Method for load balancing of multiple edge servers in mobile edge computing based on game theory

Abstract

The application relates to a game theory-based multi-edge server load balancing method in mobile edge computing. Firstly, the MEC server load balancing problem is modeled as a non-cooperative game, and a PDA (Proximal Decomposition Algorithm) regularization method is introduced to obtain a unique Nash equilibrium solution. Then, according to the established game model, a distributed mobile edge computing load balancing algorithm is proposed. Finally, through simulation experiments, the local computing strategy, the task migration strategy based on the server capacity and the task migration strategy based on the particle swarm genetic algorithm are compared and analyzed. The experimental results show that the application can effectively reduce the system response time and energy consumption, and the execution time is low, and is suitable for real scenes.

Description

Technical Field

[0001] This invention relates to a game theory-based multi-edge server load balancing method in mobile edge computing. Background Technology

[0002] In recent years, with the rapid development of 5G communication technology and the Internet of Things (IoT), IoT devices have been widely used in various fields, greatly facilitating people's daily lives. However, due to the limitations of the computing power, storage capacity, and battery power of IoT devices themselves, they often cannot provide sufficient computing resources to meet users' needs for low latency, low power consumption, and high reliability services for various computationally intensive and latency-sensitive tasks.

[0003] Mobile Cloud Computing (MCC) proposes migrating tasks from IoT devices to cloud servers in data centers. These cloud servers provide massive computing resources and storage capacity to efficiently process task requests from IoT devices. However, due to limitations in mobile cloud computing deployment models, data center-based MCC requires transmitting IoT applications and data via wide area networks (WANs). When IoT devices are far from the data center, data communication experiences significant latency, failing to meet the needs of latency-sensitive tasks and significantly impacting the Quality of Service (QoS).

[0004] Mobile Edge Computing (MEC) is a new computing paradigm proposed to address the problems arising from traditional MCC. Unlike traditional MCC, users in MEC can offload tasks to servers located at the network edge. Compared to remote cloud servers, MEC servers are closer to users, allowing them to access MEC servers with lower latency via wireless networks. This improves QoS for latency-sensitive users while reducing traffic sent to the cloud backbone.

[0005] Currently, how to rationally schedule tasks offloaded by IoT devices and balance the load among MEC servers is a major challenge in MEC research. The common practice is for IoT devices to offload their tasks to the nearest MEC server. However, due to the uneven geographical distribution of MEC servers and the uneven time distribution of tasks generated by IoT devices, some MEC servers have low loads while others are overloaded. This can lead to situations where, when IoT devices offload tasks to heavily loaded MEC servers, the task response time may not meet the latency requirements, resulting in task failure. Therefore, a reasonable load balancing algorithm is needed to balance the load on MEC servers and reduce the task response time of high-load MEC servers. Summary of the Invention

[0006] The purpose of this invention is to provide a game theory-based multi-edge server load balancing method for mobile edge computing (MEC). The MEC server load balancing problem is modeled as a non-cooperative game, and the existence of Nash equilibrium is proved by analyzing the convexity of the utility function and variational inequalities. Then, a proximal decomposition regularization (PDA) method is introduced to obtain a unique Nash equilibrium solution. Based on the established game model, a distributed mobile edge computing load balancing method is proposed to optimize the average response time and average energy consumption of MEC servers. Finally, the proposed method is evaluated from the perspectives of average task response time and average energy consumption of MEC servers, and the results are compared with those of algorithms based on average computing power allocation and particle swarm optimization.

[0007] To achieve the above objectives, the technical solution of this invention is: a multi-edge server load balancing method based on game theory in mobile edge computing. First, the MEC server load balancing problem is modeled as a non-cooperative game model, and the PDA regularization method is introduced to obtain a unique Nash equilibrium solution. Then, based on the established game model, a distributed mobile edge computing load balancing algorithm is proposed to optimize the average response time and average energy consumption of MEC servers.

[0008] In one embodiment of the present invention, the non-cooperative game model is modeled as follows:

[0009] 1) System Model

[0010] The system consists of n edge servers, 1 communication server, and several IoT devices; the edge servers are defined as... These edge servers provide computing services to nearby IoT devices; the task processing capacity and computing power of the edge servers are defined as follows: and At any given moment, the edge server receives computing requests from different IoT devices. The edge server aggregates these computing requests into a single task, defining the task arrival rate for each edge server. High-load edge servers obtain load information from communication servers and migrate part of their tasks to connected low-load edge servers; the task offloading vector between edge servers is defined as...

