CN113784340B

CN113784340B - Secret unloading rate optimization method and system

Info

Publication number: CN113784340B
Application number: CN202111080352.9A
Authority: CN
Inventors: 赵明雄; 张榕倩; 张贤琪; 杨昭杰; 肖一鸣; 王子睿
Original assignee: Yunnan University YNU
Current assignee: Yunnan University YNU
Priority date: 2021-09-15
Filing date: 2021-09-15
Publication date: 2023-03-14
Anticipated expiration: 2041-09-15
Also published as: CN113784340A

Abstract

The invention discloses a method and a system for optimizing security unloading rate. The method comprises the following steps: establishing a system model; the system model comprises a plurality of users, a plurality of MEC servers and an eavesdropper; constructing an objective function and constraint conditions of the system model; and solving the objective function by adopting a Lagrange dual method to obtain the optimal transmission power, the optimal subcarrier allocation, the optimal unloading ratio and the optimal computing resource. The invention jointly optimizes communication and distribution of computing resources in a multi-user environment through a Lagrange dual method, thereby realizing an efficient MEC system and improving the unloading rate of users.

Description

Secret unloading rate optimization method and system

Technical Field

The invention relates to the technical field of data transmission, in particular to a method and a system for optimizing a security unloading rate.

Background

With the continuous popularization of 5G in the world, higher data transmission rate attracts more and more network terminal devices, such as Internet of things devices, mobile phones, computers and the like related to production and life. At the same time, the size and number of tasks on these clients is also growing rapidly, forcing these limited computing power user devices to have to offload tasks to server-side processing. Meanwhile, the existence of "malicious eavesdroppers" makes it a challenging problem how to improve the security performance of the communication system due to the broadcast of the wireless transmission.

In the current invention, most of them do not adapt to 5G data transmission rate, and do not consider the OFDMA (orthogonal frequency division multiple access) based secure MEC (mobile edge computing) system. The OFDMA is optimal in all medium access technologies, so that the spectrum efficiency can be greatly improved, and the requirement of the 5G technology is met; meanwhile, in the inventions considering the MEC, the security of the system is not put in the research range in many cases, and the problem that the probability of the system being eavesdropped maliciously becomes high in the case of wireless transmission is not considered.

Disclosure of Invention

The invention aims to provide a method and a system for optimizing the security unloading rate, which adopt a physical layer security technology to improve the security of the system and improve the unloading rate of a user by optimizing communication and computing resource allocation.

In order to achieve the purpose, the invention provides the following scheme:

a method of secure offload rate optimization, comprising:

establishing a system model; the system model comprises a plurality of users, a plurality of MEC servers and an eavesdropper;

constructing an objective function and constraint conditions of the system model;

and solving the objective function by adopting a Lagrange dual method to obtain the optimal transmission power, the optimal subcarrier allocation, the optimal unloading ratio and the optimal computing resource.

Optionally, the objective function of the system model is as follows:

wherein P represents transmission power; Λ represents the unload ratio; x represents a subcarrier; f represents the computing resources of the user; f denotes the computing resources of the MEC server; k represents the number of users; n represents the number of subcarriers; m represents the MEC server number;

the allocation of the sub-carriers is performed,

means that a subcarrier n is allocated to a user k for offloading the task of the user k to the MEC server m, otherwise

Show thatAnd after the subcarrier n is distributed to the user k, the task security unloading rate unloaded to the server m is ensured.

Optionally, the constraint is as follows:

wherein the content of the first and second substances,

representing the local computation time of user k;

representing the delay time of the communication between the user k and the MEC server m; t is _k Represents the time delay that user k can tolerate to the maximum;

representing the energy consumption of the user K belonging to the K for local calculation;

representing that for the data unloaded to the MEC server, a user K belongs to the transmission energy consumption of K; e _k Represents the total energy consumption of user k;

representing the estimation error of a user k on the MEC server, wherein the epsilon is more than or equal to 0;

representing the data amount processed by the user k to the MEC server m;

representing the transmission power of the user K belonging to K on the subcarrier N belonging to N;

representing the maximum transmission power of the user K belonging to K;

indicates the CPU frequency allocated to the MEC server m;

represents the CPU frequency assigned to user k; f _k Represents the computational power of user k; f _m Representing the computing power of the MEC server m.

