stations, Calculate resource prices for micro base stations, The computing resources allocated to the tasks for the micro base station, is the pricing strategy and computing resource allocation set for the macro base station, Calculate resource prices for macro base stations, Computing resources allocated to tasks for macro base stations.

[0023] Using the reverse induction method, the game model is The game is decomposed into a multi-follower subgame and a dual-leader subgame, and the existence of Nash equilibria in each subgame is proved. First, the offloading strategy of the followers is solved, and then the pricing strategy and computing resource allocation of the leader are solved.

[0024] Under the condition of a fixed leader strategy, the concept of strict potential game is used to prove the existence of Nash equilibrium in the multi-follower unloading subgame.

[0025] User's utility function It can represent: ; in, for The total energy consumption of the system when there is no task demand. Uninstall strategy is determined by Changes to When , the value of the user utility function changes to: ; because for There is no need to uninstall the task, and it will not affect other users. We can get: ;

[0026] Combining the above two formulas, we get: ; The potential function can accurately quantify the impact of any unilateral strategy change adopted by any game participant on the utility of all users. Satisfy the characteristics of the potential function and define the potential function for: ;

[0027] Further obtain: ; According to the above analysis, the multi-follower subgame constitutes a potential game. Since the strategy set of the game belongs to a bounded closed set in Euclidean space, it can be concluded that the multi-follower subgame has at least one Nash equilibrium point, which can be expressed as: ; The optimal uninstallation strategy for users is solved using the subgradient iterative method, which is specifically expressed as: ; Using the subgradient method The update expression of the uninstallation strategy in the iteration is: ; ; in, and The corresponding uninstall strategies are The step size of the iteration, .

[0028] Prove that there is a unique Nash equilibrium point for the two-leader subgame.

[0029] After each round of iteration, the user provides the optimal offloading strategy to the service provider. When the user's offloading strategy is known, the utility function of the micro base station is , ask about The first and second order partial derivatives of : ; ; From the above formula, we can see that It's about is a concave function, so there exists To obtain the maximum value. about The first-order partial derivative of is zero, so we get: ; also, about The first-order partial derivative of is greater than zero, the utility value and Therefore, for any pricing strategy , we can always get the optimal computing resource allocation When micro base stations adopt the optimal pricing strategy hour, Get maximum utility.

[0030] beg about The first and second partial derivatives of are: ; ; Setting the first-order partial derivative to zero gives the Nash equilibrium point: ; Similarly, when the macro base station adopts the optimal pricing strategy hour, Get the maximum value.

[0031] From this we can see that the utility functions of the main leader and the deputy leader satisfy the characteristics of concave functions. The strategy space of the two-leader subgame belongs to a bounded closed set in Euclidean space. When the leader adopts the only optimal strategy set When , the two-leader subgame reaches the Nash equilibrium. Proof completed.

[0032] At this point, the unloading strategy in the multi-follower subgame is uniquely determined, that is, the optimal unloading strategy Therefore, the two-leader multi-follower Stan-Kohlberg game There is a unique Nash equilibrium point. And when the game Adopting the optimal strategy set When , Nash equilibrium is reached.

[0033] S3.4: Game optimization iterative solution. Macro and micro base stations optimize pricing parameters based on system revenue, adjust computing resource prices, and develop an optimal pricing algorithm for iterative optimization. Lower base station pricing encourages users to offload tasks to it, while excessively high pricing discourages users from offloading. Therefore, base stations continuously adjust their pricing strategies within a reasonable range based on their own revenue, ensuring that the computing resource allocation plan meets the optimization goal. Micro and macro base stations adjust computing resource prices through dynamic pricing to maximize revenue. Users continuously adjust their offloading ratios as base station pricing changes to minimize computing and transmission costs. Based on the game equilibrium solution, a stable resource pricing strategy is ultimately determined, resulting in an optimized task offloading and computing resource allocation plan.

[0034] S4: For sub-problem 2, a transmit power optimization model is constructed. While ensuring that the data transmission rate meets the maximum delay constraint of the task, the transmit power of each user is optimized to minimize transmission energy consumption. The Lagrangian dual method and subgradient method are used to solve the problem, and a game-based optimal response algorithm is formulated to obtain the optimal transmit power allocation plan for each user with a limited number of iterations. The specific steps are as follows: S4.1: Construct a transmission power optimization model based on the transmission power of each user. Fine-grained decomposition into A separate single power resource subproblem: ; According to the Dinkelbach method, the optimal solution of the above equation can be obtained when the following relationship is satisfied: ; in, for The minimum value of .

