A Game Theory-Based Joint Optimization Method in D2D-Assisted MEC Systems

Abstract

The present invention is applicable to the field of communication technologies, and provides a game theory-based joint optimization method in a D2D-assisted MEC system. The specific steps include: S101: constructing a system model; S102: establishing a specific optimization problem according to the constructed system model; S103: constructing the offloading mode selection as a potential game process; S104: obtaining the offloading ratio and resource allocation scheme according to the obtained offloading mode; S105: repeatedly iterating S103 and S104 to find the optimal offloading mode, the optimal offloading ratio allocation, and the optimal computing resource allocation. In the game theory-based joint optimization method in the D2D-assisted MEC system of the present invention, the overall method obtains the optimal offloading mode, the optimal offloading ratio allocation, and the optimal computing resource allocation through game theory, convex optimization, and the Lagrange multiplier method, and can meet the communication needs of users within the system, effectively reduce the execution delay of task devices within the system, and improve the quality of experience of users within the system.

Description

Technical Field

[0001] The present invention belongs to the field of communication technologies, and particularly relates to a game theory-based joint optimization method in a D2D-assisted MEC system. Background Art

[0002] With the rapid development of the fifth-generation mobile communication technology (5G), the popularity and quantity of mobile terminal devices such as smart phones, smart watches, vehicles, and tablet computers have also increased rapidly. Although new mobile devices are becoming more and more powerful in terms of central processing units (CPUs), they may not be able to complete applications with large amounts of data and low latency requirements such as deep learning, online 3D games, face recognition, location-based augmented reality or virtual reality (AR / VR), mobile social media, autonomous driving, and intelligent services in a short time. To address this problem, some computing tasks have to be offloaded to cloud servers with sufficient computing power for computing, which has promoted the development of mobile cloud computing (MCC). The servers of mobile cloud computing are centralized and generally far from the locations of mobile users, which has caused a serious burden on the access network and the backhaul link for the explosively growing computing data and introduced high latency. To address this problem, the concept of mobile edge computing (MEC) has emerged.

[0003] D2D communication is a new technology that allows direct communication between end users by sharing cell resources under the control of a cellular system. To further improve the task offloading efficiency and effectively utilize the resources within the system, some researchers have regarded the D2D offloading mode as an effective supplement to the mobile edge computing system. The introduction of D2D communication technology on the one hand makes full use of the computing resources of idle devices, and on the other hand effectively alleviates the pressure on the edge server and the cloud server, further improving the performance of the system and the QoS of users within the system.

[0004] In a mobile edge computing system, the edge server provides computing power that is more powerful than that of mobile devices but slightly weaker than that of traditional cloud servers. However, due to the distributed deployment of the edge server, which is closer to mobile devices, it can not only provide services for latency-sensitive or computationally complex applications on mobile devices nearby, but also greatly alleviate the pressure on the core network. To solve the contradiction between computationally intensive applications and resource-constrained mobile devices, more and more research regards task offloading and resource allocation as a promising solution.

[0005] In the future massive machine type communication (mMTC) scenario, there will be a huge number of terminal devices in the system. Relying solely on the computing power of the terminal devices themselves cannot respond to latency-sensitive or computationally complex services in a short time. Although the introduction of edge servers and cloud servers has greatly improved the system performance, in the face of the access of a large number of terminals, the computing resources of edge servers and cloud servers are no longer sufficient to provide adequate services. Therefore, it is imperative to introduce the offloading mode of D2D communication technology.

[0006] Therefore, in view of the above situation, there is an urgent need to develop a game theory-based joint optimization method in a D2D-assisted MEC system to overcome the deficiencies in current practical applications. Summary of the Invention

[0007] Aiming at the deficiencies of the existing technology, the purpose of the embodiments of the present invention is to provide a game theory-based joint optimization method in a D2D-assisted MEC system to solve the problems in the above background technology.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] A game theory-based joint optimization method in a D2D-assisted MEC system, the specific steps of the joint optimization method are as follows:

[0010] S101: In a D2D-assisted mobile edge computing system, construct a system model including task devices, resource devices, edge servers, and cloud servers, and initialize system parameters such as the computing power of task devices, the size of task data volume, and the computing power of edge servers;

