Task execution uncertainty-aware control method for industrial edge computing services

Abstract

The application discloses an industrial edge computing service time-sensitive control method considering task execution uncertainty, comprising the following steps: obtaining the computing task type, task execution parameter and historical execution data of an industrial scene; obtaining a conditional task execution graph through statistical analysis according to the historical execution data of the computing task; obtaining a corresponding task scene graph and occurrence probability based on the conditional task execution graph; constructing a computing service control model according to the task scene graph and the corresponding occurrence probability; solving the computing service control model by using a Lagrange decomposition algorithm to obtain an optimal industrial edge computing service control scheme; and (6) implementing specific computing resource allocation and task execution according to the optimal industrial edge computing service control scheme. The application solves the quantification problem of edge computing task execution uncertainty and significantly improves the edge computing service control quality.

Description

Technical Field

[0001] This invention relates to the field of industrial Internet of Things (IIoT) edge computing service control and application, and in particular to a time-sensitive control method for industrial edge computing services that takes into account the uncertainty of task execution. Background Technology

[0002] In the Industrial Internet of Things (IIoT) environment, to meet the time-sensitive requirements of manufacturing activities, a large amount of computing resources are deployed at the manufacturing edge, close to the data source, to effectively process various types of production data collected in real time. Typically, these distributed computing resources provide support for manufacturing activities in the form of edge computing services, offering monitoring, analysis, and decision-making capabilities.

[0003] At the same time, this production data will be transformed into a series of computational tasks with complex execution dependencies.

[0004] Chinese patent document CN112486690A discloses an edge computing resource allocation method suitable for the Industrial Internet of Things (IIoT). The method includes constructing a state space, action space, and reward function for an industrial edge computing model; selecting a set of high-quality forwarding paths and computing nodes as execution schemes for the action space using initial selection rules; selecting actions to be executed from the action space using ε-Greedy and calculating the reward for executing the action based on the reward function; iteratively updating the current network and the target network based on the selected action and its reward; and completing the training and outputting the current resource allocation scheme when the Q-value of the current network is close to that of the target network. This invention can address resource imbalances caused by differences between edge servers, dynamically balancing load resources and effectively reducing the transmission and processing time of device tasks.

[0005] In practice, this can be described using a directed acyclic graph (DAG), where vertices represent computational tasks and directed edges typically represent dependencies between two tasks. Generally, a computational task can only begin after its preceding tasks have completed processing and transmitted all the result data to it.

[0006] Due to the complexity and uncertainty of industrial scenarios, not all computational tasks are executed in actual task execution. Specifically, the execution of subsequent tasks often depends on the computation results of preceding tasks. Furthermore, some computational tasks may be mutually exclusive, and which task is actually executed is often uncertain. Therefore, the directed acyclic graph defined above is no longer sufficient to effectively represent the complex execution relationships between these industrial computational tasks.

[0007] Currently, industrial edge computing services are uniformly scheduled under the assumption that computing tasks are completely deterministic in execution, ignoring the inherent uncertainty of task execution. This can easily lead to unreasonable service control schemes, allocating resources to computing tasks that are not actually being executed, thus affecting overall task processing efficiency. Especially in industrial scenarios, the results of production data processing often need to be returned within a very short time, and the control of computing tasks must also meet timeliness requirements, making it crucial to improve service control capabilities. Summary of the Invention

[0008] This invention addresses the shortcomings of existing industrial edge computing service control methods that lack consideration of whether various tasks are actually executed. It provides a time-sensitive control method for industrial edge computing services that takes into account the uncertainty of task execution. The method uses probabilistic methods to quantitatively characterize the execution probability between computing tasks, solving the problem of quantifying the uncertainty of edge computing task execution. Furthermore, through time-sensitive modeling and optimization of industrial edge computing services based on stochastic programming, it achieves a significant improvement in the control quality of edge computing services.

[0009] The technical solution of the present invention is as follows:

[0010] A time-sensitive control method for industrial edge computing services that considers task execution uncertainty includes the following steps:

[0011] (1) Based on the operational data and network topology of the industrial edge computing service, obtain the computing task type, task execution parameters and historical execution data of the industrial scenario;

[0012] (2) Based on the historical execution data of the computing tasks, the execution dependencies between computing tasks and the conditional execution probabilities of related tasks are obtained through statistical analysis, thereby obtaining the conditional task execution graph and quantitatively characterizing the complex dependencies between industrial computing tasks.

