Multi-edge game load balancing method and system under assistance of unmanned aerial vehicle

Abstract

The invention provides a multi-edge game load balancing method and system under the assistance of an unmanned aerial vehicle, and the method comprises the following steps: 1, carrying out the load balancing modeling of a base station into a non-cooperative game model with Nash equilibrium characteristics, comprising a system network model, a base station edge transmission model, an unmanned aerial vehicle edge transmission model, a task unloading model and a calculation model. Step 2, problem definition: converting an original problem into a load balancing unloading scheme for optimizing a base station edge server and an access scheme of an unmanned aerial vehicle; and step 3, designing an adaptive distributed load balancing algorithm of the unmanned aerial vehicle. According to the technical scheme, the optimal base station is intelligently selected for assistance through the dynamic access strategy of the unmanned aerial vehicle, meanwhile, it is strictly proved that the load balancing game can be converged to the Nash equilibrium point, and the system stability is theoretically guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of edge server load balancing, and in particular to a multi-edge game load balancing method and system assisted by a drone. Background Art

[0002] In recent years, with advances in fifth-generation mobile communications technology and the rapid development of the Internet of Things (IoT), IoT devices have become ubiquitous across numerous industries, significantly improving the quality of our daily lives. However, due to the inherent limitations of end-user equipment (UE) in terms of computing power, storage capacity, and battery life, existing architectures struggle to meet the multi-dimensional user demands for service latency, energy efficiency, and reliability for compute-intensive and latency-sensitive tasks. This technological bottleneck has prompted academia and industry to actively explore new computing architectures to address these challenges.

[0003] Mobile cloud computing (MCC) offloads terminal tasks to cloud data centers, leveraging their powerful computing clusters and elastic storage resources to efficiently handle massive computing requests. However, this architecture has significant drawbacks: terminals must exchange data with remote cloud servers over a wide area network. This long-distance transmission not only introduces additional communication latency but can also increase packet loss. This makes it difficult to ensure quality of service (QoS) for latency-sensitive tasks, especially in dynamic network environments.

[0004] To address these issues, the revolutionary architecture of Mobile Edge Computing (MEC) has emerged. The core concept of the MEC framework, proposed by the European Telecommunications Standards Institute (ETSI) in 2014, is to move computing nodes down to the edge of the network. This distributed architecture deploys servers at base stations, shortening the spatial distance between computing resources and terminal devices to within a single hop. This topology optimization offers dual technical advantages: First, a significant reduction in end-to-end transmission latency (typically down to milliseconds) effectively improves the responsiveness of real-time tasks; second, it significantly reduces the traffic load on backhaul links, thereby optimizing overall network energy efficiency.

[0005] While mobile edge computing can overcome the shortcomings of mobile cloud computing, it also faces new challenges in practical applications. Computing resources are typically pre-configured in each base station where an MEC server is installed, while user resource demands fluctuate in real time. This mismatch between fixed resource supply and elastic demand, particularly when experiencing traffic bursts caused by social events or social activities, can lead to system overload and exponentially increased task response latency. To address this issue, one feasible solution is to balance the workload on edge servers by migrating computing tasks. However, due to the dispersed deployment locations of MEC servers and the limited computing resources available, designing effective load balancing strategies has become a challenging research topic. Another feasible solution is to leverage the flexibility of drones by deploying small MEC servers on them. These solutions can address this issue by supplementing the user end's computing resources through user-side task offloading, computing resource allocation, and drone trajectory control. Many companies have already considered these applications in their projects.

[0006] In recent years, academic research has extensively explored the problem of edge server load balancing. Numerous studies have employed base station edge servers to develop load balancing strategies in various scenarios to reduce network load. For example, Cabrera et al. proposed a multi-objective dynamic load balancing (DLB) method to efficiently balance computationally intensive tasks in heterogeneous edge systems. Liu et al. used a dynamic clustering algorithm for IoT networks based on deep reinforcement learning (DRL) to simultaneously balance communication load within IoT networks and computational load within edge servers. Yang et al. proposed a clustering-assisted task offloading method based on deep deterministic policy gradients (DDPG) to achieve load balancing among edge servers. However, these studies primarily rely on centralized control methods for load balancing, requiring edge servers to follow unified scheduling instructions from a central control system, guided by global optimization objectives. However, centralized control methods often require significant time to search for appropriate load balancing solutions, making them inefficient and unable to meet the real-time service requirements of UEs. To reduce decision latency and optimize load balancing performance, some research has focused on designing edge load balancing scheduling strategies using distributed architectures. For example, Mattia et al. constructed a differential model of the system and proposed an adaptive heuristic algorithm to search for load balancing solutions, balancing the latency of edge nodes in a decentralized manner. Xu et al. developed a DNN-based inference model for multi-edge systems, defined optimal inference offloading for load balancing, and based on this, proposed a distributed algorithm for DNN inference offloading, obtaining an optimal inference offloading strategy for load balancing. However, existing base station load balancing research is limited by static resource configuration models, making it difficult to cope with extreme load scenarios caused by regional traffic bursts.