[0011] (1)

[0012] in Represents edge server The amount of workload, Indicated by edge server Migrate to edge server The workload on top; for The following constraints (2a)-(2c) are satisfied:

[0013]

[0014] (2a) indicates that the migration amount of each task should be greater than or equal to 0, that is, the non-negativity of the task; (2b) indicates that the sum of the task flow calculated by the edge server itself and the migration task flow should be equal to the received task flow, that is, the consistency of the task amount before and after the edge server is unloaded; (2c) indicates that the sum of the task calculated by the edge server itself and the migration task received from other edge servers should be less than the edge server's own computing power to meet the service reliability.

[0015] 2) Transmission Model

[0016] Different edge servers are interconnected via a wireless network with dedicated channels, ensuring no interference between channels and maintaining a stable transmission rate; the transmission time per unit task between edges is defined as...

[0017] (3)

[0018] in Represents edge server Offload unit tasks to edge servers The time required for the above, when At that time, it was considered that the edge server With edge servers They are connected; and the bidirectional transmission rates of the channels are the same, that is... Edge server The size is Tasks are transferred to the edge server The required time is expressed as

[0019] (4)

[0020] 3) Computational Model

[0021] On edge servers, task completion time consists of two parts: computation latency and queuing latency. Assuming task arrival on edge servers follows a Poisson distribution, based on queuing theory, each edge server is modeled as an M / M / 1 queuing system. The aggregate task arrival rate of the server is defined as... ,server On the task The computation time is expressed as

[0022] (5)

[0023] server Task queuing time is expressed as

[0024] (6)

[0025] Therefore, edge servers Complete the task locally Time is expressed as

[0026] (7)

[0027] When the edge server All tasks are computed locally, on edge servers. The total task completion time is

[0028] (8)

[0029] When the edge server offloads tasks to other edge servers, the edge server The total task completion time is

[0030] (9)

[0031] 4) Energy consumption model

[0032] When a task is migrated to another edge server, the resulting energy consumption consists of three parts: task transmission energy consumption, computation energy consumption, and result transmission energy consumption. Since result transmission energy consumption is relatively small, it is negligible. The different CPU architectures and communication interfaces used by edge servers result in different computation and transmission power. The computation energy consumption and transmission energy consumption per unit time of the edge server are defined as follows: and So, server The energy consumption to complete task x is expressed as

[0033] (10)

[0034] Edge server The task Transmitted to edge server The required energy is expressed as

[0035] (11)

[0036] When the edge server All tasks are computed locally, on edge servers. Total energy consumption is

[0037] (12)

[0038] When the edge server offloads tasks to other edge servers, the edge server Total energy consumption is

[0039] (13)

[0040] 5) Problem Definition

[0041] To balance the response time and energy consumption of edge servers, based on formula (9), and replacing the max function in the response time with a summation function, the following utility function is defined.

[0042] (14)

[0043] in For response time weighting, Weighted by energy consumption. and ;when This indicates that the edge server prioritizes optimizing response time. This indicates that edge servers are more focused on energy consumption, when This indicates that the edge server aims to optimize both response time and energy consumption.

[0044] The goal of each edge server in the system is to dynamically schedule tasks based on the current load and network status, finding the optimal task migration decision to minimize the cost function of each edge server. For edge server i, the optimization problem is defined as follows:

[0045] (15)

[0046]

[0047] Among them, (15a), (15b), and (15c) satisfy the nonnegativity, consistency, and reliability constraints in (2a), (2b), and (2c), respectively;

[0048] In this system, each edge server is a participant in a game, aiming to find the optimal offloading decision to reduce task response time and energy consumption. The load balancing problem of the edge servers is formulated as a non-cooperative game with complete information, expressed as:

[0049] (16)

[0050] Where N is the set of edge servers participating in the game. For the policy set of edge server i, Let i be the utility function for edge server i.

[0051] In game theory, Nash equilibrium is an important condition for measuring the stability of a system; Nash equilibrium: the optimal response strategy of participant i (i.e., edge server i). For any other strategy When equation (17) is satisfied, this strategy is the Nash equilibrium point of game G;

[0052] (17)

[0053] It is evident that when the system is at Nash equilibrium, no participant can reduce its cost by unilaterally changing its strategy. Therefore, no participant in the system has any incentive to deviate from the Nash equilibrium.