Optionally, the calculation formula of the optimal subcarrier allocation is as follows:

wherein the content of the first and second substances,

indicates the optimal subcarrier allocation, k ^* Indicating unassigned users, m ^* Indicating an unallocated MEC service.

Optionally, the calculation formula of the optimal transmission power is as follows:

wherein the content of the first and second substances,

which indicates the optimum transmission power for the transmission of the data,

representing the channel power-to-noise ratio of the channel from user K e K to MEC server M e M,

representing the path from user K e K to eavesdropper N e N,

γ _k 、θ _k are all represented by the lagrange multipliers,

lagrange auxiliary variable representing that a user K belongs to K to an MEC server M belongs to M, B represents bandwidth, s _k Representing the data that user k needs to process.

Optionally, the calculation formula of the optimal calculation resource is as follows:

wherein the content of the first and second substances,

indicates the optimal CPU frequency allocated to the MEC server m,

representing Lagrange multipliers, c _m Representing the computing power of server m, s _k Data, μ, representing that user k needs to process _m 、α _k 、c _k 、η _k 、φ _k Both represent lagrangian multipliers.

The invention also provides a secure offload rate optimization system, comprising:

the model building module is used for building a system model; the system model comprises a plurality of users, a plurality of MEC servers and an eavesdropper;

the system comprises an objective function and constraint condition construction module, a constraint condition construction module and a constraint condition construction module, wherein the objective function and constraint condition construction module is used for constructing an objective function and a constraint condition of the system model;

and the objective function solving module is used for solving the objective function by adopting a Lagrange dual method to obtain the optimal transmission power, the optimal subcarrier distribution, the optimal unloading ratio and the optimal computing resource.

According to the specific embodiment provided by the invention, the invention discloses the following technical effects:

the invention provides a method for optimizing secrecy unloading rate, which comprises the following steps: establishing a system model; the system model comprises a plurality of users, a plurality of MEC servers and an eavesdropper; constructing an objective function and constraint conditions of the system model; and solving the objective function by adopting a Lagrange dual method to obtain the optimal transmission power, the optimal subcarrier allocation, the optimal unloading ratio and the optimal computing resource. The invention jointly optimizes communication and distribution of computing resources in a multi-user environment through a Lagrange dual method, thereby realizing an efficient MEC system and improving the unloading rate of users.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.

FIG. 1 is a flow chart of a security offload rate optimization method according to an embodiment of the present invention;

FIG. 2 is a graph of secure unload rate and local computation rate versus latency requirements of a task;

FIG. 3 is a graph of secret offload rate and local calculated ratio versus maximum transmit power of a user;

FIG. 4 is a graph of privacy offload rate and local computation ratio versus the number of MEC servers.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The invention adopts the physical layer security technology to improve the security of the system and improves the unloading rate of the user by optimizing communication and computing resource allocation. By adopting OFDMA, the frequency spectrum efficiency is greatly improved, and the requirement of 5G technology is met. The system includes a plurality of mobile edge computing servers, a plurality of users, and a malicious eavesdropper. Each user can split their task into two parts, one part for local computation and the other part for secure offloading to the MEC server. Considering that the task type of the user is time sensitive, and the task unloading amount cannot exceed the task requirement of the user; considering that the energy storage of a user is limited, when the transmitting power exceeds a certain range, the transmitting antenna is easy to damage; each sub-operator can only connect one user and one server, and the computation frequency allocated to the user by the server cannot exceed the computation capacity of the server. And jointly optimizing communication and optimizing the distribution of computing resources under the multi-user environment by taking the conditions as constraint conditions through a Lagrange dual method, thereby realizing an efficient MEC system.

In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.

As shown in fig. 1, the present invention provides a secure offload rate optimization method, which includes the following steps:

step 101: establishing a system model; the system model includes a plurality of users, a plurality of MEC servers, and an eavesdropper.