[0007] Thanks to their high maneuverability and rapid deployment capabilities, drones can serve as mobile edge computing nodes or aerial relay units, dynamically building temporary computing resource networks. Therefore, in recent years, some research has begun to focus on the application of drones in edge computing on the UE side. Cheng et al. studied how to deploy and schedule drones equipped with MEC to expand the computing power of the UE. Peng et al. proposed a distributed method based on multi-agent deep deterministic policy gradient (MADDPG) to optimize resource allocation in drone-vehicle network systems to maximize the number of offloaded tasks. Sun et al. constructed a multi-objective optimization model that decomposes the problem into three sub-problems. By combining the Karush-Kuhn-Tucker (KKT) and continuous convex approximation (SCA) algorithms, they achieved the comprehensive optimization goals of minimizing task completion delay, reducing overall drone energy consumption, and maximizing task offload. However, the above-mentioned research on drone-assisted edge computing only focuses on the computational offloading between drones and UEs, lacking a collaborative optimization mechanism with ground base stations. Summary of the Invention

[0008] In view of this, the purpose of the present invention is to provide a multi-edge game load balancing method and system assisted by drones, which intelligently selects the optimal base station for assistance through the dynamic access strategy of drones. At the same time, it is strictly proved that the load balancing game can converge to the Nash equilibrium point, theoretically ensuring the stability of the system.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: a multi-edge game load balancing method assisted by a drone, comprising the following steps:

[0010] Step 1: Model base station load balancing as a non-cooperative game model with Nash equilibrium characteristics, including the system network model, base station edge transmission model, drone edge transmission model, task offloading model, and computation model.

[0011] Step 2: Problem definition, which involves converting the original problem into a load balancing offloading solution for optimizing the base station edge server and the access solution for drones.

[0012] Step 3: Design an adaptive distributed load balancing algorithm for UAVs.

[0013] In a preferred embodiment, in the system network model, each base station acts as a core edge node, and the drone acts as an auxiliary edge node; the edge servers carried by the base station and the drone use heterogeneous processors, that is, the computing power provided by the two is different; in this network system model, the included base stations and The edge servers on the drones are respectively used and To indicate that the base station edge Edge with drones The positions are respectively and To represent; Assume that the computing tasks offloaded by the user terminal device to the core edge node follow the Poisson distribution model, and define these tasks as arrival tasks, using the set λ={λ1,λ2,…,λ M} represents the task arrival rate of the base station edge server, where λ i Indicates the base station edge server The task arrival rate on the edge server is the amount of tasks received by the user terminal device per unit time;

[0014] The arrival tasks of edge nodes need to automatically adjust the division granularity according to the real-time load status of ground base stations and drones. By distributing these refined subtasks to each edge node, collaborative load balancing between the base station edge and the drone edge can be achieved.

[0015] In a preferred embodiment, the transmission time of a unit task between base station edge servers in the base station edge transmission model is defined as:

[0016]

[0017] in Indicates the base station edge server Offload unit tasks to base station edge servers The time required if the base station edge server With base station edge server If there is no connection, 0, will be with the edge A collection of connected base station edge servers Defined as:

[0018]

[0019] In a preferred embodiment, in the UAV edge transmission model, the uplink channel gain from the ground base station to the UAV is expressed using the free space path loss model as:

[0020]

[0021] Where α0 represents the channel gain constant at a distance reference of 1m, Indicates the base station edge server To the drone edge server Upward distance from the edge of the ground To the edge of drones The uplink transmission data rate is calculated as follows:

[0022]

[0023] where σ 2 represents the variance of white Gaussian noise, B represents the channel bandwidth, and P c represents the transmission power of the ground base station; the transmission time D between the edge of the base station and the edge of the drone u Defined as:

[0024]

[0025] in, Indicates the base station edge server Offloading unit tasks to drone edge servers The time required.

[0026] In a preferred embodiment, in the task offloading model, if X i Represented as base station edge The offloading vector of the edge server is , then the task offloading matrix X between edge servers can be defined as:

[0027]

[0028] in, Base station edge The base station offloading vector, that is, the base station edge The amount of tasks offloaded to the edge of each base station can be expressed as:

[0029]

[0030] In particular, when i=j, Indicates the amount of tasks that the base station edge needs to perform locally. Base station edge The drone offloading vector, i.e. the base station edge The amount of tasks offloaded to the edge of the drone can be expressed as:

[0031]

[0032] Considering that the drone only acts as an auxiliary node at the edge of the base station when it is put into use, in order to avoid excessive instantaneous request traffic to some base station edge servers, which leads to a shortage of computing resources, the present invention assumes that the drone will only access one base station edge node during the time slot of the auxiliary process and be located directly above it for auxiliary computing. Not connected to the base station edge server hour, And will be connected to the base station edge server The drone edge server is defined as

[0033] In a preferred embodiment, in the calculation model, the service rates of the base station edge server and the drone edge server are respectively represented by the set and To indicate that and Indicates the base station edge server and drone edge servers The computing service rate;

[0034] Use collection To represent the load task arrival rate at the edge of the base station, including tasks executed locally by the edge server and tasks migrated to it by other edge servers; Calculated by the following formula:

[0035]

[0036] When drones are on the edge Not connected to the base station edge When Similarly, the edge of the drone The load task arrival rate is defined as It is assumed that the task will first be offloaded to the ground base station edge and the task will be split into subtasks.