[0013] (3) Based on the conditional task execution graph, generate the corresponding task scenario tree. Each leaf node of the task scenario tree represents a possible task execution scenario, thereby obtaining the corresponding task scenario graph and calculating the occurrence probability of each task scenario graph.

[0014] (4) Based on the task scenario diagram and its corresponding occurrence probability, construct a computing service control model based on multi-scenario stochastic programming;

[0015] (5) The Lagrange decomposition algorithm is used to solve the computing service control model to obtain the optimal industrial edge computing service control scheme that considers all uncertain task execution scenarios;

[0016] (6) Implement specific computing resource allocation and task execution according to the optimal industrial edge computing service control scheme, and periodically monitor the changes in actual task execution data, update the parameters of the computing service control model and the optimal industrial edge computing service control scheme.

[0017] In step (1), the computing task type refers to the types and number of computing tasks existing in the actual industrial scenario; the task execution parameters include the input data scale, the result data scale, computing resource capacity, network transmission capacity, and effective processing time limit; the historical execution data refers to the statistics of the number of subsequent tasks that are also executed under the condition that the preceding task is executed.

[0018] In step (2), the conditional task execution graph is a weighted directed acyclic graph; in the weighted directed acyclic graph, vertices represent computational tasks, directed edges represent dependencies between tasks, and the corresponding weight values ​​indicate the probability that a subsequent task may be executed when the preceding task is executed.

[0019] Furthermore, computational tasks are divided into two categories: real tasks, which are actual computational tasks that may need to be executed; and virtual computational tasks, which are tasks that do not need to be actually executed. These virtual tasks are mainly used to describe a class of mutually exclusive computational tasks.

[0020] Mutually exclusive computational tasks are multiple optional computational tasks, but only one is actually allowed to be executed.

[0021] Furthermore, directed edges are divided into two categories: one is where there is a data dependency between computational tasks, meaning that a subsequent task must receive the output data of the preceding task before it can be executed; the other is where there is a logical dependency between computational tasks, meaning that a subsequent task can only be executed after the preceding task is completed, but it does not need the output data of the preceding task.

[0022] In step (3), the probability calculation formula for the occurrence of the task scene graph is shown in equation (1):

[0023]

[0024] Among them, p(g q ) represents the task scenario diagram g q The probability of its occurrence, It is the probability value that edge e1 will be executed. This represents the probability that edge e2 will not be executed.

[0025] Equation (1) represents the task scenario diagram g. q The probability of an edge appearing is equal to the product of the probabilities of all edges that are executed and those that are not executed in the task execution scenario.

[0026] In step (4), the computational service control model uses the total expected task completion time F. t o tal To optimize the objectives, service control constraints, network transmission constraints, computing resource capacity constraints, and scenario time sensitivity constraints are comprehensively considered.

[0027] Furthermore, the total expected completion time F of the task t o tal For each task scenario, see graph g. q The corresponding total task completion time F q Rather than the probability of occurrence p(g) q The sum of the products of ) is calculated using the following formula:

[0028] F t o tal =∑ q p(g q )×F q (2).

[0029] Furthermore, the computing service control model is shown in equations (6) to (15):

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] F q ≤T q ,q=1…N1 (14)

[0039] s iq ≥0,f iq ≥0,z ik ∈{0,1},x ij , q ∈{0,1} (15)

[0040] Wherein, the objective function (6) is to minimize the total expected completion time F of the task. total ;z ikIt is a 0-1 variable, where 1 indicates that computation task i is planned to be processed at industrial computation point k; s iq ,f iq Representing the task scenario graph g respectively q The start and end times of computation task i in the calculation; x ij , q It is also a 0-1 variable, where 1 represents the task scenario graph g. q In the computation, tasks i and j are assigned to the same computation point, and task i begins after task j is completed; N1 is the number of task scenario graphs, N2 is the number of computation tasks, and N3 is the number of computation points; P ik D ij The processing time of computation task i at computation point k and the data transfer time between computation tasks i and j are respectively represented; DSS(i,q) represents the task scenario graph g. q The set of computation tasks directly connected by directed edges originating from computation task i; SS(i,q) represents the task scenario graph g. q The set of tasks that can only be executed after task i has been computed; T q Represents the task scenario diagram g q The maximum allowed completion time; M is a relatively large positive integer, which can be chosen to guarantee the completion of all computational tasks;

