Joint optimization method for task offloading and container caching in containerized edge computing

Abstract

The present invention relates to the technical fields of task offloading and container caching. Disclosed is a joint optimization method for task offloading and container caching in containerized edge computing. The specific process is as follows: first, on the basis of a containerized edge computing environment, establishing a mathematical model; then, on the basis of the mathematical model, establishing a joint optimization problem of non-linear 0-1 programming; and finally solving a non-linear 0-1 programming problem. According to the present invention, a mathematical model of a containerized edge computing environment is established, and an optimization problem for minimizing the task processing time of a terminal device is established. In addition, the joint optimization method for task offloading and container caching is provided, and according to the method, a non-linear 0-1 programming problem which is originally difficult to solve is converted by means of an equivalent conversion method into a linear 0-1 programming problem which is easy to solve, thereby solving the problem of mutual coupling of a caching decision and a task offloading decision in edge computing, and reducing image file download time and container start time in a containerized edge computing system, so as to reduce the task processing time of terminal devices.

Description

Joint optimization method of task offloading and container caching in containerized edge computing Technical Field

[0001] The present invention belongs to the technical field of task offloading and container caching, and in particular relates to a joint optimization method for task offloading and container caching in containerized edge computing. Background Art

[0002] Currently, the two main methods for jointly optimizing task offloading and service caching in edge computing environments are alternating iterative optimization and deep reinforcement learning. When solving coupling problems, the alternating iterative optimization method typically uses block coordinate descent to alternately optimize task offloading decisions and service caching decisions, but this results in very slow algorithm convergence. Furthermore, due to the limitations of block coordinate descent, alternating iterative optimization cannot effectively find the global optimal solution to non-convex problems. Deep reinforcement learning, on the other hand, requires obtaining system parameters in advance and training a suitable model by setting up an environment to solve optimization problems. Although the trained model can quickly solve problems, due to the long training time, deep reinforcement learning can often only be used as an offline algorithm, which leads to severe limitations in practical applications. Summary of the Invention

[0003] The purpose of the present invention is to provide a joint optimization method for task offloading and container caching in containerized edge computing, so as to solve the problems of slow convergence speed and long model training time when solving coupling problems in the above-mentioned technologies.

[0004] To achieve the above objectives, the present invention provides a joint optimization method for task offloading and container caching in containerized edge computing, comprising the following steps:

[0005] Step 1: Establish a mathematical model based on the containerized edge computing environment;

[0006] Step 2: Establish a joint optimization problem of nonlinear 0-1 programming based on the above mathematical model;

[0007] Step 3: Solve the nonlinear 0-1 programming problem.

[0008] Preferably, the specific process of establishing the mathematical model in step 1 is as follows: based on the characteristic parameters of the cloud server, edge server, terminal device and container in the containerized edge computing environment, the processing time of the task on the terminal device or edge server, the time when the task is unloaded from the terminal device to the edge server, the time when the edge server downloads the container image file from the cloud server, and the time when the container instance is started on the edge server are established into a mathematical model.

[0009] Preferably, the specific process of establishing the joint optimization problem of nonlinear 0-1 programming in step 2 is as follows:

[0010] S21. Establishing a task execution time expression for the terminal device;

[0011] S22. Establish a preparation time expression for the edge server container instance;

[0012] S23, establishing an optimization objective function expression;

[0013] S24. Establishing an optimization problem constraint expression;

[0014] S25. Under the constraints in S24, establish the entire optimization problem with the goal of minimizing the expression of the objective function in S23.

[0015] Preferably, the task execution time expression of the terminal device in S21 is specifically as follows:

[0016] ;

[0017] in, Indicates the task execution time of all terminal devices, , represents the task offloading decision, Indicates time slot terminal equipment The amount of tasks generated, Indicates terminal device The computational complexity of the resulting task, Indicates terminal device The calculation frequency of Representation edge server The calculation frequency of Indicates the number of terminal devices. Indicates the number of edge servers.