The first is to employ an Orthogonal Frequency Division Multiple Access (OFDMA) based MEC system with N subcarriers. The invention sets the system to have K users and M MEC servers which belong to different base stations, and sets an eavesdropper E, wherein each eavesdropper has an antenna to simulate the communication environment in real life. K = {1, \8230;, K }, M = {1, \8230;, M } and N = {1, \8230;, N } are expressed as a user, a MEC server, and a child of bandwidth B, respectivelyAnd (4) carrying wave. Using a combination of three parameters s _k ，c _k ，T _k Triple of K ∈ K to represent the task of user K, where s _k Representing the amount of input data that needs to be processed, c _k Indicating the number of CPU cycles, T, to calculate 1 bit of input data _k Is the maximum delay that the system can tolerate. Due to the limited computing and energy resources of user k, the invention sets it to access multiple MEC servers to achieve potential load balancing and will

M belongs to M, K belongs to K and is set as the data volume processed by the user K to the mth MEC server, then

Is the amount of data that user k processes locally. Make it

And

(in cycles per second) represents the assigned CPU frequency, i.e. the computing power, to user k and MEC server m, respectively. Since the computing power of the MEC server is limited, the CPU frequency allocated to the relevant user should not exceed the computing power of the user, with F _m Is shown by

System delay: the delay of the whole system comprises two parts, namely local calculation time of a user and delay generated in a secret communication stage.

Firstly, considering the local calculation time of the user, the data volume processed locally is calculated

Time taken

Namely, it is

Second is the delay incurred during secure communication. On the basis of an OFDMA system, the invention allocates subcarriers to different users so as to avoid interference in each waveband cell. The invention is to

Indicated as the allocation of subcarriers, specifically,

the sub-carrier n is intended to be allocated to user k for offloading the user's task to MEC server m, otherwise

Is provided with

And

respectively representing the channels from the user K to the eavesdropper N to the N and the MEC server M to the M. Definition of

And

is the corresponding channel power-to-noise ratio, where σ ² Is the variance of gaussian white noise. The invention assumes that the MEC server is fully aware of

But only a part of the Channel State Information (CSI) is known

The present invention defines the method for physical layer security, which is commonly used at present

Is a CSI uncertainty model wherein

K belongs to K, and N belongs to N. Wherein, the first and the second end of the pipe are connected with each other,

to represent

The estimated value at the MEC server is,

indicating the error of its estimate, i.e.

Wherein ∈ ≧ 0 is as the boundary (MEC server synchronizes the condition). Thus, the secure offload rate (in bits/second) from user K ∈ K to MEC server M ∈ M is

Wherein

The received noise power on the MEC server is consistent with the eavesdropper's view, then

And the transmission power of the user K epsilon K on the subcarrier N epsilon N is defined. Thus in the communication phaseTime delay of

The method is divided into two parts: time to task secure offload

And the time of the task in the MEC server M E M

The time delay in the communication phase is then:

wherein

Since the user local computation and task unloading are carried out concurrently, the total time delay of the user K belonging to the K is the user local computation time

And delays caused by secure communication phases

Can be expressed as

Energy loss: since the MEC server is usually supplied by the grid, the invention only considers the energy consumption of the user.

Likewise, the local computation mode is considered first. Recording the energy efficiency coefficient calculated by the CPU chip of the user K belonging to K as eta _k Then the power consumption model of the processor is

(joules/second). Thus, user K ∈ K is local toThe calculated energy consumption is:

for the data unloaded to the MEC server, the transmission energy consumption of the user K belonging to K is as follows:

thus, the total energy consumption of user K ∈ K is

Step 102: and constructing an objective function and a constraint condition of the system model.

The aim of the invention is to maximize the user's secret offload rate by jointly optimizing the transmission power P, the offload ratio Λ, the subcarriers X and the computational resources (F, F). For convenience of notation, define

I.e. formulating the problem as follows:

wherein E _k The maximum energy of the system is the maximum energy,

the maximum transmission power for user K ∈ K. The above formula formulatesA series of constraints that make it possible to guarantee: completing tasks under the time delay requirement of a user; the total energy consumption and power allocation among subcarriers do not exceed the maximum energy budget and transmission power of each user; each subcarrier can be used by only one User-MEC pair to avoid same frequency interference, and the MEC server m occupies the most U _m The subcarrier ensures a certain degree of unloaded data volume for the MEC server to process; the sum of the allocated CPU frequencies must be less than the computing power of the MEC server.