[0041] Equation (7) constrains that a computational task can only be processed at one computation point; Equation (8) indicates that the difference between the start time and the end time of a computational task is equal to its processing time at a certain computation point; Equation (9) indicates that when two directly related tasks are processed at the same computation point, data transmission time is not considered; otherwise, the start time of the latter task needs to include data transmission time; Equations (10), (11), and (12) are non-overlapping constraints, indicating that when two computational tasks are arranged at the same computation point, the processing times of these two tasks are not allowed to overlap; Equation (13) indicates that the total task completion time corresponding to each task execution graph should not be less than the end time of the last task; Equation (14) is a time-sensitive constraint, that is, the total task completion time corresponding to each task execution graph should meet the corresponding processing time sensitivity requirements; Equation (15) is the range of values ​​for the variable.

[0042] Step (5) includes:

[0043] (5-1) Introduce 0-1 variable z ik,q Taking 1 indicates the task scenario graph g q The computation task i is processed at computation point k, otherwise it is set to 0, and then the constraints of the original computation service control model are decomposed according to the task scenario diagram.

[0044] (5-2) Establish unpredictability constraints to characterize the uncertainty of task execution in the service control phase, as shown in equation (3):

[0045]

[0046] (5-3) The unpredictable constraints between task scenarios are processed using Lagrange duality theory, and the computational service control sub-model of each task scenario graph is further obtained.

[0047] (5-4) Initialize the Lagrange multiplier ω ik,q =0, solve for the service control sub-model corresponding to each task scenario graph;

[0048] (5-5) The variable values ​​z obtained from each sub-model ik,q Calculate the weighted average The specific formula is as follows:

[0049]

[0050] (5-6) Calculate the iteration termination condition If the value is less than the threshold, proceed to the next step; otherwise, update the Lagrange multipliers using formula (5), as shown below:

[0051]

[0052] in, and These are the Lagrange multipliers corresponding to the s-th and s+1-th iterations, respectively, and ρ is the iteration step size;

[0053] (5-7) The value obtained Round down to the nearest z ik,q The value of is substituted into the computing service control model for solution, and the final optimal industrial edge computing service control scheme is obtained.

[0054] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0055] Compared to traditional methods, this invention proposes a time-sensitive control method for industrial edge computing services that considers task execution uncertainty. First, it obtains conditional task execution graphs and related service control model parameters by analyzing historical data of industrial computing services. Based on this, a scenario tree generation method is used to obtain a series of task scenario graphs and their associated occurrence probabilities. Then, a computing service control model based on multi-scenario stochastic programming is constructed. Subsequently, the Lagrange decomposition algorithm is used to solve this computing service control model. Unpredictability constraints are introduced to characterize the task execution uncertainty in the service control stage. Finally, the optimal service control scheme considering all uncertain task execution scenarios is obtained. This method effectively integrates knowledge of the uncertainties involved in task execution in actual industrial edge computing scenarios, aiming to minimize the total expected task completion time. The final scheme satisfies strict time-sensitive constraints while considering the possibility of multiple task execution scenarios, thus improving the quality of industrial edge computing service control. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of the edge computing service resource topology in a certain industrial scenario, where CN1 to CN5 represent five industrial computing nodes.

[0057] Figure 2 A flowchart illustrating a time-sensitive control method for industrial edge computing services that takes into account the uncertainty of task execution;

[0058] Figure 3 This is a schematic diagram illustrating the execution of a conditional task in a specific industrial scenario.

[0059] Figure 4 This is a schematic diagram of a task scenario in a specific industrial setting. Detailed Implementation

[0060] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the embodiments described below are intended to facilitate the understanding of the present invention and do not limit it in any way.