[0018] Preferably, the preparation time of the edge server container instance in S22 includes task unloading time, container instance startup time and container image file download time;

[0019] The task offloading time of the terminal device in time slot t is expressed as

[0020] (1)

[0021] The container instance startup time of the edge server in time slot t is expressed as

[0022] (2)

[0023] The container image file download time of the edge server in time slot t is expressed as

[0024] (3)

[0025] in, represents the task unloading time of the terminal device in time slot t, Indicates the number of terminal devices. Indicates the number of edge servers. , represents the task offloading decision, Indicates time slot terminal equipment The amount of tasks generated, Indicates terminal device Offloading tasks to edge servers The transmission rate, represents the container instance startup time of the edge server in time slot t, , represents the container instance caching decision, , indicating whether the task of terminal device i requires image file s, Indicates an image file The time when the container instance was started, represents the container image file download time of the edge server in time slot t, , represents the image file cache decision, Indicates an image file The size of Represents an edge server The rate at which image files are downloaded from the cloud server. Represents the collection of all image files.

[0026] Preferably, the optimization objective function expression in S23 is specifically as follows:

[0027] (4)

[0028] in, Indicates the task execution time of all terminal devices, represents the task unloading time of the terminal device in time slot t, represents the container instance startup time of the edge server in time slot t, Indicates the container image file download time of the edge server in time slot t.

[0029] Preferably, the optimization problem constraints in S24 include task offloading decision variable constraints, edge server container instance cache capacity constraints, edge server container image file cache capacity constraints, edge server cache decision logic constraints and 0-1 variable constraints;

[0030] The task offloading decision variable constraints are expressed as

[0031] ;

[0032] The cache capacity constraint of the edge server container instance is expressed as

[0033] ;

[0034] The cache capacity constraint of the edge server container image file is expressed as

[0035] ;

[0036] The edge server cache decision logic constraint is expressed as

[0037] ;

[0038] ;

[0039] The 0-1 variable constraint is expressed as

[0040] ;

[0041] in, , represents the container instance caching decision, Represents a collection of all image files. , indicating whether the task of terminal device i requires image file s, Represents a mirror The amount of RAM occupied by the launched container instance, Indicates the The maximum container instance cache capacity of an edge server, , represents the image file cache decision, Indicates an image file The size of Indicates the The maximum image file cache capacity of an edge server, Represents a collection of terminal devices. Represents a collection of edge servers.

[0042] Preferably, the specific process of solving the nonlinear 0-1 programming problem in step 3 is as follows:

[0043] S31. Based on the objective function, a new objective function is formed by introducing three equality constraints;

[0044] S32. Convert the three equality constraints into nine new inequality constraints by introducing equivalent transformations;

[0045] S33. Solve the transformed linear 0-1 programming problem using a solver or a linear integer programming algorithm based on the new objective function and the nine new inequality constraints in steps S31 and S32 in combination with the six inequality constraints in the original objective function.

[0046] Preferably, the three equality constraints in S31 are specifically:

[0047] (5)

[0048] (6)

[0049] (7)

[0050] According to equations (1)(2)(3)(4)(5)(6)(7), the new objective function is as follows:

[0051] ;

[0052] ;

[0053] in,

[0054]

[0055] , represents the task offloading decision, , represents the container instance caching decision, , represents the image file cache decision, , Represents a collection of terminal devices. Represents a collection of edge servers, Represents the collection of all image files.

[0056] Preferably, the equivalent conversion in S32 is specifically as follows: for any , three inequality constraints, , which is equivalent to the equality constraint ;

[0057] The nine new inequality constraints are as follows:

[0058]

[0059]

[0060] in, , represents the task offloading decision, , represents the container instance caching decision, , indicating the image file caching decision.

[0061] Therefore, the present invention adopts the above-mentioned joint optimization method of task offloading and container caching in containerized edge computing, which has the following beneficial effects: through the equivalent conversion method, the originally difficult nonlinear 0-1 programming problem is converted into an easy-to-solve linear 0-1 programming problem, which solves the problem of mutual coupling between caching decisions and task offloading decisions in edge computing, reduces the image file download time and container startup time in the containerized edge computing system, and thus reduces the task processing time of the terminal device.

[0062] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] FIG1 is a diagram of a container edge computing scenario according to the present invention;

[0064] FIG2 is a schematic diagram of a containerized edge server and cloud server according to the present invention;

[0065] FIG3 is a flowchart of the execution of the algorithm of the present invention in an application. DETAILED DESCRIPTION

[0066] Example

[0067] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort shall fall within the scope of protection of the present invention.