Step 103: and solving the objective function by adopting a Lagrange dual method to obtain the optimal transmission power, the optimal subcarrier allocation, the optimal unloading ratio and the optimal computing resource.

The current form of OP is difficult to handle due to the coupled variables of the constraint and the objective function. To solve this problem, the formulation problem can be converted into five sub-problems: 1) P _Λ Optimizing the unloading ratio; 2) P _c Communication resource allocation; 3) P _F Optimizing computing resources of the MEC server; 4) P is _f Optimizing user computing resources; 5)

And updating the auxiliary variable. The invention then optimizes them in an iterative manner while keeping the other variables unchanged. And takes into account the worst case security offload rate, i.e.

n∈N。

1) Optimization of unloading ratio

Since the objective function of OP is independent of Λ, the corresponding problem can be considered as a feasible problem given (X, P, F), leading to a feasible solution for the unload ratio as

This is about

The linear programming problem of m.di-elect cons.M can be solved by tools like CVX (a convex optimized software package). However, even if a feasible solution Λ is obtained ^* OP is still a mixed integer nonlinear programming, and it is often difficult to find an optimal solution due to high computational complexity. But according to the principle of time-sharing condition: when the number of subcarriers tends to infinity in a multicarrier system, the dual gap becomes zero. Therefore, for the non-convex resource allocation problem of the multi-carrier system, an optimal solution can be obtained in the dual domain.

However, due to derivation

Is in a constraint condition

On the denominator of (a), then OP cannot be directly converted into the dual domain. Therefore, the invention needs to set a new non-negative auxiliary variable

M is in the same order as M, and OP is converted into the following problem

And a Lagrangian function of OP of

Wherein α, β, γ, θ, μ, ψ,

ν is a correspondingly constrained non-negative lagrange multiplier. Definition of

To satisfy the constraint

N is the set of all possible P's for N, χ is the constraint

Of all possible sets of X's of (a),

to satisfy the constraint

Of all the possible sets of F's,

to satisfy the constraint

Of all possible sets of f (f) of,

to satisfy the constraint

And M belongs to all possible phi sets of M, defining a Lagrangian dual function as:

wherein

The lagrangian dual problem is further given:

for a given auxiliary variable and a Lagrange multiplier, the resource related variable is obtained by adopting a primal-dual method, and then is updated according to a closed form of the auxiliary variable. And finally, updating the corresponding Lagrange multiplier by using a secondary gradient method. Four other sub-problems are given below

Wherein

2) Communication resource allocation

Regarding the system communication resource, the allocation of sub-carriers and the optimization of transmission power are mainly divided.

For a subcarrier, given { P, F, F, Λ, Φ }, it is assumed that all subcarriers are allocated to users, i.e., all subcarriers are allocated to users

Then there is k ^* ，m ^* Make

And by

Find out

Thereby completing the optimization of the sub-carriers.

For transmission power, X can be obtained by using the above equation ^* Using KKT conditions and

as a requirement for transmission power optimizationTo solve, the optimum transmission power can be obtained as

The quadratic equation and the sum can be obtained by the root-solving formula of a

And (4) deducing the proof.

3) MEC server computing resource optimization

With newly obtained (X) ^* ，P ^* ) And given

According to KKT conditions and solving, the optimal computing resource distributed to the user k can be obtained as

Find the optimal solution as

4) User server computing resource optimization

Similarly, with newly obtained (X) ^* ，P ^* ，F ^* ) Optimal capacity allocation f for the user ^* Can be obtained by the following formula

According to the given KKT condition (Λ, Φ). Furthermore, it can be deduced from the above formula

And solving by a secant method.