[0054] In one embodiment of the present invention, the specific implementation of introducing the PDA regularization method to obtain a unique Nash equilibrium solution is as follows:

[0055] When all participants update their strategies simultaneously, convergence to a Nash equilibrium may be impossible. Therefore, the PDA regularization method is introduced to iteratively converge game G to a unique Nash equilibrium solution. Based on the PDA regularization method, game G is redefined as...

[0056] (18)

[0057] in For regularization parameters, It is an edge server The previous round of mission migration decisions;

[0058] Meanwhile, edge servers The optimization problem has also been changed to

[0059] (19)

[0060]

[0061] In one embodiment of the present invention, the distributed mobile edge computing load balancing algorithm is as follows: At the beginning, each edge server transmits its own processing power, computing energy consumption, and load task to the communication server in the system. The communication server puts this information into the public information exchange module. At the beginning of each iteration, the edge server obtains public information from the communication server, and then calculates its strategy by solving the optimization problem (19) based on the information obtained from other edge servers. The obtained strategy is transmitted to the communication server, and the communication server updates the public information exchange module according to the obtained strategy. Finally, a precision control parameter ϵ is set. If the difference between the strategy of the edge server in this round and the strategy in the previous round is less than ϵ, this state is considered to be the Nash equilibrium state, and the communication server notifies all edge servers to stop iterating.

[0062] Compared to existing technologies, this invention offers the following advantages: It solves the load balancing problem among edge servers in IoT scenarios with multiple edge servers. Aiming to optimize the average response time and average energy consumption of edge servers, the problem is modeled as a non-cooperative game, and the PDA method is introduced to prove the existence of a unique Nash equilibrium solution. Then, a distributed mobile edge server load balancing method based on game theory is presented. Experimental results show that the average response latency obtained by this invention is 18.39% and 9.91% better than local computing and the computing power allocation strategy, respectively; the average energy consumption is 2.42% and 7.33% better than local computing and the computing power allocation strategy, respectively. The system cost is 3.96% lower than that of the particle swarm optimization (PSO) algorithm, but the computation time is only 1.81% of that of the PSO algorithm, demonstrating high execution efficiency. Attached Figure Description

[0063] Figure 1 The effect of ϵ on the number of algorithm iterations.

[0064] Figure 2 This refers to the load changes on the edge servers during algorithm execution.

[0065] Figure 3 This represents the change in cost of the edge server system during algorithm execution.

[0066] Figure 4 This section compares the algorithm performance in different scenarios.

[0067] Figure 5 This is a flowchart of the method of the present invention. Detailed Implementation

[0068] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0069] like Figure 5As shown, this invention provides a game theory-based multi-edge server load balancing method for mobile edge computing. First, the MEC server load balancing problem is modeled as a non-cooperative game model, and the PDA regularization method is introduced to obtain a unique Nash equilibrium solution. Then, based on the established game model, a distributed mobile edge computing load balancing algorithm is proposed to optimize the average response time and average energy consumption of MEC servers.

[0070] The following is a detailed implementation process of the present invention.

[0071] 1. Problem Model

[0072] 1.1 System Model

[0073] The system consists of n edge servers, 1 communication server, and several IoT devices. We define the edge servers as... These edge servers provide computing services to nearby IoT devices. Due to differences in CPU architecture, edge servers vary in task processing capabilities and computing power. The task processing capability and computing power of each edge server are defined as follows: and At any given moment, the edge server receives computing requests from different IoT devices. The edge server aggregates these requests into a single task, and we define the task arrival rate for each edge server as... Due to the limited computing power of edge servers, high-load edge servers obtain load information from communication servers and migrate part of their tasks to connected low-load edge servers to improve the user experience for IoT devices. The communication server does not need to exist independently; it can be a process within an edge server. We define the task offloading vector between edges as...

[0074] (1)

[0075] in Represents edge server The amount of workload, Indicated by edge server Migrate to edge server The workload. For The following constraints (2a)-(2c) are satisfied:

[0076]

[0077] Of the constraints above, (2a) indicates that the migration amount of each task should be greater than or equal to 0, i.e., the non-negativity of the task. (2b) indicates that the sum of the task flow computed by the edge server itself and the migrated task flow should be equal to the received task flow, i.e., the consistency of the task amount before and after the edge server is unloaded. (2c) indicates that the sum of the tasks computed by the edge server itself and the tasks migrated from other edge servers should be less than the edge server's own computing power to meet the service reliability requirements.