[0037] In a preferred embodiment, the total delay during the offloading process is described as the following four key components: 1) the dedicated line transmission delay between base station edges; 2) the task response delay on the base station edge; 3) the uplink transmission delay from the base station edge to the drone edge; 4) the task response delay on the drone edge;

[0038] Establish an M / M / 1 queuing model for the edge server service system; base station edge server Average queuing delay of tasks on Expressed as:

[0039]

[0040] The computational execution delay of task w Expressed as:

[0041]

[0042] The task response delay on the edge server includes two parts: queuing delay and calculation execution delay; the task w is on the edge server of the base station. Response delay on Expressed as:

[0043]

[0044] Get the base station edge server Migrate to Base Station Edge Server The average completion time of the executed tasks is calculated as follows:

[0045]

[0046] Obtain base station edge server Migrate to drone edge servers Average task completion time

[0047] In a preferred embodiment, step 3 includes a UAV adaptive distributed load balancing algorithm UADLBA, which is divided into two stages. Stage 1 is the UAV's adaptive access strategy, and stage 2 is a non-cooperative game at the base station edge. Stage 1 requires the UAV to obtain global information of all base stations. When deploying each UAV, the algorithm adaptively finds the most suitable base station edge under the current system load state and accesses it. Stage 2 runs on the base station server in a distributed architecture, and finds the Nash equilibrium point of the system after multiple iterations on each server.

[0048] In a preferred embodiment, step 3 also includes edge Distributed load balancing algorithm: At the beginning, the default offloading strategy of the base station edge server is local processing, that is, no migration offloading is performed, and some of the server's operating status information is broadcast to the adjacent edge server. Next, the edge server traverses the adjacent edge offloading vector set and uses the CVX solver to calculate the task offloading strategy, from which the optimal task offloading strategy is selected; after the decision is made, it is compared with the previous round of decisions. If the difference is less than the limit step size, it indicates that load balancing is achieved, and the iteration is stopped. Finally, the offloading strategy converged to by the iteration is returned.

[0049] The present invention also provides a multi-edge game load balancing system assisted by a drone, which runs the multi-edge game load balancing method assisted by a drone.

[0050] Compared with existing technologies, the present invention offers the following advantages: It proposes a drone-assisted multi-edge game load balancing method and system. This method leverages the mobility, flexible deployment, and line-of-sight communication advantages of drones to dynamically supplement computing resources for traditional ground base stations. To achieve efficient collaboration between the base station edge and the drone edge, the present invention systematically studies the load balancing optimization problem in a drone-assisted edge environment. A multi-drone-assisted multi-edge server system architecture is proposed, integrating a collaborative model for base station static load balancing and drone dynamic resource scheduling. This overcomes the limitations of traditional base station static load balancing optimization by leveraging the mobility of drones to establish a dynamic computing resource pool, alleviating base station computing bottlenecks. Through joint optimization, a balanced temporal and spatial load distribution is achieved to accommodate extreme high-load edge computing scenarios. To address the complexity of the optimization problem, the present invention decouples it into two collaborative optimization subproblems: base station edge server load balancing and drone access strategy. First, base station load balancing is modeled as a non-cooperative game with Nash equilibrium properties, and then a drone adaptive distributed load balancing algorithm is proposed. This method intelligently selects the optimal base station for assistance through the drone's dynamic access strategy. It also rigorously proves that the load balancing game converges to a Nash equilibrium point, theoretically ensuring system stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A schematic diagram of a system model of a preferred embodiment of the present invention;

[0052] Figure 2 A schematic diagram of load changes of a base station edge server in a preferred embodiment of the present invention;

[0053] Figure 3 This is a schematic diagram of task completion time of a base station edge server in a preferred embodiment of the present invention;

[0054] Figure 4 Schematic diagram of the average utility value of the edge system in multiple scenarios of a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0055] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0056] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meaning as commonly understood by those skilled in the art to which the present application belongs.

[0057] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form, and it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations.

[0058] like Figure 1 As shown, the present invention proposes a multi-edge game load balancing method and system assisted by a drone, including the following aspects:

[0059] 1. System Network Model

[0060] The present invention proposes a network architecture consisting of a large number of base stations equipped with edge servers and a number of drones. In this architecture, each base station acts as a core edge node, while the drones act as auxiliary edge nodes. At the same time, the edge servers carried by the base stations and drones use heterogeneous processors, that is, the computing power provided by the two is different. Based on the positional relationship between the UE and the adjacent core edge nodes, the UE can offload computing tasks that cannot be completed independently to the core edge computing nodes to utilize the computing resources of the core edge nodes. In addition, the drones in the system, as auxiliary edge nodes, can receive computing tasks from high-load core edge nodes through reasonable location deployment strategies.

[0061] In this network system, the M base stations and the edge servers on the N drones are respectively used and To indicate that the base station edge Edge with drones The positions are respectively and Similar to the design in Lin's work, this paper assumes that the computing tasks offloaded by user terminal devices to core edge nodes follow the Poisson distribution model and defines these tasks as "arrival tasks". M} represents the task arrival rate of the base station edge server, where λ i Indicates the base station edge server The task arrival rate is the amount of tasks received by the edge server from the user terminal device per unit time.

[0062] The fundamental contradiction faced by traditional edge computing systems lies in the static resource pre-configuration of edge servers (such as fixed computing capacity of base stations) and the dynamic burstiness of user demand (peaks may exceed the total computing capacity of base stations). Existing solutions mainly rely on overall task migration strategies, but this approach has obvious flaws: simply transferring tasks from overloaded nodes to underloaded nodes may cause secondary overloads on the receiving nodes, which essentially only transfers rather than solves the load imbalance problem. To address this problem, the air-ground collaborative load balancing framework proposed in the present invention adopts a non-complete task offloading strategy. The arrival tasks of edge nodes need to automatically adjust the division granularity according to the real-time load status of ground base stations and drones. By distributing these refined subtasks to each edge node, collaborative load balancing between the base station edge and the drone edge can be achieved.