[0035] S4.2: Based on the system model, construct transmission delay and energy consumption constraints; enable user tasks to be completed within the maximum tolerable delay Completed within: ; in, is the noise power, is the interference term, The amount of data for the calculation task, is the bandwidth, is the channel gain; the transmission energy consumption is calculated as: ; set up is a non-negative parameter, constraining the single power resource subproblem Rewritten as an equivalence constraint , converted into a parameter optimization problem: ;

[0036] To solve the above equation, we first need to Solve the problem with the value of , and then use the obtained Value pair given The value is updated and the above two steps are repeated until the optimal solution is obtained.

[0037] S4.3: Use the Lagrangian dual method and subgradient method to solve this problem. The Lagrangian function can be expressed as: ; in, , which correspond to the constraints in the parameter optimization problem and constraints The dual problem of parameter optimization can be expressed as: ; Since the parameter optimization problem is convex and satisfies the Slater condition, the dual problem has strong duality. Using the Karosh-Kuhn-Tucker condition, the Lagrangian function Ask about By taking the first-order partial derivative of and setting its first-order derivative to zero, we can get the closed-form solution of the power resource allocation strategy: ;

[0038] The subgradient of the Lagrange multiplier can be expressed as: ; ; Using the subgradient method The Lagrange multiplier in the iteration can be updated as: ; ; in, and They correspond to the Lagrange multipliers in the The step size of the iteration. When the subgradient iteration algorithm converges, the optimal Lagrange multiplier solution can be obtained. Substituting it into the closed-form solution of the power resource allocation strategy, the optimal power resource allocation strategy can be obtained .

[0039] S4.4: Develop a game-based optimal response algorithm, and gradually adjust the power allocation strategy under the energy consumption feedback mechanism until the system energy consumption converges to the optimal level while meeting the data transmission rate and delay constraints.

[0040] S5: Based on the computation offloading optimization, the base station uses a dynamic optimal pricing mechanism to adjust the allocation of computing and communication resources to adapt to changes in the network environment, further optimize system energy consumption and computation offloading efficiency, and arrive at the optimal computation offloading decision and resource allocation strategy. The specific steps are as follows: S5.1: Dynamically adjust computing resource pricing. Within the Stan-Kohlberg game framework, macro and micro base stations, as computing resource providers, dynamically adjust their pricing strategies based on the computing resource demands of user devices. Based on the optimal pricing algorithm, macro and micro base stations adjust prices, influencing user task offloading decisions and adjusting the task offloading ratio. S5.2: Dynamic iteration is performed in conjunction with transmit power optimization. After base station pricing is adjusted, users adjust their task offload ratios based on the latest pricing strategy and optimize computing resource allocation. A game-based best response algorithm is used to dynamically optimize computing resource pricing, optimal task offload ratios, and optimal transmit power. S5.3: Iterate optimization until the system energy consumption converges to the optimal value, and set the maximum number of iterations In each round of iteration, the computing resource pricing is updated, the optimal task offloading strategy is calculated, the transmission power is optimized according to the task offloading strategy, the current total energy consumption of the system is calculated, and it is judged whether convergence is achieved; if the convergence conditions are met, the final optimal strategy is output, otherwise the iteration continues until the minimum total energy consumption is achieved.

[0041] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. The edge computing offloading and transmission power optimization method based on dual-leader game is characterized by: The steps include: S1: Build a macro-micro heterogeneous three-layer network model. This model includes a cloud computing layer, an edge layer, and a user layer. The user layer consists of multiple end-user devices, and the edge layer consists of multiple micro base stations. Micro base stations connect macro base stations to end users, enabling end users to offload computing tasks at the network edge. S2: Based on the macro-micro heterogeneous three-layer network model, a low-energy computing task offloading model is constructed. Users divide the task into three parts according to the computing task requirements and device performance: the first part of the task is calculated locally, the second part of the task is offloaded to the micro base station, and the third part of the task is offloaded to the macro base station. For these three computing modes, computing delay and energy consumption models are established, and a joint optimization problem of task offloading, computing resource allocation, and communication resource allocation is constructed. The optimization goal is to minimize the total energy consumption of the system while meeting the maximum delay constraint of the task. To reduce the complexity of the optimization problem, the block coordinate descent method is used to decompose the optimization problem into two sub-problems: Sub-problem 1: Optimize the task offloading strategy and computing resource allocation under given communication resources; Sub-problem 2: Optimize the transmission power resource allocation when the task offloading and computing resource allocation have been determined. S3: For sub-problem 1, we construct a task offloading and computing resource allocation strategy based on a dual-leader game. By building a Stan-Kohlberg game framework, the macro base station serves as the primary leader, the micro base station serves as the secondary leader, and the end user serves as the follower. The user determines the task offloading ratio and computing resource requirements based on the base station's pricing strategy. We achieve optimal resource allocation through Nash equilibrium and develop an optimal pricing algorithm to optimize resource utilization and computing offloading efficiency. S4: For sub-problem 2, a transmit power optimization model is constructed. While ensuring that the data transmission rate meets the maximum latency constraint of the task, each user's transmit power is optimized to minimize transmission energy consumption. The Lagrangian dual method and subgradient method are used to solve the problem, and a game-based optimal response algorithm is developed to obtain the optimal transmit power allocation plan for each user within a limited number of iterations. S5: Based on the optimization of computational offloading, the base station combines a dynamic optimal pricing mechanism to adjust the allocation scheme of computing resources and communication resources to adapt to changes in the network environment, further optimize system energy consumption and computational offloading efficiency, and obtain the optimal computational offloading decision and resource allocation strategy.