[0078] 1.2 Transmission Model

[0079] In our system, different edge servers are interconnected via a dedicated wireless network with no interference between channels and a stable transmission rate. Similar to existing research, we define the transmission time per task between edges as...

[0080] (3)

[0081] in Represents edge server Offload unit tasks to edge servers The time required for the above, when At that time, it was considered that the edge server With edge servers They are connected. Furthermore, the bidirectional transmission rates of the channel are the same, that is... Edge server The size is Tasks are transferred to the edge server The required time can be expressed as

[0082] (4)

[0083] 1.3 Calculation Model

[0084] On edge servers, task completion time consists of two parts: computation latency and queuing latency. Assuming task arrival on edge servers follows a Poisson distribution, based on queuing theory, we model each edge server as an M / M / 1 queuing system. The aggregate task arrival rate of the servers is defined as... ,server On the task The computation time can be expressed as

[0085] (5)

[0086] server The task queuing time can be expressed as

[0087] (6)

[0088] Therefore, edge servers Complete the task locally Time can be expressed as

[0089] (7)

[0090] When the edge server All tasks are computed locally, on edge servers. The total task completion time is

[0091] (8)

[0092] When the edge server offloads tasks to other edge servers, the edge server The total task completion time is

[0093] (9)

[0094] 1.4 Energy Consumption Model

[0095] When a task is migrated to another edge server, the resulting energy consumption consists of three parts: task transmission energy consumption, computation energy consumption, and result transmission energy consumption. Since result transmission energy consumption is relatively small and can be ignored, the transmission energy consumption will be equated with task transmission energy consumption below. Because edge servers use different CPU architectures and communication interfaces, their computational power and transmission power vary. We define the edge server's computational energy consumption and transmission energy consumption per unit time as follows: and So, server The energy consumption to complete task x can be expressed as

[0096] (10)

[0097] Edge server The task Transmitted to edge server The required energy can be expressed as

[0098] (11)

[0099] When the edge server All tasks are computed locally, on edge servers. Total energy consumption is

[0100] (12)

[0101] When the edge server offloads tasks to other edge servers, the edge server Total energy consumption is

[0102] (13)

[0103] 1.5 Problem Definition

[0104] To balance the response time and energy consumption of edge servers, we define the following utility function based on formula (9), replacing the max function in the response time with a summation function.

[0105] (14)

[0106] in For response time weighting, Weighted by energy consumption. and .when This indicates that the edge server prioritizes optimizing response time. This indicates that edge servers are more focused on energy consumption, when This indicates that the edge server aims to optimize both response time and energy consumption.

[0107] The goal of each edge server in the system is to dynamically schedule its tasks based on the current load and network status, finding the optimal task migration decision to minimize the cost function of each edge server. For edge server i, the optimization problem can be defined as follows:

[0108] (15)

[0109]

[0110] Among them, (15a), (15b), and (15c) satisfy the nonnegativity, consistency, and reliability constraints in (2a), (2b), and (2c), respectively.

[0111] 2. Game Theory Formulation and Proof

[0112] 2.1 Game Theory Formulation

[0113] Game theory studies the process by which participants, based on the information they possess, execute appropriate strategies from their allowed set of strategies and gain rewards. In our mobile edge computing system, each edge server is a participant in the game, aiming to find the optimal offloading decision to reduce task response time and energy consumption. For edge server i, its tasks can be completed locally or offloaded to other edge servers. Similarly, other edge servers can also offload tasks to edge server i. Therefore, the total task completion time and total energy consumption of edge server i depend not only on its own offloading strategy but also on the offloading strategies of other edge servers. We can formulate the load balancing problem of edge servers as a non-cooperative game with complete information, expressed as:

[0114] (16)

[0115] Where N is the set of edge servers participating in the game. For the policy set of edge server i, Let i be the utility function for edge server i.

[0116] In game theory, Nash equilibrium is an important condition for measuring the stability of a system. The definition of Nash equilibrium is given below.

[0117] Definition 1 (Nash Equilibrium). When participant i's optimal response strategy... For any other strategy When equation (17) is satisfied, the strategy is the Nash equilibrium point of game G.

[0118] (17)

[0119] According to Definition 1, when a system is at a Nash equilibrium, no participant can reduce its cost by unilaterally changing its strategy. Therefore, no participant in the system has an incentive to deviate from the Nash equilibrium.

[0120] 2.2 Proof of the Existence of Nash Equilibrium

[0121] In this section, we transform the game into a variational inequality and prove the existence of the Nash equilibrium for which we formulate the game.