[0063] 2. Transmission Model

[0064] (1) Base station edge transmission model

[0065] Assume that the base station edge nodes are interconnected through a dedicated cable network. Each link is supported by its own independent channel. Data is transmitted in a serialized form in these channels to maintain data integrity and transmission order. At the same time, these network links enable bidirectional communication, and the communication delay remains consistent regardless of the direction of data transmission. Similar to existing research, the transmission time of a unit task between base station edge servers is defined as:

[0066]

[0067] in Indicates the base station edge server Offload unit tasks to base station edge servers The time required, especially if the base station edge server With base station edge server If there is no connection, will be with the edge A collection of connected base station edge servers Defined as:

[0068]

[0069] (2) UAV edge transmission model

[0070] Assuming that the communication channel from the drone to the base station is mainly dominated by the line-of-sight (LOS) link channel, and that the drone can access the ground base station through orthogonal frequency division multiplexing, the interference between the drone-ground base station link can be ignored. The uplink channel gain from the ground base station to the drone can be expressed using the free space path loss model as:

[0071]

[0072] Where α0 represents the channel gain constant at a distance reference of 1m, Indicates the base station edge server To the drone edge server The upward distance, according to Shannon's formula, from the edge of the ground To the edge of drones The uplink transmission data rate can be calculated as follows:

[0073]

[0074] where σ 2 represents the variance of white Gaussian noise, B represents the channel bandwidth, and P c The present invention assumes that the tasks offloaded by the edge server will not be offloaded again, and the output data volume of the calculation result is usually much smaller than the input data volume, so the downlink transmission time by the UAV edge server can be ignored. Therefore, the transmission time D between the base station edge and the UAV edge is u It can be defined as:

[0075]

[0076] in, Indicates the base station edge server Offloading unit tasks to drone edge servers The time required.

[0077]

[0078]

[0079] Table 1 Symbol definitions

[0080] 3. Task Offloading Model

[0081] If you use X i Represented as base station edge The offloading vector of the edge server is , then the task offloading matrix X between edge servers can be defined as:

[0082]

[0083] in, Base station edge The base station offloading vector, that is, the base station edge The amount of tasks offloaded to the edge of each base station can be expressed as:

[0084]

[0085] In particular, when i=j, Indicates the amount of tasks that the base station edge needs to perform locally. Base station edge The drone offloading vector, i.e. the base station edge The amount of tasks offloaded to the edge of the drone can be expressed as:

[0086]

[0087] Considering that the drone only acts as an auxiliary node at the edge of the base station when it is put into use, in order to avoid excessive instantaneous request traffic to some base station edge servers, which leads to a shortage of computing resources, the present invention assumes that the drone will only access one base station edge node during the time slot of the auxiliary process and be located directly above it for auxiliary computing. Not connected to the base station edge server hour, And will be connected to the base station edge server The drone edge server is defined as

[0088] 4. Computational Model

[0089] The present invention uses the service rates of the base station edge server and the drone edge server as the set and To indicate that and Indicates the base station edge server and drone edge servers The calculation service rate.

[0090] The present invention uses a collection is used to represent the load task arrival rate at the edge of the base station, including tasks executed locally by the edge server and tasks migrated to it by other edge servers.

[0091] It can be calculated by the following formula:

[0092]

[0093] It should be noted that when the drone is on the edge Not connected to the base station edge When Similarly, the edge of the drone The load task arrival rate is defined as This method assumes that tasks are first offloaded to the edge of the ground base station and then split into subtasks. The decision time for each subtask is very short compared to the overall communication and computational latency, and therefore negligible. Furthermore, in many computationally intensive applications (such as face recognition and video analysis), the output data size of the computation results is typically much smaller than the input data size. Therefore, the time required to transmit the computation results back to the user device is also negligible.

[0094] In summary, the total latency during offloading can be described as the following four key components: 1) dedicated line transmission delay between base station edges; 2) task response delay at the base station edge; 3) uplink transmission delay from the base station edge to the drone edge; and 4) task response delay at the drone edge.

[0095] Considering that edge nodes face a large number of concurrent requests when processing computing tasks generated by users, and the computing resources of edge nodes are limited, queuing is inevitable when dealing with these challenges. Therefore, based on queuing theory, this paper establishes an M / M / 1 queuing model for the service system of edge servers. Average queuing delay of tasks on It can be expressed as:

[0096]

[0097] The computational execution delay of task w It can be expressed as:

[0098]

[0099] The task response delay on the edge server includes two parts: queuing delay and computation execution delay. Therefore, task w is Response delay on It can be expressed as:

[0100]

[0101] From this we can get the base station edge server Migrate to Base Station Edge Server The average completion time of the executed tasks can be calculated as follows:

[0102]

[0103] Similarly, the base station edge server can be obtained Migrate to drone edge servers Average task completion time

[0104] 5. Problem Definition

[0105] The present invention aims to study the system optimization problem of edge servers under the rational decision-making behavior of pursuing the maximization of their own interests. The optimization goal is to minimize the average completion time of tasks on all edge nodes and achieve load balancing of the entire edge system. However, the direct access objects of the base station edge and the drone edge are different, and there are also differences in the task transmission process. It is very complicated to load balance the base station server and the drone server at the same time. Considering that the drone edge server only accesses one base station edge server in a short time slot, and both use queuing theory to abstract the service process, the amount of tasks unloaded from the base station edge to the drone edge is set to δ, then the drone edge can be obtained by formula (13) Average completion rate of unit tasks:

[0106]

[0107] Therefore, the service process of drone edge computing offloading tasks can be integrated into the queue service at the base station edge, and the original problem can be transformed into two sub-problems: optimizing the load balancing offloading solution of the base station edge server and the access solution of the drone.