5) Auxiliary variable update

Similarly, with newly obtained (X) ^* ，P ^* ，F ^* ，f ^* ，Λ ^* ) The invention can solve the equation

Obtaining an optimal solution

Is composed of

6) Lagrange multiplier update

Completing the optimization to obtain W ^* And in turn begins updating the lagrange multipliers (α, β, γ, μ, ψ, φ, ν). Since the lagrangian dual problem is always convex, these variables can be updated using a secondary gradient method.

7) Convergence and complexity

Since each sub-problem can be solved by an optimal solution, the algorithm of the present invention can converge to a locally optimal solution of OP with a total computational complexity of

Wherein L is _iter The number of iterations is optimized for the alternation. The details of the algorithm proposed by the present invention are given in algorithm 1.

Algorithm 1: suggestion algorithm

Initialization (W, alpha, beta, gamma, theta, mu, psi, phi, v) and algorithm precision index epsilon ₁ Wherein e is ₁ Is a very small constant control accuracy, sets the loop variable z =0, and specifies z _max Is the maximum number of iterations.

1 repetition (from 1 to 14)

By solving problem P _Λ Finding a feasible solution to the unload ratio

3: repeat (from 3 to 12)

4: repeat (from 4 to 10)

5 determination of optimal subcarrier allocation by equation 15

6-determination of optimum Transmission Power by equation 16

Optimizing MEC Server computing resource Allocation by equation 19

Optimization of user computing resource allocation by equation 20 and secant method

9 updating the auxiliary variable Φ by equation 22

10 until convergence of the Lagrangian function

11 updating of alpha, beta, gamma, theta, mu, psi, phi and v

12 until α, β, γ, θ, μ, ψ, φ and v converge

13: z＝z+1

14 until the continuous interpolation of the objective function is less than e ₁ Or z>z _max

It should be noted in the above method that the number of sub-carriers does not accurately represent the data unloading amount, but at least to some extent, because the number of sub-carriers affects the transmission rate and greatly affects the data unloading amount. Therefore, the method adopts the number of the subcarriers to simplify the unloading data amount which can be processed on the MEC server, and can further refine the data unloading amount if a more accurate simulation reality communication environment is needed. Meanwhile, in a communication system where the load is not heavy, interference between sub-carrier cells can be more effectively suppressed using a frequency hopping OFDMA technique.

Meanwhile, the present invention uses the following settings in the simulation: the channel model follows Rayleigh fading, and the average channel power gain is specified

Wherein beta is ₀ Path loss d for reference distance of = -30dBm ₀ 1m, d is the distance between the respective transceiving nodes, α =2.1 is the path loss exponent. Moreover, the present invention isMing set z _max ＝100，K＝5，N＝64，M＝3，T _k ＝T ^max ＝0.12s，

B＝12.5KHz，d _k ＝9×10 ⁵ bits，η _k ＝10 ^-24 ，c _k ＝1100cycles/bit，F _k ＝0.7GHz，F _m ＝1.1GHz，

And

in the range of [50, 55 ]]m，

m∈M。

The numerical result of the final simulation proves the superior performance of the algorithm (PA) provided by the invention compared with the reference scheme, namely 1) equal power distribution (EPA), namely, the user equivalently distributes the transmission power to the distributed sub-carriers; 2) And (FO) completely unloading, namely completely unloading the tasks to the MEC server by the user for processing.

In fig. 2, the present invention gives the latency requirements of the task and the secret offload rate and local computation ratio. As the task delay requirements gradually decrease, both the privacy offload rate and the Local Computation Ratio (LCR) increase. This is because when the latency requirements of a task get loose, the user will have more ample local computation time, resulting in a local CPU frequency

The method reduces the local computing energy consumption. Thus, more energy is available for transmission, which in turn allows for higher transmit power and LCR. In addition, the inventive method is characterized in thatSince the security offload rate is proportional to the transmit power, the greater the transmit power, the higher the security offload rate. It was also observed that PA can achieve additional 0.77% to 1.14% and 1.49% to 2.89% secure unload rates at different delay requirements compared to EPA and FO.