[0011] S102: According to the system model constructed in S101, obtain the calculation methods of latency in the D2D offloading mode, MEC offloading mode, and cloud offloading mode, and establish a specific optimization problem with the goal of minimizing the total latency of task devices in the system;

[0012] S103: According to the optimization problem established in S102, construct the offloading mode selection as a potential game process, and update the offloading mode of one task device in each iteration;

[0013] S104: According to the offloading mode obtained in S103, for the task devices that select the D2D offloading mode and the cloud offloading mode, obtain the task offloading ratio through convex optimization; for the task devices that select the MEC offloading mode, first obtain the expression of the task offloading ratio through convex optimization, then substitute it into the optimization problem, and then obtain the numerical value of the computing resource allocation through the Lagrange multiplier method, and finally substitute the obtained numerical value into the task offloading ratio expression to obtain the task offloading ratio;

[0014] S105: Repeat and iterate S103 and S104 until convergence or the maximum number of iterations is reached to find the optimal offloading mode, the optimal computing resource allocation, and the optimal offloading ratio allocation.

[0015] As a further technical solution of the present invention, in S101, the specific steps for constructing the computing offloading and resource allocation model in the D2D-assisted mobile edge computing system are as follows:

[0016] S1011: In the system model, first assume a quasi-static network scenario, that is, the positions of the users remain unchanged during the computing offloading; secondly, assume that the computationally intensive tasks of the task devices are divided into two parts for processing; therefore, the system model is divided into a D2D offloading mode, an MEC offloading mode, and a cloud offloading mode.

[0017] S1012: For the D2D offloading mode, the task device offloads the part of the task to be executed to the idle D2D device for execution, while the remaining part is executed locally; for the MEC offloading mode, the task device offloads the part of the task to be executed to the edge server for execution, while the remaining part is executed locally; for the cloud offloading mode, the task device offloads the part of the task to be executed to the cloud server for execution, while the remaining part is executed locally.

[0018] S1013: Let the total CPU resources of the edge server be f mec ; the set of access task devices TD is N = {1, 2......, N}, and each task device has a latency-sensitive task T i = <D i , X i , f i l > (i ∈ N), where D i is the task data size, in bytes; X i is the computing resources required for one bit of the computing task, in cycles / bit, and f i l is the computing power of TD i , in CPU frequency / CPU cycles per second.

[0019] S1014: Define O = {d2d, mec, cloud} as the offloading modes that the task device can choose; define the mode selection factor as Define α i as the ratio of the offloaded task of TD i .

[0020] As a further technical solution of the present invention, in S102, the calculation method of the latency under each offloading mode and the specific steps for establishing the optimization problem are as follows:

[0021] S1021: Use the OFDMA scheme for the uplink and ignore the interference between links. Therefore, the uplink transmission rates of the D2D link and the cellular link are respectively and

[0022] where: p i is the TD i transmission power, B d and B m are the uplink bandwidths of the D2D link and the cellular link respectively, h i,d and h i,m are the channel gains between the TD i and the resource device and the edge server respectively;

[0023] According to T i , the local processing delay is expressed as

[0024] S1022: When the task device selects the D2D offloading mode, the offloading delays of some tasks and the processing delay of the resource device are respectively and Since it is partial offloading, some tasks are offloaded to the resource device through the uplink D2D link and the task device also processes the remaining tasks locally while the resource device is processing. Therefore, the delay in the D2D offloading mode is

[0025] S1023: When the task device selects the MEC offloading mode, the offloading delays of some tasks and the processing delay of the edge server are respectively and

[0026] where: f i m is the computing power allocated by the edge server to the offloading tasks;

[0027] Similarly, since it is partial offloading, the delay in the MEC offloading mode is

[0028] S1024: When the task device selects the cloud offloading mode, The cloud offloading process is divided into two stages, namely the access stage and the backhaul stage. The transmission delay in the access stage is

[0029] Assume that the delay for some tasks to be transmitted through the core network to the cloud server and processed at the cloud server is a constant, denoted by T core ; Similarly, since it is partial offloading, the delay in the cloud offloading mode is

[0030] S1025: The optimization problem is expressed as:

[0031]

[0032] As a further technical solution of the present invention, in S1024, the access phase means that some tasks are transmitted to the edge service through the cellular uplink, and the backhaul phase means that some tasks are relayed to the cloud server through the fiber optic backhaul link at the edge server.