[0122] Theorem 1. For each edge server Its unloading decision set is closed and convex, and its utility function is... It is continuously differentiable.

[0123] Proof. According to formula (15) for edge servers Uninstallation decision And satisfying constraints (15a), (15b), and (15c), according to the definition of a closed convex set, the decision set is closed convex. Then, based on equations (5), (6), (10), (11), and (14), we define the utility function... Rewritten as

[0124] (20)

[0125] right Taking the partial derivative yields

[0126] (twenty one)

[0127] because The partial derivatives of the utility function exist and are continuous, which can be obtained as follows: It is continuously differentiable.

[0128] Theorem 2. When the decisions of other edge servers do not change, the edge server The utility function is a convex function.

[0129] Proof. We will use the utility function obtained in Theorem 1. The partial derivative is defined as the gradient. According to the definition of a convex function, we only need to prove the utility function. Hessian matrix If the function is positive definite, then it is a convex function. for

[0130] (twenty two)

[0131] in

[0132]

[0133] Therefore, utility function Hessian matrix diagonal elements are The diagonal matrix. For all edge servers, the (15c) constraint is satisfied, i.e. Therefore, the utility function Hessian matrix diagonal elements , It is positive definite. When the decisions of other edge servers remain unchanged, according to the definition of a convex function, the edge server... The utility function is a convex function.

[0134] Theorem 3. When It is a non-empty closed convex set. When the function is a continuously differentiable convex function, then the game can be solved. Equivalence and Variational Inequality The solution. If the function If it is strictly monotonic, then the variational inequality has at most one solution, and the corresponding game has at most one equilibrium solution.

[0135] Proof. According to Theorem 1, we obtain the gradient of the utility function. Defined as

[0136] (twenty three)

[0137] Next, we will prove The monotonicity. If If it is monotonous, then the following conditions must be met.

[0138] (twenty four)

[0139] Formula (22) is equivalent to

[0140] (25)

[0141] For formula (23), take , can be obtained

[0142] (26)

[0143] therefore, The Jacobian matrix is

[0144] (27)

[0145] We proved in Theorem 2 It is a positive definite matrix, therefore It is also a positive definite matrix, a function It is a strictly monotonic function. For Since formula (26) holds true, formula (25) also holds true. It is strictly monotonic. Therefore, our game has at least one Nash equilibrium solution.

[0146] 3. Game Theory-Based Load Balancing Methods

[0147] Based on the above analysis, a non-cooperative game G with complete information was constructed, and the existence of Nash equilibrium solutions for game G was proven. Because the participants in the game are selfish, focusing only on minimizing their own costs and disregarding the impact of changes in their strategies on other participants, an iterative algorithm can be naturally proposed. In each iteration, each participant... Find the optimal task migration strategy under the current load conditions to minimize its own utility function. Then, when all participants update their policies simultaneously, convergence to a Nash equilibrium may fail. To address this issue, we introduce the PDA regularization method. The PDA method is suitable for solving convex Nash equilibrium problems; this technique generalizes the monotonic Nash equilibrium solution set to Nash equilibria with specific structures. Using the PDA method, we can iteratively converge our game G to a unique Nash equilibrium solution. Based on the PDA regularization method, we redefine game G as...

[0148] (18)

[0149] in For regularization parameters, It is an edge server The previous round of mission migration decisions.

[0150] Meanwhile, edge servers The optimization problem has also been changed to

[0151] (19)

[0152]

[0153] Next, we propose a distributed load balancing algorithm to solve the optimization problem (19), as shown in Algorithm 1.

[0154] Algorithm 1. Distributed Load Balancing Algorithm

[0155] enter:

[0156] Output: Nash equilibrium solution

[0157] 1. Initialization

[0158] 2. Edge server i transmits its processing power, computing power consumption, and workload to the communication server.

[0159] 3. while Nash equilibrium has not been reached (do)

[0160] 4. Edge server i obtains information about other edge servers from the communication server.

[0161] 5. for each i do

[0162] 6. Calculate the unloading vector

[0163] 7. Edge Server iTransmission to the communication server

[0164] 8. end for

[0165] 9.

[0166] 10.k k+1

[0167] 11.if

[0168] 12. Upon reaching equilibrium, the communication server notifies the user to stop iteration.