[0068] A joint optimization method for task offloading and container caching in containerized edge computing includes the following steps:

[0069] Step 1: Establish a mathematical model based on the containerized edge computing environment. Based on the characteristic parameters of the cloud server, edge server, terminal device, and container in the containerized edge computing environment, establish a mathematical model of the processing time of the task on the terminal device or edge server, the time when the task is offloaded from the terminal device to the edge server, the time when the edge server downloads the container image file from the cloud server, and the time when the container instance is started on the edge server;

[0070] Step 2: Based on the above mathematical model, a joint optimization problem of nonlinear 0-1 programming is established. The specific process is as follows:

[0071] S21. Establish a task execution time expression for the terminal device. The specific expression is as follows:

[0072] ;

[0073] in, Indicates the task execution time of all terminal devices, , represents the task offloading decision, Indicates time slot terminal equipment The amount of tasks generated, Indicates terminal device The computational complexity of the resulting task, Indicates terminal device The calculation frequency of Representation edge server The calculation frequency of Indicates the number of terminal devices. Indicates the number of edge servers;

[0074] S22. Establish a preparation time expression for the edge server container instance. The preparation time for the edge server container instance includes task unloading time, container instance startup time, and container image file download time.

[0075] The task offloading time of the terminal device in time slot t is expressed as

[0076] (1);

[0077] The container instance startup time of the edge server in time slot t is expressed as

[0078] (2)

[0079] The container image file download time of the edge server in time slot t is expressed as

[0080] (3)

[0081] in, represents the task unloading time of the terminal device in time slot t, Indicates the number of terminal devices. Indicates the number of edge servers. , represents the task offloading decision, Indicates time slot terminal equipment The amount of tasks generated, Indicates terminal device Offloading tasks to edge servers The transmission rate, represents the container instance startup time of the edge server in time slot t, , represents the container instance caching decision, , indicating whether the task of terminal device i requires image file s, Indicates an image file The time when the container instance was started, represents the container image file download time of the edge server in time slot t, , represents the image file cache decision, Indicates an image file The size of Represents an edge server The rate at which image files are downloaded from the cloud server. Represents the collection of all image files;

[0082] S23. Establish an optimization objective function expression. The specific expression is as follows:

[0083] (4)

[0084] in, Indicates the task execution time of all terminal devices, represents the task unloading time of the terminal device in time slot t, represents the container instance startup time of the edge server in time slot t, represents the container image file download time of the edge server in time slot t;

[0085] S24. Establish an optimization problem constraint expression, where the optimization problem constraints include task offloading decision variable constraints, edge server container instance cache capacity constraints, edge server container image file cache capacity constraints, edge server cache decision logic constraints, and 0-1 variable constraints.

[0086] The task offloading decision variable constraints are expressed as

[0087] ;

[0088] The cache capacity constraint of the edge server container instance is expressed as

[0089] ;

[0090] The cache capacity constraint of the edge server container image file is expressed as

[0091] ;

[0092] The edge server cache decision logic constraint is expressed as

[0093] ;

[0094] ;

[0095] The 0-1 variable constraint is expressed as

[0096] ;

[0097] in, , represents the container instance caching decision, Represents a collection of all image files. , indicating whether the task of terminal device i requires image file s, Represents a mirror The amount of RAM occupied by the launched container instance, Indicates the The maximum container instance cache capacity of an edge server, , represents the image file cache decision, Indicates an image file The size of Indicates the The maximum image file cache capacity of an edge server, Represents a collection of terminal devices. Represents a collection of edge servers;

[0098] S25. Under the constraints in S24, the entire optimization problem is established with the goal of minimizing the expression of the objective function in S23;

[0099] Step 3: Solve the nonlinear 0-1 programming problem. The specific process is as follows:

[0100] S31. Based on the objective function, a new objective function is formed by introducing three equality constraints. The three equality constraints are:

[0101] (5)

[0102] (6)

[0103] (7)

[0104] According to equations (1)(2)(3)(4)(5)(6)(7), the new objective function is as follows:

[0105] ;

[0106] ;

[0107] in,

[0108]

[0109] , represents the task offloading decision, , represents the container instance caching decision, , represents the image file cache decision, , Represents a collection of terminal devices. Represents a collection of edge servers, Represents the collection of all image files;