[0033] As a further technical solution of the present invention, in S103, the specific steps for constructing the offloading mode selection as a potential game process are as follows:

[0034] For each TD in the system i , when the offloading methods of other TDs have been given , TD i will select an optimal offloading mode with the goal of minimizing its own delay. The offloading mode selection problem is expressed as Since there is a competitive relationship among the task devices in the system, the offloading mode selection is constructed as a game N represents the participants of the game, that is, all the task devices in the system; is the strategy space of TD i , that is, the offloading mode; L i represents the delay function of the participant.

[0035] As a further technical solution of the present invention, in S104, the specific steps for calculating resource allocation and offloading ratio allocation are as follows:

[0036] S1041 For the task devices that select the D2D offloading mode, the optimization problem is expressed as follows:

[0037]

[0038] The optimal offloading ratio in the D2D offloading mode is obtained through convex optimization as

[0039] S1042 For the task devices that select the cloud offloading mode, the optimization problem is expressed as:

[0040]

[0041] The optimal offloading ratio in the cloud offloading mode is obtained through convex optimization as

[0042] S1043 For the task devices that select the MEC offloading mode, the optimization problem is expressed as:

[0043] Secondly, substitute it into the optimization problem and rewrite the original optimization problem as:

[0044]

[0045]

[0046] As a further technical solution of the present invention, in step S1043, construct the Lagrangian function:

[0047]

[0048] And obtain TD i through KKT condition iteration i m The optimal computing resource allocation f i m Finally, substitute f

[0049] into the optimal offloading ratio expression to solve for the optimal offloading ratio in the MEC offloading mode.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0051] The D2D-assisted mobile edge computing system introduces D2D communication technology and uses it as one of the offloading modes. The introduction of D2D communication technology can make full use of the idle computing resources in the system to provide corresponding services for task devices, and can relieve the pressure on the edge server and the cloud server, and further improve the quality of experience of users in the system;

[0052] The present invention constructs a D2D-assisted mobile edge computing system model, introduces the offloading decision of D2D communication technology into it, constructs a three-layer architecture including D2D offloading mode, MEC offloading mode and cloud offloading mode, and constructs an optimization problem with the goal of minimizing the total delay of task devices in the system. Through the analysis of the optimization problem, the offloading mode selection problem is constructed as a potential game process, and the offloading mode of a task device is updated in each iteration update process. According to the obtained offloading mode, the offloading ratio and computing resource allocation problem are solved by convex optimization and Lagrange multiplier method, and finally repeated iteration is performed until convergence or the maximum number of iterations to obtain the optimal offloading mode, optimal offloading ratio and optimal computing resource allocation;

[0053] To more clearly illustrate the structural features and functions of the present invention, the following will combine the drawings and specific embodiments to detail the present invention. Brief Description of the Drawings

[0054] Figure 1 It is a schematic diagram of the D2D-assisted mobile edge computing system model in the present invention.

[0055] Figure 2 It is a flowchart of the joint optimization method based on game theory in the D2D-assisted MEC system of the present invention.

[0056] Figure 3 It is a schematic diagram of the principle of the joint optimization method based on game theory in the D2D-assisted MEC system of the present invention. Specific implementation manners

[0057] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0058] The following describes the specific implementation of the present invention in detail with reference to specific embodiments.

[0059] As Figures 1 to 3 shown, as a joint optimization method based on game theory in a D2D-assisted MEC system provided by an embodiment of the present invention, the specific steps of the joint optimization method are as follows:

[0060] S101: In a D2D-assisted mobile edge computing system, construct a system model including task devices, resource devices, edge servers, and cloud servers, and initialize system parameters such as the computing capabilities of task devices, the amount of task data, and the computing capabilities of edge servers;

[0061] S102: According to the system model constructed in S101, obtain the calculation methods of the delays in the D2D offloading mode, MEC offloading mode, and cloud offloading mode, and establish a specific optimization problem with the goal of minimizing the total delay of task devices in the system;

[0062] S103: According to the optimization problem established in S102, construct the offloading mode selection as a potential game process, and update the offloading mode of one task device in each iteration;