[0108] Define Base Station Edge Server The utility function of :

[0109]

[0110] in represents the average task service rate of the base station edge server connected to the auxiliary drone edge. Therefore, the individual goal of each base station edge server in the system is: based on the current network conditions and the offloading strategy of the adjacent base station edge server X -i , dynamically adjust its own task allocation decisions and explore the optimal task migration solution X i , in order to minimize its own utility function. The optimization problem can be defined as:

[0111]

[0112] Among them, C1 indicates that the migration task volume of the base station edge server is non-negative, C2 indicates that the total task volume of the base station edge server remains unchanged before and after unloading, C3 indicates that the total task volume of the base station edge server cannot exceed the maximum computing capacity, C4 indicates that the base station edge server has 0 or more drone edges participating in auxiliary computing, and C5 indicates that the drone edge can only access one base station edge.

[0113] 6. Algorithm Design

[0114] The present invention constructs a non-cooperative game based on the multi-edge collaborative load balancing problem in the drone-assisted MEC scenario. Throughout the process, the base station edge, as a game participant, selfishly participates in load balancing, that is, it does not consider the impact of its own strategy on the decision-making of other adjacent base station edges. The drone edge, as an auxiliary node of the base station edge, provides it with additional computing resources and indirectly participates in the game process as a fixed cost for the game participants. Therefore, the basic framework of the algorithm is to derive the optimal strategy selection for task migration of game participants through an iterative algorithm. In each round of iteration, according to the constructed utility function optimization model, its minimum value is solved, and finally gradually converges to obtain the optimal strategy combination of all game participants in the task migration scenario.

[0115] During the unloading process, in order to fully utilize the flexibility and scalability of the UAV edge, the present invention proposes an adaptive load balancing algorithm (UAVAdaptive Load Balancing Algorithm, UALBA) that supports UAV-assisted scenarios, as shown in Algorithm 1.

[0116] Algorithm 1. Adaptive load balancing algorithm

[0117] Input: λ, H, F c 、F u 、D c ,δ,M,N,α0

[0118] Output: X *

[0119]

[0120]

[0121] Considering the problems of frequent global state synchronization and exponential communication overhead in centralized load balancing at the edge, it is difficult to meet the low latency requirements of edge services. Based on the game model constructed in the previous article and Algorithm 1, the present invention further designs a UAV adaptive distributed load balancing algorithm (UAVAdaptive Distributed LoadBalancing Algorithm, UADLBA) to support the optimal task offloading strategy with the assistance of UAVs. The algorithm divides Algorithm 1 into two stages. Stage 1 is the adaptive access strategy of the UAV (lines 2-10), and stage 2 is the non-cooperative game at the base station edge (lines 11-23). ​​In stage 1, the UAV needs to obtain global information of all base stations. When deploying each UAV, the algorithm can adaptively find the most suitable base station edge under the current system load state and access it. Stage 2 can run on the base station server in a distributed architecture, and find the Nash equilibrium point of the system after multiple iterations on each server. Algorithm 2 provides the specific steps: Initially, the base station edge server's default offloading strategy is local processing, meaning no migration offloading is performed. The server's partial operating status information is broadcast to adjacent edge servers (line 1). Next, the edge server traverses the set of adjacent edge offloading vectors, uses the CVX solver to calculate task offloading strategies, and selects the optimal task offloading strategy (lines 3-10). After the decision is made, it is compared with the previous round's decision. If the difference is less than the limit step size, load balancing is achieved and iteration is terminated (lines 11-14). Finally, the offloading strategy that the iteration converges to is returned (lines 15-16).

[0122] Algorithm 2. Edge Distributed load balancing algorithm

[0123] Input: λ i 、F c 、D c 、

[0124] Output:

[0125]

[0126]

[0127] 7. Algorithm Proof

[0128] In the edge computing system with multiple edge nodes studied in the present invention, the edge server and the adjacent nodes achieve collaborative work through local information interaction. In the game, the edge servers are selfish, and they minimize their own utility functions as much as possible based on the local information of the adjacent edges. In view of this characteristic, the present invention abstracts the competitive behavior of the edge servers in the task migration process into a non-cooperative game model with incomplete information. Under this model framework, each edge server, as an independent participant in the game, only has fragmentary information about the system. They need to rely on this limited local information to infer the potential strategies of other participants, and then seek the optimal task migration strategy, aiming to shorten the average task completion time of their own tasks. Therefore, the present invention formalizes this problem into a non-cooperative game G with equal status among the participants, and the game expression is:

[0129]

[0130] in, is the set of base station edge servers participating in the game, X i Base station edge server Uninstallation policy set, Q i For edge servers The utility function of .

[0131] In game theory, Nash equilibrium is considered a key indicator for evaluating system stability. The following is the definition of the Nash equilibrium point for the edge collaborative load balancing problem of the present invention:

[0132] Definition 1. Define uninstall strategy is the Nash equilibrium point of the game. At this point, any game participant Strategy All satisfied

[0133]

[0134] in, For game participants Any strategy,

[0135] From Definition 1, we can see that when the system is in Nash equilibrium, any participant cannot reduce the system cost by changing its own strategy.

[0136] This paper conducts an in-depth analysis of the non-cooperative game model constructed based on the drone-assisted multi-edge collaborative load balancing problem. By using mathematical analysis and deduction methods, the game is converted into a variational inequality, and the existence of the Nash equilibrium point of the model is proved.

[0137] Theorem 1. For each base station edge server Its uninstall policy set X iis closed and convex, and the utility function Q i is continuously differentiable.