[0110] S32, by introducing equivalent transformation, the three equality constraints are transformed into nine new inequality constraints. The equivalent transformation is as follows: , three inequality constraints, , which is equivalent to the equality constraint ;

[0111] The nine new inequality constraints are as follows:

[0112] ;

[0113] in, , represents the task offloading decision, , represents the container instance caching decision, , represents the image file cache decision;

[0114] S33. Solve the transformed linear 0-1 programming problem using a solver or a linear integer programming algorithm based on the new objective function and the nine new inequality constraints in steps S31 and S32 in combination with the six inequality constraints in the original objective function.

[0115] As shown in Figure 1, consider a scenario consisting of three layers: cloud server layer, edge server layer, and terminal device layer. Assume that there is a cloud server in the cloud server layer and a edge servers, and at the terminal device layer The application executing tasks on the edge server is a container instance, which is started by the corresponding container image file. All container images used to start container instances are stored on the cloud server. When a task is executed on the edge server, the edge server needs to pull the container image file from the cloud server and then start the container instance. By caching container instances and container images on the edge server, container preparation time can be reduced.

[0116] As shown in Figure 2, Docker technology is introduced into edge computing systems, resulting in container-based edge servers and cloud servers. On a container-based cloud server, both the task-processing program and the environment required to run the program (all necessary components, such as libraries, frameworks, and other dependencies) are packaged into a container image file. The cloud server maintains a container image repository, storing all the images needed to process tasks on end devices. On the container-based edge server, the Docker client downloads the container image file from the cloud server's repository. The Docker daemon on the edge server then launches the image file into the corresponding container instance, which then provides services for processing end device tasks. Downloading container images and launching container instances are time-consuming. Therefore, the container image file and container instance are cached in the edge server's ROM and RAM, respectively, to reduce this time consumption.

[0117] Figure 3 illustrates the application of this algorithm in a real-world scenario. At time M1, the cloud server collects data from the edge server and end device. Then, at time M2, the proposed JOOC algorithm is used to resolve task offloading and container caching decisions. At time M3, the cloud server sends task offloading and container caching commands to the edge server and end device. At time M4, the end device offloads the task to the edge server. At time M5, the edge server sends a request to the cloud server to download the required container image file. At time M6, the cloud server sends the container image file to the edge server. At time M7, the edge server launches the container instance. At time M8, the edge server processes the task offloaded by the end device and returns the task processing results to the end device at M9.

[0118] Therefore, the present invention adopts the above-mentioned joint optimization method of task offloading and container caching in containerized edge computing, and transforms the originally difficult nonlinear 0-1 programming problem into an easy-to-solve linear 0-1 programming problem through the equivalent conversion method, thereby solving the problem of mutual coupling between caching decisions and task offloading decisions in edge computing, reducing the image file download time and container startup time in the containerized edge computing system, and thus reducing the task processing time of the terminal device.

[0119] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A joint optimization method for task offloading and container caching in containerized edge computing, characterized in that: The following steps are involved: Step 1: Establish a mathematical model based on the containerized edge computing environment; Step 2: Establish a joint optimization problem of nonlinear 0-1 programming based on the above mathematical model; Step 3: Solve the nonlinear 0-1 programming problem.

2. The joint optimization method for task offloading and container caching in containerized edge computing according to claim 1 is characterized in that: The specific process of establishing the mathematical model in step 1 is as follows: according to the characteristic parameters of the cloud server, edge server, terminal device and container in the containerized edge computing environment, the processing time of the task on the terminal device or edge server, the time when the task is unloaded from the terminal device to the edge server, the time when the edge server downloads the container image file from the cloud server, and the time when the container instance is started on the edge server are established into a mathematical model.

3. The joint optimization method for task offloading and container caching in containerized edge computing according to claim 1, characterized in that: The specific process of establishing the joint optimization problem of nonlinear 0-1 programming in step 2 is as follows: S21, establishing a task execution time expression for the terminal device; S22, establishing a preparation time expression for the edge server container instance; S23, establishing an optimization objective function expression; S24, establishing an optimization problem constraint expression; S25. Under the constraints in S24, the entire optimization problem is established with the goal of minimizing the expression of the objective function in S23.