[0063] S104: According to the offloading mode obtained in S103, for the task devices that select the D2D offloading mode and the cloud offloading mode, obtain the task offloading ratio through convex optimization; for the task devices that select the MEC offloading mode, first obtain the expression of the task offloading ratio through convex optimization, then substitute it into the optimization problem, and then obtain the value of the computing resource allocation through the Lagrange multiplier method. Finally, substitute the obtained value into the task offloading ratio expression to obtain the task offloading ratio;

[0064] S105: Repeatedly iterate and execute S103 and S104 until convergence or the maximum number of iterations to find the optimal offloading mode, the optimal computing resource allocation, and the optimal offloading ratio allocation.

[0065] In this embodiment, the present invention constructs a D2D-assisted mobile edge computing system model, introduces the offloading decision of D2D communication technology into it, constructs a three-layer architecture including D2D offloading mode, MEC offloading mode, and cloud offloading mode, and constructs an optimization problem with the goal of minimizing the total delay of task devices in the system. Through the analysis of the optimization problem, the offloading mode selection problem is constructed as a potential game process, and the offloading mode of a task device is updated in each iteration update process. According to the obtained offloading mode, the offloading ratio and computing resource allocation problems are solved by convex optimization and Lagrange multiplier method. Finally, repeat the iteration until convergence or the maximum number of iterations to obtain the optimal offloading mode, the optimal offloading ratio, and the optimal computing resource allocation.

[0066] The method proposed by the present invention can, on the one hand, meet the service requirements of different users while making full use of system resources, and on the other hand, can effectively reduce the total delay of task devices in the system and improve the quality of experience of users in the system.

[0067] As Figures 1 to 3 shown, as a preferred embodiment of the present invention, in S101, the specific steps for constructing the computing offloading and resource allocation model in the D2D-assisted mobile edge computing system are as follows:

[0068] S1011: In the system model, first assume a quasi-static network scenario, that is, the positions of users remain unchanged during computing offloading; secondly, assume that the computationally intensive tasks of task devices are divided into two parts for processing; therefore, the system model is divided into D2D offloading mode, MEC offloading mode, and cloud offloading mode.

[0069] S1012: For the D2D offloading mode, the task device offloads the part of the task to be executed to an idle D2D device for execution, and the remaining part is executed locally; for the MEC offloading mode, the task device offloads the part of the task to be executed to the edge server for execution, and the remaining part is executed locally; for the cloud offloading mode, the task device offloads the part of the task to be executed to the cloud server for execution, and the remaining part is executed locally.

[0070] S1013: Let the total CPU resources of the edge server be f mec ; the set of access task devices TD is N = {1, 2......, N}, and each task device has a delay-sensitive task T i = <D i , X i , f il > (i ∈ N), where D i is the task data size, in bytes; X i is the computing resource required for one bit of the computing task, in cycles / bit, f i l is the computing power of TD i in CPU frequency / CPU cycles per second;

[0071] S1014: Define O = {d2d, mec, cloud} as the offloading modes available for the task device; Define the mode selection factor as Define α i as the proportion of the TD i offloading tasks.

[0072] As Figures 1 to 3 shown, as a preferred embodiment of the present invention, in S102, the specific steps for calculating the delay in each offloading mode and establishing the optimization problem are as follows:

[0073] S1021: For the uplink, use the OFDMA scheme and ignore the interference between links. Therefore, the uplink transmission rates of the D2D link and the cellular link are respectively and

[0074] where: p i is the TD i transmission power, B d and B m are the uplink bandwidths of the D2D link and the cellular link respectively, h i,d and h i,m are the channel gains between the TD i and the resource device and the edge server respectively;

[0075] According to T i , the local processing delay is expressed as

[0076] S1022: When the task device selects the D2D offloading mode, the offloading delay and the resource device processing delay of part of the tasks are respectively and Since it is partial offloading, part of the tasks are offloaded to the resource device through the uplink D2D link and while the resource device is processing, the task device is also locally processing the remaining tasks. Therefore, the delay in the D2D offloading mode is

[0077] S1023: When the task device selects the MEC offloading mode, the offloading delay and the edge server processing delay of part of the tasks are respectively and