[0138] Proof: According to formula (16), each base station edge server Uninstall strategy X i Satisfy constraints C1-C3, where According to the definition of closed convex set, the unloading vector X i It is closed convex.

[0139] Next we need to prove the continuity of the derivative of the utility function. The utility function of is rewritten as:

[0140]

[0141] Let Q i right After taking partial derivatives, we can get:

[0142]

[0143] Because Q i The partial derivative of exists and is continuous, indicating that the utility function Q i is continuously differentiable.

[0144] Theorem 2. When the task offloading strategies of other edge servers remain unchanged, the current edge server The utility function Q i is a strictly convex function.

[0145] Proof: According to the basic definition of convex function, it is necessary to analyze and verify the utility function Q i The Hessian matrix H(Q i ) is positive definite, thus confirming that the function satisfies the convex condition. i ) can be expressed as:

[0146]

[0147] in

[0148]

[0149] When the game reaches the Nash equilibrium state (i.e., the offloading strategies of other servers remain stable), the edge server The utility function Q i The Hessian matrix H(Q i ) presents a special diagonal structure. Combined with the constraint C3 of formula (16), it can be proved that the diagonal elements of the matrix are all positive, thus meeting the positive definiteness requirement. Based on the convex function judgment criterion, the utility function Q can be obtainedi The conclusion is strictly convex.

[0150] Theorem 3. When X i Satisfy the non-empty closed convex set constraint, and Q i When the convex function is continuously differentiable, the problem of finding the equilibrium solution of the game G can be transformed into solving the corresponding variational inequality VI(X,q). Furthermore, when the gradient q of the utility function satisfies the strict monotonicity condition, it is guaranteed that the game has at least one Nash equilibrium point.

[0151] Proof: Through preliminary analysis, we know that X i is a non-empty set. Based on the argumentation of Theorem 1 and Theorem 2, we can determine that the set X i It is also a closed convex set, and the utility function Q i It has the characteristics of a continuously differentiable convex function. The research results of reference

[26] deeply reveal the essential connection between game theory and variational inequality theory. According to the analysis results, the problem of solving the equilibrium solution of game G is equivalent to the problem of solving the corresponding variational inequality VI(X,q). Next, the monotonicity of the gradient q of the utility function is proved.

[0152] If the gradient q is monotonic, then the following conditions hold:

[0153] (XX * ) T (q(X)-q(X * ))≥0 (24) is equivalent to

[0154]

[0155] in

[0156]

[0157] q i The Jacobian matrix can be expressed as:

[0158]

[0159] Based on the proof of Theorem 2, it has been proved that H(Q i ) has positive definiteness, from which we can deduce This mathematical property ensures that the function q i Satisfying the strict monotonicity condition, through analysis, we can see that for Then there is It can be deduced that Equation (25) must hold, thus proving that the gradient function q maintains strict monotonicity as a whole. Based on the above analysis and combined with the basic theorem of game theory, it can be determined that this game model has at least one Nash equilibrium solution.

[0160] 8. Experimental Configuration

[0161] In order to verify the effectiveness of the UADLBA method for load balancing of UAV-assisted MEC systems, the present invention conducted a large number of simulation experiments and implemented the following four comparative algorithms: local computing strategy (Local), UAV-assisted local computing strategy (ULocal), SBOA and PSOGA methods. The local computing strategy means that the UAV does not access the edge of the base station, and the tasks at the base station edge are only executed locally without task offloading; the UAV-assisted local computing strategy means that the UAV will use the adaptive access strategy in Algorithm 1, but the base station edge will not perform task offloading; the SBOA method can be simply understood as a method in which the UAV does not access the edge of the base station, but a distributed load balancing decision is made between the base station edges; the PSOGA method means that the UAV will access the edge of the base station, but the task offloading decision between the base station edges is obtained by PSOGA. The PSOGA algorithm adopts a centralized architecture design, and realizes efficient approximate solutions to complex optimization problems by simulating the combination of particle swarm intelligent search mechanism and genetic mutation operations. The present invention defines the task migration ratio of each base station edge as the search space, and defines the task migration strategy of the base station edge as particles. The specific parameter settings are as follows: P num =100, N=1000, R mut =0.05, c1=c2=2, ω∈[0.3,0.8].

[0162] The experiments were run on a system equipped with a 3.00 GHz Intel(R) Core(TM) i5-9500F CPU and 16 GiB of RAM. Simulations were performed using a Shanghai base station distribution dataset with longitude and latitude information. The simulation environment was based on Python 3.11, using Pandas 2.1 and Numpy 1.24 to build the system model. CVXPY 1.5 and CPLEX 22.1 were used to solve the convex problem. Specific experimental parameters are listed in Table 2.

[0163]

[0164] Table 2 Experimental parameter settings

[0165] IX. Experimental Results

[0166] The present invention observes the changes in task load and task completion time of a random set of adjacent edge sets among 30 base station edges to prove that the proposed UADLBA method can effectively converge to Nash equilibrium. Figure 2 、 Figure 3 It shows that by observing the base station edge e1 and its adjacent edges e2, e7, e 10The changes in task load and task completion time of the adjacent edge set composed of , where the base station edge e1 is connected to the drone edge u8. Figure 2 and Figure 3 As shown, e1, e7, e 10 The load and task completion time show a monotonically increasing / decreasing trend until they reach a stable value in multiple iterations. This is because e1, which is initially highly loaded, unloads tasks to adjacent edges, thereby reducing the load and task completion time. The load and task completion time of e2 first increase and then decrease. This is because e2 is initially in a low-load state, and its adjacent edges tend to unload tasks to it, resulting in a surge in load. e2 then chooses to unload its own initially arrived tasks to other adjacent edges to reduce the load. At the same time, it can be found that e2, e7, and e 10 When reaching a steady state, the loads are similar. This is because the task service rates are similar, and when the system reaches stability, it fully utilizes the computing resources of each edge. However, e1's load is higher in the steady state because the auxiliary drone edge is connected to e1, which increases e1's task service rate and its maximum load capacity. After multiple rounds of iterations, the task load and task completion time tend to be relatively stable. Therefore, UADLBA can converge to a Nash equilibrium within a limited number of iterations.