4. The joint optimization method for task offloading and container caching in containerized edge computing according to claim 3 is characterized in that: The task execution time expression of the terminal device in S21 is specifically as follows: ; in, Indicates the task execution time of all terminal devices. , represents the task offloading decision, Indicates time slot Terminal equipment The amount of tasks generated, Indicates terminal equipment The computational complexity of the resulting task, Indicates terminal equipment The calculation frequency of Representation edge server The calculation frequency of Indicates the number of terminal devices. Indicates the number of edge servers.

5. The joint optimization method for task offloading and container caching in containerized edge computing according to claim 4 is characterized in that: The preparation time of the edge server container instance in S22 includes task unloading time, container instance startup time and container image file download time; The task offloading time of the terminal device in time slot t is expressed as （1） The container instance startup time of the edge server in time slot t is expressed as （2） The container image file download time of the edge server in time slot t is expressed as （3） in, represents the task unloading time of the terminal device in time slot t, Indicates the number of terminal devices. Indicates the number of edge servers. , represents the task offloading decision, Indicates time slot Terminal equipment The amount of tasks generated, Indicates terminal equipment Offloading tasks to edge servers The transmission rate, represents the container instance startup time of the edge server in time slot t, , represents the container instance caching decision, , indicating whether the task of terminal device i requires image file s, Indicates image file The time when the container instance was started, represents the container image file download time of the edge server in time slot t, , represents the image file cache decision, Indicates image file The size of Represents edge server The rate at which image files are downloaded from the cloud server. Represents a collection of all image files.

6. The joint optimization method for task offloading and container caching in containerized edge computing according to claim 5, characterized in that: The optimization objective function expression in S23 is specifically as follows: （4） in, Indicates the task execution time of all terminal devices. represents the task unloading time of the terminal device in time slot t, represents the container instance startup time of the edge server in time slot t, Indicates the container image file download time of the edge server in time slot t.

7. The joint optimization method for task offloading and container caching in containerized edge computing according to claim 6, characterized in that: The optimization problem constraints in S24 include task offloading decision variable constraints, cache capacity constraints of edge server container instances, cache capacity constraints of edge server container image files, edge server cache decision logic constraints, and 0-1 variable constraints; The task offloading decision variable constraints are expressed as ; The cache capacity constraint of the edge server container instance is expressed as ; The cache capacity constraint of the edge server container image file is expressed as ; The edge server cache decision logic constraint is expressed as ; ; The 0-1 variable constraint is expressed as ; in, , represents the container instance caching decision, Represents a collection of all image files. , indicating whether the task of terminal device i requires image file s, Represents a mirror The amount of RAM used by the launched container instance. Indicates The maximum container instance cache capacity of edge servers, , represents the image file cache decision, Indicates image file The size of Indicates The maximum image file cache capacity of an edge server, Represents a collection of terminal devices. Represents a collection of edge servers.

8. The joint optimization method for task offloading and container caching in containerized edge computing according to claim 7, characterized in that: The specific process of solving the nonlinear 0-1 programming problem in step 3 is as follows: S31, forming a new objective function by introducing three equality constraints on the basis of the objective function; S32, converting three equality constraints into nine new inequality constraints by introducing equivalent transformation; S33. Solve the converted linear 0-1 programming problem by a solver or a linear integer programming algorithm according to the new objective function and the nine new inequality constraints in steps S31 and S32 combined with the six inequality constraints in the original objective function.

9. The joint optimization method for task offloading and container caching in containerized edge computing according to claim 8, characterized in that: The three equality constraints in S31 are specifically: （5） （6） （7） According to equations (1)(2)(3)(4)(5)(6)(7), the new objective function is as follows: ； ； , represents the task offloading decision, , represents the container instance caching decision, , represents the image file cache decision, ， Represents a collection of terminal devices. represents the edge server set, Represents a collection of all image files.

10. The joint optimization method for task offloading and container caching in containerized edge computing according to claim 9, characterized in that: The equivalent conversion in S32 is specifically as follows: , three inequality constraints, , which is equivalent to the equality constraint ; The nine new inequality constraints are as follows: ； in, , represents the task offloading decision, , represents the container instance caching decision, , indicating the image file cache decision.

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