[0061] Taking the edge computing service control problem in a certain industrial scenario as an example, such as Figure 1 and Figure 2 As shown, the specific steps of a time-sensitive control method for industrial edge computing services that considers task execution uncertainty are as follows:

[0062] (1) Based on the operational data and network topology of the industrial edge computing service, obtain the computing task type, task execution parameters and historical execution data of the industrial scenario;

[0063] The types of computing tasks refer to the types and quantities of computing tasks that exist in actual industrial scenarios; task execution parameters include the scale of input data, the scale of result data, computing resource capabilities, network transmission capabilities, and effective processing time limits; historical execution data refers to the statistics of the number of subsequent tasks that were also executed under the condition that the preceding tasks were executed.

[0064] (2) Based on the historical execution data of edge computing services in this industrial scenario, statistical analysis is used to derive the execution dependencies between tasks and the conditional execution probabilities of related tasks, thereby obtaining a conditional task execution graph to quantitatively characterize the complex dependencies between industrial computing tasks, such as... Figure 3 As shown in the figure, the edge weights represent the probability that the subsequent task may be executed under the condition that the preceding task is executed;

[0065] The conditional task execution graph described in step (2) is a special type of weighted directed acyclic graph. Figure 3 This is a specific instance. Vertices still represent computational tasks, divided into two categories: real tasks (solid circles) and virtual tasks (dashed circles). Real tasks are tasks that actually exist and may need to be executed. Virtual tasks do not require actual execution and are used to describe mutually exclusive tasks—multiple options but only one is allowed to be executed. Directed edges represent data dependencies between tasks; that is, a subsequent task requires the output of the preceding task to execute. The corresponding weight value indicates the probability that the subsequent task might execute given the execution of the preceding task. A weight of 1 means that the subsequent task must execute if the preceding task is executed.

[0066] (3) Based on the conditional task execution graph, a corresponding task scenario tree is generated, where each leaf node represents a possible task execution scenario, resulting in a corresponding task scenario graph. The probability of occurrence p(g) of each task scenario graph is then calculated using formula (1). q ),like Figure 4 As shown;

[0067]

[0068] Among them, p(g q ) represents the task scenario diagram g q The probability of its occurrence, It is the probability value that edge e1 will be executed. This represents the probability that edge e2 will not be executed; Equation (1) represents the task scenario graph g. qThe probability of occurrence is equal to the product of the probability values ​​of all executed edges and non-executed edges in the scenario; the task execution graph described in step (3) is a type of directed acyclic graph, where the vertices represent the computational tasks that are actually executed in the task scenario. The directed edges are divided into two categories: one is that there is a data dependency between tasks, that is, the subsequent task must receive the output result data of the preceding task before it can be executed, which is represented by solid lines; the other is that there is a logical dependency between tasks, that is, the subsequent task must be completed before it can be executed, but it does not need the output result of the preceding task, which is represented by dashed lines.

[0069] (4) Based on these task scenario diagrams and their corresponding occurrence probabilities, an industrial edge computing service control model based on multi-scenario stochastic programming is constructed. The computing service control model is based on the total expected completion time F of the task. t o tal To optimize the objective, namely, to define the graph g for each task scenario. q The corresponding total task completion time F q Rather than the probability of occurrence p(g) q The product of ) is calculated as shown in formula (2), and then the service control constraints, network transmission constraints, computing resource capacity constraints and scenario time sensitivity constraints are taken into account.

[0070] F t o tal =∑ q p(g q )×F q (2)

[0071] The specific computing service control model is shown in equations (6) to (15):

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080] F q ≤T q ,q=1…N1 (14)

[0081]

[0082] Wherein, the objective function (6) is to minimize the total expected completion time F of the task. total ;z ik It is a 0-1 variable, where 1 indicates that computation task i is planned to be processed at industrial computation point k; s iq ,f iq Representing the task scenario graph g respectively q The start and end times of computation task i in the calculation; x ij , q It is also a 0-1 variable, where 1 represents the task scenario graph g. q In the computation, tasks i and j are assigned to the same computation point, and task i begins after task j is completed; N1 is the number of task scenario graphs, N2 is the number of computation tasks, and N3 is the number of computation points; P ik D ij The processing time of computation task i at computation point k and the data transfer time between computation tasks i and j are respectively represented; DSS(i,q) represents the task scenario graph g. q The set of computation tasks directly connected by directed edges originating from computation task i; SS(i,q) represents the task scenario graph g. q The set of tasks that can only be executed after task i has been computed; T q Represents the task scenario diagram g q The maximum allowed completion time; M is a relatively large positive integer, which can be chosen to guarantee the completion of all computational tasks;