[0167] The present invention uses the system average utility value As a performance indicator. Figure 4 The performance of each strategy is compared from three scenarios, among which scenario one is a low-load base station edge system consisting of a base station edge with a low load rate of 80% (load rate below 20%) and a base station edge with a high load rate of 20% (load rate above 80%); scenario two is a medium-load base station edge system consisting of a base station edge with a low load rate of 50% and a base station edge with a high load rate of 50%; scenario three is a high-load base station edge system consisting of a base station edge with a medium load rate of 20% (load rate around 50%) and a base station edge with a high load rate of 80%. The results show that the UADLBA method proposed in the present invention can achieve good results in all three scenarios. As Figure 4As shown, the UADLBA method improves the local computation strategy by 30.1%, 32.8%, and 41.3% in the three scenarios, respectively. It also improves the SBOA method by 3.7%, 8.1%, and 29.0%, respectively. This is because the SBOA method only considers load balancing between base stations. In extreme scenarios where the vast majority of base stations are highly loaded, it cannot appropriately offload tasks to the edges of each base station to reduce the load rate of each edge. Therefore, the more edges in the system are highly loaded, the less effective the load balancing strategy. However, it is slightly inferior to the PSOGA method by 0.9%, 1.3%, and 1.5%. This is because PSOGA trades execution time for performance, and can find a near-optimal task offloading strategy over multiple iterations. Based on the above data, the UADLBA method proposed in this paper performs better than other strategies and is also highly adaptable to different scenarios.

[0168] Next, the present invention evaluates the decision-making time of the UADLBA, SBOA, and PSOGA algorithms. Table 3 shows the average decision time for finding a load balancing solution for these three comparison methods in three different scenarios. In the three different scenarios, the average decision time of SBOA and UADLBA is not much different, but the reason why UADLBA is slightly higher than SBOA is that the UADLBA method also considers the adaptive access strategy of the drone. PSOGA is a centralized optimization method, which leads to excessively high execution time and cannot adapt to the real-time changing multi-edge environment. It can be inferred from the above data that the UADLBA method proposed in the present invention can maintain a high execution efficiency in different edge computing scenarios and is applicable to various edge computing scenarios.

[0169] Scenario UADLBA SBOA PSOGA Low 1.43 1.31 1234.17 Medium 1.46 1.36 1336.32 High 1.48 1.37 1387.61

[0170] Table 3 Load balancing decision time

[0171] 10. Product Usage Process or Method

[0172] This method is a game-theory-based load balancing scheduling method (UADLBA). UADLBA can achieve efficient load balancing in drone-assisted edge systems. First, the problem is split into two sub-problems: load balancing of the base station edge server and access plan for drones. The main steps are as follows:

[0173] Step 1: Generate the initial state of the system based on the data in the training set, including the task arrival rate, service rate and unit task network delay of each base station edge.

[0174] Step 2: The drone swarm independently generates access decisions at the base station edge based on the load situation at the base station edge, offloading some tasks for the ground base station to improve the service rate of the ground base station.

[0175] Step 3: When the iterations of the ground base station edge and the adjacent edge converge, each edge in the adjacent edge cluster performs a non-cooperative game and calculates the current optimal offloading solution through the convex optimization method. When the iteration limit is reached or the system cost no longer changes, the iteration is exited.

[0176] When the number of iterations reaches a certain value or the system cost no longer changes, it indicates that load balancing is achieved and the iteration stops. Finally, the unloading strategy converged to by the iteration is returned. This strategy is the optimal load balancing strategy of the edge system with the assistance of the current drone swarm.

[0177] The present invention mainly studies how to achieve efficient load balancing in the edge system assisted by drones. First, the problem is divided into two sub-problems: load balancing of base station edge servers and access scheme of drones, and the load balancing of base station edge servers is modeled as a non-cooperative game model with Nash equilibrium. Next, the UADLBA method is proposed. The UADLBA method not only selects the optimal base station edge server for access assistance through the adaptive access strategy of drones, but also ensures that the load balancing game of base station edge servers converges to the Nash equilibrium point. Finally, the performance of the present invention is compared with the PSOGA algorithm and the SBOA algorithm. The simulation experimental results show that compared with other benchmark methods, the UADLBA method proposed in the present invention can achieve better optimization effects in execution time and average task completion delay, and is suitable for edge computing scenarios with extreme high loads.

Claims

1. A multi-edge game load balancing method assisted by drones, characterized in that: The following steps are involved: Step 1: Model base station load balancing as a non-cooperative game model with Nash equilibrium characteristics, including the system network model, base station edge transmission model, drone edge transmission model, task offloading model, and computation model. Step 2: Problem definition, which involves converting the original problem into a load balancing offloading solution for optimizing the base station edge server and the access solution for drones. Step 3: Design an adaptive distributed load balancing algorithm for UAVs.