In fig. 3, the present invention studies the relationship of the secret offload rate and the locally calculated ratio to the maximum transmission power of the user. The results show that the privacy offload rate and LCR increase with increasing maximum transmit power of the user. This is because the greater the maximum transmit power of a user, the greater the transmit power of the user. In the case of the same total transmission energy consumption, the larger the instantaneous transmission power, the higher the rate, and the shorter the transmission time, but the less the total transmission data, the higher the LCR. As the maximum transmit power increases, additional 1.07% to 14.32% and 2.36% to 20.29% security offload rates are available for PA versus EPA and FO.

In fig. 4, the present invention explores the relationship of privacy offload rate and local computation ratio to the number of MEC servers. The results show that as the number of MEC servers increases, the security offload rate increases and LCR decreases. This is because as the number of MEC servers increases, users may gain better channels and be more likely to offload more data during the same time period, resulting in higher privacy rates and lower LCRs.

the model building module is used for building a system model; the system model includes a plurality of users, a plurality of MEC servers, and an eavesdropper.

And the object function and constraint condition building module is used for building the object function and the constraint condition of the system model.

The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the description of the method part.

The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the foregoing, the description is not to be taken in a limiting sense.

Claims

1. A secure offload rate optimization method, comprising:

establishing a system model; the system model comprises a plurality of users and a plurality of mobile edge computing MEC servers; an eavesdropper eavesdrops on the system model;

constructing an objective function and a constraint condition of the system model;

solving the objective function by adopting a Lagrange dual method to obtain optimal transmission power, optimal subcarrier allocation, optimal unloading ratio and optimal computing resources;

the objective function of the system model is as follows:

wherein P represents transmission power; Λ represents the unload ratio; x represents a subcarrier; f represents the computing resources of the user; f denotes the computing resources of the MEC server; k represents the number of users; n represents the number of subcarriers; m represents the number of MEC servers;

indicating the allocation of the sub-carriers,

means that the nth sub-carrier is allocated to user k for offloading the task of user k to MEC server m, otherwise

Indicating a task secrecy unloading rate for unloading to the MEC server m after the subcarrier n is allocated to the user k;

the constraints are as follows:

wherein the content of the first and second substances,

representing the local computation time of a user k, and l represents the local;

representing the delay time of the communication between the user k and the MEC server m; t is a unit of _k Represents the time delay that user k can tolerate to the maximum;

representing the energy consumption of a user K belonging to K for local calculation;

representing the transmission energy consumption of a user K belonging to K for the data unloaded to the MEC server; e _k Represents the total energy consumption of user k;

representing the estimation error of user k on the MEC server;

representing the data amount processed by the user k to the MEC server m;

representing the transmission power of a user K belonging to K on a subcarrier N belonging to N;

representing the maximum transmission power of the user K belonging to K;

indicates the CPU frequency allocated to the MEC server m;

2. The secure offload rate optimization method of claim 1, wherein the optimal subcarrier allocation is calculated as follows:

indicating an unallocated MEC service.

3. The secure offload rate optimization method of claim 1, wherein the optimal transmit power is calculated as follows:

wherein the content of the first and second substances,

representing the path from user K e K to eavesdropper N e N,

γ _k 、θ _k are all representative of the lagrange multipliers,

4. The secure offload rate optimization method of claim 1, wherein the optimal computational resource is calculated as follows:

wherein, the first and the second end of the pipe are connected with each other,

indicates the optimal CPU frequency allocated to the MEC server m,

representing the Lagrangian multiplier, c _m Representing the computing power, s, of the server m _k Data representing the user k needs to process, mu _m 、α _k 、c _k 、η _k 、φ _k Both represent lagrange multipliers.

5. A secure offload rate optimization system, comprising:

the model building module is used for building a system model; the system model comprises a plurality of users and a plurality of mobile edge computing MEC servers; an eavesdropper eavesdrops on the system model;

the target function solving module is used for solving the target function by adopting a Lagrange dual method to obtain the optimal transmission power, the optimal subcarrier distribution, the optimal unloading ratio and the optimal computing resource;

the objective function of the system model is as follows:

wherein P represents transmission power; Λ represents the unload ratio; x represents a subcarrier; f represents the computing resources of the user; f represents the computing resources of the MEC server; k represents the number of users; n represents the number of subcarriers; m represents the number of MEC servers;