[0169] 13.end if

[0170] 14. end while

[0171] 15. return

[0172] Initially, each edge server transmits its processing power, computational energy consumption, and workload to the communication server in the system. The communication server then places this information into the public information exchange module. At the start of each iteration, the edge server obtains public information from the communication server and, based on the information from other edge servers, solves the optimization problem (19) to calculate its policy. The obtained policy is then transmitted to the communication server, which updates the public information exchange module accordingly. Finally, we set a precision control parameter ϵ. If the difference between the edge server's policy in the current iteration and its policy in the previous iteration is less than ϵ, we consider this state to be the Nash equilibrium state, and the communication server notifies all edge servers to stop iterating. By introducing ϵ, the number of iterations required to reach the equilibrium state can be significantly reduced.

[0173] 4. Experimental Simulation and Results

[0174] 4.1 Experimental Setup

[0175] The simulation environment runs on a system equipped with a 3.10GHz Intel(R) Core(TM) i5-10500 CPU and 8GiB RAM. The distributed load balancing algorithm is implemented in Python 3.10, using CVXPY 1.2 and its solver CPLEX to solve the optimization problem. The computing power F of the edge servers and the task arrival rate are also considered. The data follows a normal distribution. Due to the limitations of queuing theory, the initial task arrival rate of the edge service cannot exceed its computing capacity. The transmission time D per task of the edge server is proportional to the distance between edge servers. The computing power P and transmission power W per unit time of the edge server also follow a normal distribution. The regularization parameter in the PDA method is set to 0.02, and the precision control parameter ϵ is set to 0.01. Specific relevant parameters are shown in Table 1.

[0176] Table 1 Edge Server Parameters

[0177]

[0178] To verify the effectiveness of the proposed method, we conducted comparative experiments with three other offloading strategies: a local computation-only strategy, a task migration strategy based on server capacity, and a task migration strategy based on particle swarm optimization (PSO). The Local Computation (LC) strategy involves edge servers performing only local computation without migrating arriving tasks. This avoids the additional overhead of transmission latency and energy consumption; however, the average computation time and energy consumption depend on the initial task distribution.

[0179] Capacity-Based Task Immigration (CTI) is a strategy where edge servers offload their arriving tasks to other edge servers proportionally to their computing capabilities. Since tasks can be processed in parallel across edge servers, this strategy can reduce average computation latency. However, because it doesn't consider the computational and transmission energy consumption of the edge servers, as well as the network conditions between edges, this strategy may still lead to increased average energy consumption and significant transmission latency.

[0180] The task migration strategy based on the Particle Swarm Optimization-Genetic Algorithm (PSO-GA) is a centralized optimization algorithm inspired by avian predation behavior and Darwin's theory of evolution. Through particle search and mutation, it can obtain approximate optimal solutions to optimization problems. In this paper, the task migration ratio is defined as the search space, and the task migration strategies of all edge servers are defined as particles. The relevant parameters used are shown in Table 2.

[0181] Table 2 PSO-GA Algorithm Parameters

[0182]

[0183] 4.2 Experimental Results and Analysis

[0184] 4.2.1 Algorithm Convergence

[0185] In this section, we verify the convergence of the proposed algorithm through experiments, setting parameters... The effect of the precision control parameter ϵ on the average number of iterations of the algorithm is as follows: Figure 1As shown, when ϵ approaches 0, the algorithm requires a large number of iterations to converge. As ϵ increases, the number of iterations decreases, but the obtained result deviates significantly from the equilibrium point. Therefore, to obtain a more accurate solution within an acceptable number of iterations, we set ϵ = 0.01 for subsequent experiments.

[0186] We randomly selected three edge servers in the system to observe their load during algorithm execution. Figure 2 ) and system cost ( Figure 3 The load changes. Edge server 1 and edge server 2 are high-load servers, while edge server 3 is a low-load server. During the iteration process, the load of the high-load edge server gradually decreases, and its system cost decreases accordingly, while the load of the low-load edge server gradually increases, and its system cost increases accordingly. After 4 rounds of iteration, the load of the edge servers and the system cost tend to stabilize, indicating that our algorithm can quickly obtain a unique Nash equilibrium solution.

[0187] 4.2.2 Impact of Weighting Coefficients on Delay and Energy Consumption

[0188] Response time weight Energy consumption weight These represent the edge server's emphasis on response time and energy consumption, respectively. When the edge server performs latency-sensitive tasks, settings can be configured... This is to achieve a shorter response time. When the edge server is performing energy-intensive tasks, it can be configured to... This can effectively reduce system energy consumption. We tested this in three random scenarios. , ; , ; , The obtained average response time and average energy consumption were statistically analyzed, as shown in Table 3. It can be seen that when the response time weight... As the energy consumption weight increases, the average response time of the obtained unloading scheme decreases; when the energy consumption weight increases... As the value increases, the average energy consumption of the unloading decreases.