[0083] Equation (7) constrains that a computation task can only be processed at one computation point; Equation (8) indicates that the difference between the start time and the end time of a computation task is equal to its processing time at a certain computation point; Equation (9) indicates that when two directly related tasks are processed at the same computation point, data transmission time is not considered; otherwise, the start time of the latter task needs to include data transmission time; Equations (10), (11), and (12) are non-overlapping constraints, indicating that when two computation tasks are arranged at the same computation point, the processing times of these two tasks are not allowed to overlap; Equation (13) indicates that the total task completion time corresponding to each task execution graph should not be less than the end time of the last task; Equation (14) is a time-sensitive constraint, that is, the total task completion time corresponding to each task execution graph should meet the corresponding processing time-sensitive requirements; Equation (15) is the range of values ​​for the variable;

[0084] (5) For models (6) to (15), the Lagrange decomposition algorithm is used to solve the above computational service control model. The specific process is as follows:

[0085] (5-1) Introduce 0-1 variable z ik,qTaking 1 indicates the task scenario graph g q Whether task i is processed in computing resource k, otherwise take 0, and then decompose the constraints of the original computing service control model according to each task scenario diagram;

[0086] (5-2) At the same time, an unpredictability constraint is established to characterize the uncertainty of task execution in the service control phase, as shown in equation (3):

[0087]

[0088] (5-3) The unpredictable constraints between task scenarios are processed using Lagrange duality theory, and the computational service control sub-model of each task scenario graph is further obtained.

[0089] (5-4) Initialize the Lagrange multiplier ω ik,q =0, solve for the service control sub-model corresponding to each task scenario graph;

[0090] (5-5) The variable values ​​z obtained from each sub-model ik,q Calculate the weighted average The specific formula is as follows:

[0091]

[0092] (5-6) Therefore, the iteration termination condition is calculated. If the value is less than a certain threshold, proceed to the next step; otherwise, update the Lagrange multiplier ω using formula (5), as shown below:

[0093]

[0094] in, and These are the Lagrange multipliers corresponding to the s-th and s+1-th iterations, respectively, and ρ is the iteration step size;

[0095] (5-7) The value obtained Round down to the nearest z ik,q The value of is substituted into the original model for solution, and the final industrial edge computing service control scheme is obtained.

[0096] (6) Implement specific computing resource allocation and task execution according to the optimal computing service control scheme, and periodically monitor changes in actual task execution data to update service control model parameters and optimal control scheme.

[0097] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A time-sensitive control method for industrial edge computing services considering task execution uncertainty, characterized in that, Includes the following steps: (1) Based on the operation data and network topology of the industrial edge computing service, obtain the computing task type, task execution parameters and historical execution data of the industrial scenario; the computing task type refers to the types and number of computing tasks existing in the actual industrial scenario; the task execution parameters include the input data scale, result data scale, computing resource capacity, network transmission capacity and effective processing time limit; The historical execution data refers to the statistics of the number of subsequent tasks that were also executed under the condition that the preceding task was executed; (2) Based on the historical execution data of the computing tasks, the execution dependencies between computing tasks and the conditional execution probabilities of related tasks are obtained through statistical analysis, thereby obtaining the conditional task execution graph and quantitatively characterizing the complex dependencies between industrial computing tasks. (3) Based on the conditional task execution graph, a corresponding task scenario tree is generated. Each leaf node of the task scenario tree represents a possible task execution scenario, thereby obtaining the corresponding task scenario graph and calculating the occurrence probability of each task scenario graph. The conditional task execution graph is a weighted directed acyclic graph. In the weighted directed acyclic graph, vertices represent computation tasks, directed edges represent dependencies between tasks, and the corresponding weight values ​​indicate the probability that the subsequent task may be executed when the preceding task is executed. Computational tasks are divided into two categories: real tasks, which are actual computational tasks that may need to be executed; and virtual tasks, which are tasks that do not need to be actually executed and are mainly used to describe a class of mutually exclusive computational tasks. Directed edges are divided into two categories: one is where there is a data dependency between computational tasks, that is, a subsequent task must receive the output data of the preceding task in order to execute; and the other is where there is a logical dependency between computational tasks, that is, a subsequent task must be completed before it can execute, but it does not need the output data of the preceding task. (4) Based on the task scenario diagram and its corresponding occurrence probability, construct a computational service control model based on multi-scenario stochastic programming; (5) The Lagrange decomposition algorithm is used to solve the computing service control model to obtain the optimal industrial edge computing service control scheme that considers all uncertain task execution scenarios; (6) Implement specific computing resource allocation and task execution according to the optimal industrial edge computing service control scheme, and periodically monitor the changes in actual task execution data, update the parameters of the computing service control model and the optimal industrial edge computing service control scheme.