2. The multi-edge game load balancing method assisted by a drone according to claim 1 is characterized in that: In the system network model, each base station acts as a core edge node, and the drone acts as an auxiliary edge node. The edge servers carried by the base station and the drone use heterogeneous processors, that is, the computing power provided by the two is different. In this network system model, the included base stations and The edge servers on the drones are respectively used and To indicate that the base station edge Edge with drones The positions are respectively and To represent; Assume that the computing tasks offloaded by the user terminal device to the core edge node follow the Poisson distribution model, and define these tasks as arrival tasks, using the set λ={λ1,λ2,…,λ M } represents the task arrival rate of the base station edge server, where λ i Indicates the base station edge server The task arrival rate on the edge server is the amount of tasks received by the user terminal device per unit time; The arrival tasks of edge nodes need to automatically adjust the division granularity according to the real-time load status of ground base stations and drones. By distributing these refined subtasks to each edge node, collaborative load balancing between the base station edge and the drone edge can be achieved.

3. The multi-edge game load balancing method assisted by a drone according to claim 1 is characterized in that: In the base station edge transmission model, the transmission time of a unit task between base station edge servers is defined as: in Indicates the base station edge server Offload unit tasks to base station edge servers The time required if the base station edge server With base station edge server If there is no connection, will be with the edge A collection of connected base station edge servers Defined as:

4. The multi-edge game load balancing method assisted by a drone according to claim 1 is characterized in that: In the UAV edge transmission model, the uplink channel gain from the ground base station to the UAV is expressed using the free space path loss model as: Where α0 represents the channel gain constant at a distance reference of 1m, Indicates the base station edge server To the drone edge server Upward distance from the edge of the ground To the edge of drones The uplink transmission data rate is calculated as follows: where σ 2 represents the variance of white Gaussian noise, B represents the channel bandwidth, and P c represents the transmission power of the ground base station; the transmission time D between the edge of the base station and the edge of the drone u Defined as: in, Indicates the base station edge server Offloading unit tasks to drone edge servers The time required.

5. The multi-edge game load balancing method assisted by a drone according to claim 1 is characterized in that: In the task offloading model, if X i Represented as base station edge The offloading vector of the edge server is , then the task offloading matrix X between edge servers can be defined as: in, Base station edge The base station offloading vector, that is, the base station edge The amount of tasks offloaded to the edge of each base station can be expressed as: In particular, when i=j, Indicates the amount of tasks that the base station edge needs to perform locally. Base station edge The drone offloading vector, i.e. the base station edge The amount of tasks offloaded to the edge of the drone can be expressed as: Considering that the drone only acts as an auxiliary node at the edge of the base station when it is put into use, in order to avoid excessive instantaneous request traffic to some base station edge servers, which leads to a shortage of computing resources, the present invention assumes that the drone will only access one base station edge node during the time slot of the auxiliary process and be located directly above it for auxiliary computing. Not connected to the base station edge server hour, And will be connected to the base station edge server The drone edge server is defined as 6. The multi-edge game load balancing method assisted by a drone according to claim 1, characterized in that: In the calculation model, the service rates of the base station edge server and the drone edge server are respectively expressed as and To indicate that and Indicates the base station edge server and drone edge servers The computing service rate; Use collection To represent the load task arrival rate at the edge of the base station, including tasks executed locally by the edge server and tasks migrated to it by other edge servers; Calculated by the following formula: When drones are on the edge Not connected to the base station edge When Similarly, the edge of the drone The load task arrival rate is defined as It is assumed that the task will first be offloaded to the ground base station edge and the task will be split into subtasks.

7. The multi-edge game load balancing method assisted by a drone according to claim 5, characterized in that: The total delay during the offloading process is described by the following four key components: 1) the dedicated line transmission delay between base station edges; 2) the task response delay on the base station edge; 3) Uplink transmission delay from the base station edge to the drone edge; 4) Task response delay on the drone edge; Establish an M / M / 1 queuing model for the edge server service system; base station edge server Average queuing delay of tasks on Expressed as: The computational execution delay of task w Expressed as: The task response delay on the edge server includes two parts: queuing delay and calculation execution delay; the task w is on the edge server of the base station. Response delay on Expressed as: Get the base station edge server Migrate to Base Station Edge Server The average completion time of the executed tasks is calculated as follows: Obtain base station edge server Migrate to drone edge servers Average task completion time 8. The multi-edge game load balancing method assisted by a drone according to claim 1 is characterized in that: Step 3 includes the UAV adaptive distributed load balancing algorithm UADLBA, which is divided into two stages: stage 1 is the UAV’s adaptive access strategy, and stage 2 is the non-cooperative game at the base station edge; In phase 1, drones need to obtain global information about all base stations. When deploying each drone, the algorithm adaptively finds the most suitable base station edge under the current system load state and connects to it. Phase 2 runs on the base station server in a distributed architecture, and after multiple iterations on each server, the system's Nash equilibrium point is found.

9. The multi-edge game load balancing method assisted by a drone according to claim 8, characterized in that: Step 3 also includes the edges Distributed load balancing algorithm: Initially, the default offloading strategy of the base station edge server is local processing, that is, no migration offloading is performed, and some of the server's operating status information is broadcast to adjacent edge servers. Next, the edge server traverses the adjacent edge offloading vector set and uses the CVX solver to calculate the task offloading strategy, from which the optimal task offloading strategy is selected; After the decision is made, it is compared with the previous round of decision. If the difference is less than the limit step size, it indicates that load balance is achieved, and the iteration is stopped. Finally, the unloading strategy that the iteration converges to is returned.

10. A multi-edge game load balancing system assisted by drones, characterized in that: Run the multi-edge game load balancing method assisted by a drone as described in any one of claims 1 to 9.

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