[0189] Table 3 Different Scenarios , The impact of

[0190]

[0191] 4.2.3 Performance Comparison

[0192] To compare the performance of the game theory-based distributed load balancing method with local computing, computing power allocation-based methods, and particle swarm optimization (PSO) genetic algorithm, we conducted comparative experiments on 100 random scenarios. The results are shown in Table 4. The proposed algorithm outperforms local computing and computing power allocation-based methods by 18.39% and 9.91% respectively in average response latency, and is only 6.54% slower than PSO. In terms of energy consumption, it outperforms local computing and computing power allocation-based methods by 2.42% and 7.33% respectively, and is only 0.83% slower than PSO. Regarding overall system cost, it outperforms local computing and computing power allocation-based methods by 12.08% and 8.80% respectively, and is only 3.96% slower than PSO. It can be seen that the game theory-based distributed load balancing method proposed in this paper significantly outperforms local computing and computing power allocation-based methods, and has a relatively small difference in performance compared to PSO. Figure 4 The average system cost obtained by each algorithm in three scenarios is given, which more intuitively confirms the above conclusion.

[0193] Table 4 Algorithm Performance Comparison

[0194]

[0195] Although the Particle Swarm Optimization (PSO) algorithm yields better results than the algorithm presented in this paper, its average execution time of 52.51 seconds is unacceptable. In contrast, the algorithm proposed in this paper requires an average execution time of only 0.95 seconds, just 1.81% of that of the PSO algorithm. Therefore, the proposed method is more practical and suitable for real-world scenarios.

[0196] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A game theory-based multi-edge server load balancing method in mobile edge computing, characterized in that, First, the MEC server load balancing problem is modeled as a non-cooperative game model, and the PDA regularization method is introduced to obtain a unique Nash equilibrium solution. Then, based on the established game model, a distributed mobile edge computing load balancing algorithm is proposed to optimize the average response time and average energy consumption of MEC servers. The specific implementation of the PDA regularization method to obtain the unique Nash equilibrium solution is as follows: When all participants update their strategies simultaneously, convergence to a Nash equilibrium may be impossible. Therefore, the PDA regularization method is introduced to iteratively converge game G to a unique Nash equilibrium solution. Based on the PDA regularization method, game G is redefined as follows: Where N is the set of edge servers participating in the game. For the policy set of edge server i, For regularization parameters, It is an edge server The previous round of mission migration decisions, Let the utility function for edge server i be defined as follows: in For response time weighting, Weighted by energy consumption. and ; Represents edge server Complete the task locally Time; Represents edge server The size is Tasks are transferred to the edge server The time required; Indicates server The energy consumption required to complete task x; Represents edge server The task Transmitted to edge server Energy required; n is the number of edge servers; Indicated by edge server Migrate to edge server The workload on top; Represents edge server The arrival rate of aggregated tasks; Meanwhile, edge servers The optimization problem has also been changed to in This represents the policy set of all other edge servers in the system besides edge server i. This represents the task arrival rate of edge server i; This represents the processing capacity of edge server i; the three formulas from top to bottom in the constraints respectively indicate that the migration amount of each task should be greater than or equal to 0, that is, the non-negativity of the task; The sum of the task flow computed by the edge server itself and the task flow migrated should equal the received task flow, that is, the consistency of the task volume before and after the edge server is unloaded. The sum of the edge server's own computing tasks and the tasks it accepts from other edge servers should be less than the edge server's own computing capacity to ensure service reliability. The distributed mobile edge computing load balancing algorithm is as follows: Initially, each edge server transmits its processing power, computing energy consumption, and workload to the communication server in the system. The communication server then places this information into the public information exchange module. At the start of each iteration, the edge server obtains public information from the communication server, and then, based on the information from other edge servers, solves an optimization problem to calculate its strategy. The obtained strategy is then transmitted to the communication server, which updates the public information exchange module accordingly. Finally, a precision control parameter ϵ is set. If the difference between the edge server's strategy in this round and the strategy in the previous round is less than ϵ, this state is considered a Nash equilibrium state, and the communication server notifies all edge servers to stop iterating.