2. The edge computing offloading and transmission power optimization method based on dual-leader game according to claim 1 is characterized in that: The cloud computing layer in S1 includes a macro base station equipped with a cloud server, which is responsible for remote centralized processing of computing tasks; the edge layer is composed of multiple micro base stations, forming The micro base station is responsible for receiving, processing or forwarding user tasks, and is connected to the macro base station through high-speed optical fiber for efficient data transmission; the user layer includes Terminal user devices are sensors, smart phones, and other devices with computing needs. Users offload computing tasks through micro base stations or macro base stations. The first cell in the micro base station range A user is defined as ,in is a collection of micro base stations, For each cell user set.

3. The edge computing offloading and transmission power optimization method based on dual-leader game according to claim 1 is characterized in that: In S2, a low-energy offloading model is constructed based on the macro-micro network three-layer model. The total energy consumption of the system is minimized through task offloading decision-making, computing resource allocation, and transmission power allocation. The specific steps for modeling this problem are as follows: S2.1: Make fine-grained task offloading decisions and assign user computing tasks to It is divided into three parts; the first part is calculated on the local device; the second part is calculated in proportion Unload to the micro base station in the same cell for calculation; the third part is calculated by ratio Offload to macro base station for calculation; the proportion of unoffloaded tasks meets ; S2.2: Calculate local latency and energy consumption; Local computing latency Expressed as: ； in, The local computing power of the user's device, To calculate the number of CPU cycles required; Local computing energy consumption Expressed as: ； in, is the effective switch capacitance coefficient; S2.3: Calculate the latency and energy consumption of micro and macro base stations; Computational delay of task offloading to micro base stations Expressed as: ； in, The computing resources allocated to the tasks for the micro base station; the computing tasks are offloaded to the energy consumption of the micro base station ; Computational latency of task offloading to macro base stations Expressed as: ； in, Computing resources allocated to macro base stations; energy consumption of computing tasks offloaded to macro base stations ; S2.4: Computational latency based on task offloading to macro base stations and transmission energy consumption , calculate the total delay of task execution respectively Total energy consumption : ； ； in, is the maximum value; S2.5: Establish a system total energy consumption optimization problem model to minimize the system total energy consumption while ensuring network resource constraints and performance constraints; the task offloading ratio should be between 0 and 1, and the sum of the ratios of tasks offloaded to micro base stations and macro base stations should not be greater than 1; the computing resources allocated by the base station to the task are positive numbers, and the sum of the computing resources provided for all tasks does not exceed the maximum computing resources of the base station; the user transmission power does not exceed the maximum transmission power; the total delay of task execution shall not exceed the maximum tolerable delay .