2. The time-sensitive control method for industrial edge computing services considering task execution uncertainty according to claim 1, characterized in that, In step (3), the probability calculation formula for the occurrence of the task scene graph is shown in equation (1): （1） in, Representing the task scenario diagram The probability of its occurrence, It is the edge The probability value of being executed. Representing an edge The probability value that it will not be executed.

3. The time-sensitive control method for industrial edge computing services considering task execution uncertainty according to claim 1, characterized in that, The aforementioned computing service control model uses the total expected completion time of the task. To optimize the objectives, service control constraints, network transmission constraints, computing resource capacity constraints, and scenario time sensitivity constraints are comprehensively considered.

4. The time-sensitive control method for industrial edge computing services considering task execution uncertainty according to claim 3, characterized in that, The computing service control model is shown in equations (6) to (15): （6） （7） （8） （9） （10） （11） （12） （13） （14） （15） The objective function (6) is to minimize the total expected completion time of the task. ; Task scenario diagram The corresponding total task completion time; It is a 0-1 variable; a value of 1 indicates a computational task. i Planned to be assigned to industrial computing points k deal with; It is a 0-1 variable; a value of 1 indicates a computational task. j It was planned to be processed at industrial computing point k; These represent the task scenario diagrams respectively. Computational tasks in i The start and end times; These represent the task scenario diagrams respectively. Computational tasks in j The start and end times; It is also a 0-1 variable, with a value of 1 representing a task scenario diagram. Computational tasks in i , j They were assigned to the same computation point and the same task i In the mission j Begin after completion; It refers to the number of task scenario images. It is to calculate the number of tasks. It calculates the number of points; Representing computational tasks i At the calculation point k Processing time and computational tasks i and j Data transmission time between; Representing the task scenario diagram From computing tasks i The set of computational tasks directly connected by the starting directed edges; This represents the task scenario diagram. It can only be used in computing tasks i A set of tasks that can only be executed after completion; Representing the task scenario diagram The maximum allowed completion time; M is a positive constant that can be chosen to guarantee the completion of all computational tasks; Representing the task scenario diagram The last task The end time.

5. The time-sensitive control method for industrial edge computing services considering task execution uncertainty according to claim 1, characterized in that, Step (5) includes: (5-1) Introducing 0-1 variables Taking 1 indicates the task scenario diagram. The following computational tasks i At the calculation point k If the condition is not met, the value is set to 0; otherwise, the constraint conditions of the original computing service control model are decomposed according to the task scenario diagram. (5-2) Establish unpredictability constraints to characterize the uncertainty of task execution in the service control phase, as shown in equation (3): （3） in, These are 0-1 variables; a value of 1 indicates the value in the task scenario diagram. , , The following computational tasks Planned to be assigned to industrial computing points deal with; (5-3) The unpredictability constraints between task scenarios are processed using Lagrange duality theory, and the computational service control sub-model of each task scenario graph is further obtained. (5-4) Initialize the Lagrange multipliers Solve for the service control sub-model corresponding to each task scenario graph; (5-5) Variable values ​​obtained from each sub-model Calculate the weighted average The specific formula is as follows: （4） (5-6) Calculate the termination condition of the iteration If the value is less than the threshold, proceed to the next step; otherwise, update the Lagrange multipliers using formula (5), as shown below: （5） in, and These are the Lagrange multipliers corresponding to the s-th and s+1-th iterations, respectively. This is the iteration step size; (5-7) The obtained values Rounding down to the nearest whole number corresponds to all The value of is substituted into the computing service control model for solution, and the final optimal industrial edge computing service control scheme is obtained.

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