2. The game theory-based multi-edge server load balancing method in mobile edge computing according to claim 1, characterized in that, The modeling method for the non-cooperative game theory model is as follows: 1) System Model The system consists of n edge servers, 1 communication server, and several IoT devices; the edge servers are defined as... These edge servers provide computing services to nearby IoT devices; the task processing capacity and computing power of the edge servers are defined as follows: and At any given moment, the edge server receives computing requests from different IoT devices. The edge server aggregates these computing requests into a single task, defining the task arrival rate for each edge server. High-load edge servers obtain load information from communication servers and migrate part of their tasks to connected low-load edge servers; the task offloading vector between edge servers is defined as... in Represents edge server The amount of workload, Indicated by edge server Migrate to edge server The workload on top; for The following constraints (2a)-(2c) are satisfied: (2a) indicates that the migration amount of each task should be greater than or equal to 0, that is, the non-negativity of the task; (2b) indicates that the sum of the task flow calculated by the edge server itself and the migration task flow should be equal to the received task flow, that is, the consistency of the task amount before and after the edge server is unloaded; (2c) indicates that the sum of the task calculated by the edge server itself and the migration task received from other edge servers should be less than the edge server's own computing power to meet the service reliability. 2) Transmission Model Different edge servers are interconnected via a wireless network with dedicated channels, ensuring no interference between channels and maintaining a stable transmission rate; the transmission time per unit task between edges is defined as... in Represents edge server Offload unit tasks to edge servers The time required for the above, when At that time, it was considered that the edge server With edge servers They are connected; and the bidirectional transmission rates of the channels are the same, that is... Edge server The size is Tasks are transferred to the edge server The required time is expressed as 3) Computational Model On edge servers, task completion time consists of two parts: computation delay and queuing delay. Assuming that task arrival on edge servers follows a Poisson distribution, based on queuing theory, each edge server is modeled as an M / M / 1 queuing system. Define the arrival rate of the server's aggregated tasks. ,server On the task The computation time is expressed as server Task queuing time is expressed as Therefore, edge servers Complete the task locally Time is expressed as When the edge server All tasks are computed locally, on edge servers. The total task completion time is When the edge server offloads tasks to other edge servers, the edge server The total task completion time is 4) Energy consumption model When a task is migrated to another edge server, the resulting energy consumption consists of three parts: task transmission energy consumption, computing energy consumption, and result transmission energy consumption; since the result transmission energy consumption is small, it can be ignored. Edge servers use different CPU architectures and communication interfaces, resulting in variations in their computing and transmission power. We define the computing power consumption and transmission power consumption per unit time of an edge server as follows: and So, server The energy consumption to complete task x is expressed as Edge server The task Transmitted to edge server The required energy is expressed as When the edge server All tasks are computed locally, on edge servers. Total energy consumption is When the edge server offloads tasks to other edge servers, the edge server Total energy consumption is 5) Problem Definition To balance the response time and energy consumption of edge servers, based on formula (9), and replacing the max function in the response time with a summation function, the following utility function is defined. in For response time weighting, Weighted by energy consumption. and ;when This indicates that the edge server prioritizes optimizing response time. This indicates that edge servers are more focused on energy consumption, when This indicates that the edge server aims to optimize both response time and energy consumption. The goal of each edge server in the system is to dynamically schedule the tasks of the edge server based on the current load and network status of the edge servers in the system, find the optimal migration decision for the edge server tasks, and minimize the cost function of the edge server itself. For edge server i, the optimization problem is defined as follows: Among them, (15a), (15b), and (15c) satisfy the nonnegativity, consistency, and reliability constraints in (2a), (2b), and (2c), respectively; In the system, each edge server is a participant in a game, and its goal is to find the optimal offloading decision to reduce the response time and energy consumption of the task. The load balancing problem of edge servers is formulated as a non-cooperative game with complete information, and the game expression is as follows: (16) Where N is the set of edge servers participating in the game. For the policy set of edge server i, Let i be the utility function for edge server i; In game theory, Nash equilibrium is an important condition for measuring the stability of a system; Nash equilibrium: the optimal response strategy of participant i (i.e., edge server i). For any other strategy When equation (17) is satisfied, this strategy is the Nash equilibrium point of game G; (17) It is evident that when the system is at Nash equilibrium, no participant can reduce its cost by unilaterally changing its strategy. Therefore, no participant in the system has any incentive to deviate from the Nash equilibrium.

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