4. The edge computing offloading and transmission power optimization method based on dual-leader game according to claim 1 is characterized in that: The specific steps of S3 are as follows: S3.1: Construct a dual-leader game model. The macro base station acts as the primary leader, determining the pricing strategy for computing resources and influencing the resource allocation strategy of the micro base station. The micro base station acts as the secondary leader, setting the pricing of its own computing resources based on the macro base station's pricing strategy. The end user acts as a follower, determining the task offloading ratio based on the base station's pricing strategy, calculating the resource requirements, and calculating the task execution cost, including the costs of local computing, micro base station computing, and macro base station computing. S3.2: Establish a utility function model for all parties involved in the game, minimize the total cost of task calculation and transmission, and establish a user utility function: ； in, and The unit price of computing resources for micro and macro base stations, respectively, The amount of data for the calculation task, is the user's transmission power and the data transmission rate between the user and the micro base station for: ； in, is the bandwidth, is the transmit power, is the channel gain between the user and the micro base station, is the power spectral density of Gaussian white noise, For the community except the Other users of users, For the exception of other micro base stations of micro base stations, For the In the community The transmission power of each user, For the In the community User and The channel gain between micro base stations, and Similarly, the main considerations are the signal interference from other users in the same cell and the signal interference from users in other cells; Based on macro base station pricing, micro base stations optimize their own computing resource pricing strategy and maximize utility: ； As the main leader, the macro base station has the following functions: ; ； S3.3: Constructing a Stan-Kohlberg game model with two leaders and multiple followers , The user's uninstall policy set, Pricing strategy and computing resource allocation set for micro base stations, Calculate resource prices for micro base stations, The computing resources allocated to the tasks for the micro base station, is the pricing strategy and computing resource allocation set for the macro base station, Calculate resource prices for macro base stations, Allocate computing resources to tasks for macro base stations; solve task offloading and computing resource allocation strategies based on Nash equilibrium; solve the game equilibrium through backward induction, splitting the game problem into multi-follower subgames and dual-leader subgames; prove that the game model satisfies strict potential game conditions and that the strategy space belongs to a bounded closed set in Euclidean space, ensuring the existence of a unique Nash equilibrium point for the game; use backward induction to gradually obtain the optimal solution to the game; users, micro base stations, and macro base stations all choose the optimal strategy within their respective strategy spaces, achieving system stability, and no player can improve their utility by changing their strategy; Prove that the utility functions of the primary leader and the secondary leader satisfy the properties of concave functions; the strategy space of the two-leader subgame belongs to a bounded closed set in Euclidean space; when the leader adopts the only optimal strategy set When , the two-leader subgame reaches the Nash equilibrium state; The unloading strategy in the multi-follower subgame is uniquely determined, that is, the optimal unloading strategy ; Two-leader and multiple-follower Stan-Kohlberg game There is a unique Nash equilibrium point; and when the game Adopting the optimal strategy set When , Nash equilibrium is reached; S3.4: Game optimization iterative solution: macro base stations and micro base stations optimize pricing parameters based on system revenue, adjust computing resource prices, and formulate the best pricing algorithm for iterative optimization so that the computing resource allocation plan meets the optimization goal; micro base stations and macro base stations adjust computing resource prices through dynamic pricing to maximize revenue; users continuously adjust the offloading ratio during the base station pricing change process to minimize computing and transmission costs; based on the game equilibrium solution, a stable resource pricing strategy is finally determined, and an optimized task offloading and computing resource allocation plan is formed.

5. The edge computing offloading and transmission power optimization method based on dual-leader game according to claim 1 is characterized in that: The specific steps of S4 are as follows: S4.1: Construct a transmission power optimization model based on the transmission power of each user. Perform fine-grained optimization analysis to ensure that the data transmission rate meets the maximum delay constraint and minimizes the transmission energy consumption. Since all power resources in the macro and micro networks are independent and do not conflict with each other, the optimization problem is decomposed into Independent power resource subproblems are solved one by one using the Dinkelbach method; transmission energy consumption is reduced while meeting data transmission rate and maximum delay constraints; the model considers the proportion of user offload tasks and further optimizes transmission energy consumption by adjusting the transmit power; S4.2: Based on the system model, construct the constraints of transmission delay and energy consumption; Allows user tasks to complete tasks within the maximum tolerable delay Completed within: ； Among them, the transmission energy consumption is calculated as: ； S4.3: Multiple user devices in the system will offload tasks at the same time. The power optimization problem needs to be solved using the Lagrange dual method and the subgradient method to control the computational complexity and formulate the optimal power allocation plan. is a non-negative parameter. By solving the Karosh-Kuhn-Tucker condition, the optimal transmit power allocation is obtained: ； in, and are different Lagrange multipliers respectively; S4.4: Develop a game-based optimal response algorithm, and gradually adjust the power allocation strategy under the energy consumption feedback mechanism until the system energy consumption converges to the optimal level while meeting the data transmission rate and delay constraints.

6. The edge computing offloading and transmission power optimization method based on dual-leader game according to claim 1 is characterized in that: The specific steps of S5 are as follows: S5.1: Dynamically adjust computing resource pricing. Within the Stan-Kohlberg game framework, macro and micro base stations, as computing resource providers, dynamically adjust their pricing strategies based on the computing resource demands of user devices. Based on the optimal pricing algorithm, macro and micro base stations adjust prices, influencing user task offloading decisions and adjusting the task offloading ratio. S5.2: Dynamic iteration is performed in conjunction with transmit power optimization. After base station pricing is adjusted, users adjust their task offload ratios based on the latest pricing strategy and optimize computing resource allocation. A game-based best response algorithm is used to dynamically optimize computing resource pricing, optimal task offload ratios, and optimal transmit power. S5.3: Iterate optimization until the system energy consumption converges to the optimal value, and set the maximum number of iterations ,In each round of iteration, the computing resource pricing is updated, the optimal task offloading strategy is calculated, the transmission power is optimized according to the task offloading strategy, the current total energy consumption of the system is calculated, and whether convergence is achieved; If the convergence conditions are met, the final optimal strategy is output; otherwise, the iteration continues until the minimum total energy consumption is reached.

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