[0078] where: f i m is the computing power allocated by the edge server to the offloading task;

[0079] Also, since it is partial offloading, the latency in the MEC offloading mode is

[0080] S1024: When the task device selects the cloud offloading mode, the cloud offloading process is divided into two stages, namely the access stage and the backhaul stage. The transmission latency in the access stage is

[0081] Assume that the latency for part of the task to be transmitted through the core network to the cloud server and processed at the cloud server is a constant, denoted by T core ; Also, since it is partial offloading, the latency in the cloud offloading mode is

[0082] S1025: The optimization problem is expressed as:

[0083]

[0084] As Figures 1 to 3 shown, as a preferred embodiment of the present invention, in S1024, the access stage refers to part of the task being transmitted to the edge service through the cellular uplink, and the backhaul stage refers to part of the task being relayed to the cloud server by the edge server through the fiber optic backhaul link.

[0085] As Figures 1 to 3 shown, as a preferred embodiment of the present invention, in S103, the specific steps for constructing the offloading mode selection as a potential game process are as follows:

[0086] For each TD i in the system, when the offloading methods of other TDs have been given, TD i will select an optimal offloading mode with the goal of minimizing its own latency. This offloading mode selection problem is expressed as Since there is a competitive relationship among the task devices in the system, the offloading mode selection is constructed as a game N represents the participants in the game, that is, all the task devices in the system; is the strategy space of TD i , that is, the offloading mode; L i represents the latency function of the participant.

[0087] As Figures 1 to 3As shown, as a preferred embodiment of the present invention, in S104, the specific steps for calculating resource allocation and offloading ratio allocation are as follows:

[0088] S1041 For the task devices that select the D2D offloading mode, the optimization problem is expressed as follows:

[0089]

[0090] The optimal offloading ratio in the D2D offloading mode is obtained through convex optimization as

[0091] S1042 For the task devices that select the cloud offloading mode, the optimization problem is expressed as:

[0092]

[0093] The optimal offloading ratio in the cloud offloading mode is obtained through convex optimization as

[0094] S1043 For the task devices that select the MEC offloading mode, the optimization problem is expressed as:

[0095] Secondly, substitute it into the optimization problem, and rewrite the original optimization problem as:

[0096]

[0097] As Figures 1 to 3 shown, as a preferred embodiment of the present invention, in step S1043, construct the Lagrangian function:

[0098]

[0099] And the optimal computing resource allocation f i of TD i m is obtained through KKT condition iteration. Finally, substitute f i m into the optimal offloading ratio expression to solve for the optimal offloading ratio in the MEC offloading mode.

[0100] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A game theory-based joint optimization method in a D2D-assisted MEC system, characterized in that, The specific steps of the joint optimization method are as follows: S101: In the D2D-assisted mobile edge computing system, construct a system model including task devices, resource devices, edge servers, and cloud servers, and initialize system parameters such as the computing capabilities of task devices, the sizes of task data volumes, and the computing capabilities of edge servers; The specific steps of constructing a computing offloading and resource allocation model in the D2D-assisted mobile edge computing system are as follows: S1011: In the system model, first select a quasi-static network scenario, that is, the positions of users remain unchanged during computing offloading; second, set the computationally intensive tasks of task devices to be processed in two parts; thus, the system model is divided into D2D offloading mode, MEC offloading mode, and cloud offloading mode; S1012: For the D2D offloading mode, the task device offloads the part of the task to be executed to an idle D2D device for execution, and the remaining part is executed locally; for the MEC offloading mode, the task device offloads the part of the task to be executed to the edge server for execution, and the remaining part is executed locally; for the cloud offloading mode, the task device offloads the part of the task to be executed to the cloud server for execution, and the remaining part is executed locally; S1013: Set the total CPU resources of the edge server to ; The set of access task devices TD is , and each task device has a latency-sensitive task to be executed , where is the task data size, in bytes; is the computing resource required for one bit of the computing task, in cycles / bit, is the computing power of, in CPU frequency / CPU cycles per second; S1014: Define as the selectable offloading mode for the task device; define the mode selection factor as ; define as the proportion of offloading tasks; S102: According to the system model constructed in S101, obtain the calculation methods of delays in the D2D offloading mode, MEC offloading mode, and cloud offloading mode, and establish a specific optimization problem with the goal of minimizing the total delay of task devices in the system; S103: According to the optimization problem established in S102, construct the offloading mode selection as a potential game process, and update the offloading mode of a task device in each iteration; The specific steps of constructing the offloading mode selection as a potential game process are as follows: For each in the system , when the offloading methods of other TDs have been given , it will select an optimal offloading mode with the goal of minimizing its own time delay. The offloading mode selection problem is expressed as ; Since there is a competitive relationship among the task devices in the system, the offloading mode selection is constructed as a game , denotes the participants in the game, that is, all the task devices in the system; is 's strategy space, that is, the offloading mode; denotes the time delay function of the participant; S104: According to the offloading mode obtained in S103, for task devices that select the D2D offloading mode and cloud offloading mode, obtain the task offloading ratio through convex optimization; For task devices that select the MEC offloading mode, first obtain the expression of the task offloading ratio through convex optimization, then substitute it into the optimization problem, and then obtain the numerical value of the computing resource allocation through the Lagrange multiplier method. Finally, substitute the obtained numerical value into the task offloading ratio expression to obtain the task offloading ratio; S105: Repeat the iteration of S103 and S104 until convergence or the maximum number of iterations, and obtain the best offloading mode, the best computing resource allocation, and the best offloading ratio allocation.

2. The game theory-based joint optimization method in a D2D-assisted MEC system according to claim 1, characterized in that, In S102, the calculation methods of delays in each offloading mode and the specific steps of establishing the optimization problem are as follows: S1021: Use the OFDMA scheme for the uplink and ignore the interference between links. Therefore, the uplink transmission rates of the D2D link and the cellular link are respectively and ; Wherein: is the transmission power, and are the uplink bandwidths of the D2D link and the cellular link respectively, and are respectively the channel gains between the resource device and the edge server; According to , the local processing delay is expressed as ; S1022: When the task device selects the D2D offloading mode, , the offloading delay and the resource device processing delay of some tasks are respectively and . Since it is partial offloading, some tasks are offloaded to the resource device through the uplink D2D link and while the resource device is processing, the task device is also locally processing the remaining tasks. Therefore, the delay in the D2D offloading mode is ; S1023: When the task device selects the MEC offloading mode, , the offloading delay and the edge server processing delay of some tasks are respectively and ; Wherein: is the computing power allocated by the edge server to the offloading task; Similarly, due to partial offloading, the latency in the MEC offloading mode is ; S1024: When the task device selects the cloud offloading mode, , the cloud offloading process is divided into two stages, namely the access stage and the backhaul stage. The transmission delay in the access stage is ; The latency for selecting some tasks to be transmitted to the cloud server through the core network and processed on the cloud server is a constant, denoted by ; Also, since it is partial offloading, the latency in the cloud offloading mode is ; S1025: The optimization problem is expressed as: ； 。 3. The game theory-based joint optimization method in a D2D-assisted MEC system according to claim 2, characterized in that, In S1024, the access stage refers to the transmission of part of the tasks to the edge service through the cellular uplink, and the backhaul stage refers to the relay of part of the tasks from the edge server to the cloud server through the fiber optic backhaul link.

4. The game theory-based joint optimization method in a D2D-assisted MEC system according to claim 2, characterized in that, In S104, the specific steps of computing resource allocation and offloading ratio allocation are as follows: S1041 For task devices that select the D2D offloading mode, the optimization problem is expressed as follows: ； ； The optimal offloading ratio in the D2D offloading mode is obtained through convex optimization as ; S1042 For task devices that select the cloud offloading mode, the optimization problem is expressed as: ； ； The optimal offloading ratio in the cloud offloading mode is obtained through convex optimization as ; S1043 For task devices that select the MEC offloading mode, the optimization problem is expressed as: , and then substitute it into the optimization problem to rewrite the original optimization problem as: ； 。 5. The joint optimization method based on game theory in the D2D-assisted MEC system according to claim 4, characterized in that, In step S1043, a Lagrangian function is constructed: ； And it is obtained by iterating through the KKT conditions for the optimal computing resource allocation , and finally is substituted into the optimal offloading ratio expression to solve for the optimal offloading ratio in the MEC offloading mode.

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