Distributed task offloading and resource allocation method and system for multi-user multi-mec wireless network

Abstract

The application discloses a distributed task offloading and resource allocation method and system for a multi-user multi-MEC wireless network, and the method comprises the following steps: S1, initialization; S2, establishing an optimization model; S3, using the proposed optimal offloading algorithm to solve the task offloading problem for the task offloading problem with fixed resource allocation, and obtaining an optimal offloading strategy; S4, dividing the optimal resource allocation problem into a frequency resource allocation problem and a bandwidth resource and subchannel joint allocation problem, obtaining an optimal solution of the frequency resource allocation through a Lagrange dual method, dividing the bandwidth resource and subchannel joint allocation problem into a fixed subchannel optimal bandwidth allocation problem and an optimal bandwidth allocation optimal subchannel allocation problem, obtaining the fixed subchannel optimal bandwidth allocation problem, and simultaneously solving the optimal bandwidth allocation optimal subchannel allocation problem; S5, updating the bandwidth resource allocation and subchannel allocation of the user; and S6, repeating S5 according to a time slot until the total overhead of the system converges.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mobile edge computing network, and particularly relates to a distributed task offloading and resource allocation method and system for a multi-user multi-MEC wireless network. BACKGROUND

[0002] With the rapid development of mobile applications and the Internet of Things, the cloud infrastructure and wireless access network are required to have ultra-low latency, user experience continuity, high reliability and the like. These strict requirements promote the demand for highly localized services at the network edge close to the end user. Based on this, the concept of mobile edge computing emerges as the times require. Mobile edge computing improves the computing capacity of the network edge by deploying high-performance servers closer to the user, solves the problems of limited resources of mobile devices and excessive network load pressure of cloud computing, and can meet the demand for ultra-low latency and ultra-low energy consumption.

[0003] However, due to the required communication between the user equipment and the MEC server in the uplink wireless channel, task offloading generates additional overhead in terms of delay and energy consumption. In addition, in a system with a large number of offloaded users, the limited computing resources at the MEC server will significantly affect the task execution delay. Therefore, offloading decision and execution resource allocation are key issues for efficient computing offloading. Previously, this problem has been partially solved by optimizing offloading decisions, communication resources or computing resources, but all of them are only focused on systems with a single MEC server. Based on the defects existing in the prior art, the application discloses a distributed task offloading and resource allocation method and system for a multi-user multi-MEC wireless network. The application relates to a channel allocation algorithm based on Lagrange dual method and heuristic. SUMMARY

[0004] The application discloses a distributed task offloading and resource allocation method and system for a multi-user multi-MEC wireless network. In a multi-user multi-MEC server wireless network, the application models the system overhead (the weighted sum of the system total delay and the system total energy consumption) as the target with the user's offloading decision, bandwidth resource, subchannel allocation and server's computing resource as the constraint, and proposes an algorithm for joint computing offloading and resource allocation. The algorithm divides the original problem into a task offloading problem with fixed users, bandwidth resources, subchannel allocation and server's computing resources, and a resource allocation problem with an optimal value function corresponding to the optimal offloading problem. The application proposes an optimal offloading algorithm to solve the offloading problem, uses Lagrange dual technology to solve the resource allocation problem, and uses a heuristic subchannel allocation algorithm to solve the subchannel allocation problem. Finally, a distributed approximate optimization algorithm is proposed to solve the global optimal solution.

[0005] In order to achieve the purpose of the present application, the present application adopts the following technical solutions:

[0006] A distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network, comprising the following steps:

[0007] Step one, initialization phase: each node obtains the basic configuration information of the network through information interaction;

[0008] Step two, establish an optimization model: with the goal of minimizing the total system overhead, according to the task offloading constraints and user resource allocation constraints, establish a joint optimization model of offloading decision and resource allocation, and decompose the original optimization problem into a task offloading problem with fixed resource allocation and an optimal resource allocation problem corresponding to the optimization task offloading problem;

[0009] Step three, use the optimal offloading algorithm to solve the task offloading problem for the task offloading problem with fixed resource allocation, and obtain the optimal offloading strategy;

[0010] Step four, for the optimal resource allocation problem corresponding to the optimization task offloading problem, the optimal resource allocation mainly includes bandwidth resource allocation, frequency resource allocation and subchannel allocation, so the optimal resource allocation problem corresponding to the optimization task offloading problem is divided into a frequency resource allocation problem and a bandwidth resource and subchannel joint allocation problem, for the frequency resource allocation, the optimal solution can be obtained by the Lagrange dual method, and for the bandwidth resource and subchannel joint allocation problem, the problem is divided into a fixed subchannel to solve the optimal bandwidth allocation problem and an optimal bandwidth allocation to solve the optimal subchannel allocation problem, the Lagrange dual technology is used to obtain the optimal solution of the fixed subchannel to solve the optimal bandwidth allocation problem, and a heuristic subchannel allocation algorithm is used to solve the optimal bandwidth allocation to solve the optimal subchannel allocation problem;

[0011] Step five, set the step length of iteration update, use the Lagrange dual method and the heuristic subchannel allocation algorithm in step four, and update the bandwidth resource allocation and subchannel allocation of the user through the information parameters of the task and the configuration information of the user;

[0012] Step six, repeat step five according to the time slot, until the total system overhead converges.

[0013] Further, in step one, each node obtains the basic configuration information of the network through information interaction, and the basic configuration information includes topology information, transmission power, link distance, task data size of user equipment, local computing resources and MEC computing resources, etc. Further, the optimization model established in step two is:

[0014]

[0015] where y represents the set of binary offloading decisions of users, X represents the user sub-channel allocation matrix, b represents the set of bandwidth resources allocated to users by the MEC server, and f represents the set of computing resources allocated to users by the MEC server. Equation (2) represents the task offloading decision of a user; equation (3) represents that each task can be executed locally or offloaded to at most one MEC server; equation (4) represents the selection of sub-channel allocation; equation (5) represents that a user can only use one sub-channel; equation (6) represents that a sub-channel can only be allocated to one user for use; equation (7) represents that the number of sub-channels of a user to each server cannot be greater than the total number of sub-channels, and equation (8) represents that the MEC server allocates positive computing resources to each user; equation (9) represents that the computing resources allocated to a user cannot exceed the maximum computing capacity of the MEC server; and equation (10) represents that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server. Equation (11) represents the signal-to-noise ratio of a user u to a base station s on a sub-channel j.

[0016] Further, in order to solve the problem P0, the original optimization problem is divided into two sub-problems, i.e., the original optimization problem is decomposed into a task offloading problem P1 with fixed resource allocation and an optimal resource allocation problem P2 corresponding to the optimization task offloading problem, and the optimal solution of the original problem is finally obtained by solving the decomposed problems.

[0017] In step three, in the task offloading problem with fixed resource allocation, the original optimization problem P0 is converted into problem P1 by fixing the remaining optimization variables except the set of task offloading decisions y, and is specifically represented as:

[0018]

[0019] s.t(2)(3)

[0020] where equation (2) represents that each task can be executed locally or offloaded to at most one MEC server, and equation (3) represents the selection of sub-channel allocation.

[0021] The optimal offloading strategy y solved by problem P1 is * substituted into equation (1), and since the users of local computing do not involve the aspect of resource allocation, the optimal resource allocation problem P2 corresponding to the optimization task offloading problem is represented as:

[0022]

[0023] s.t(4)(5)(6)(7)(8)(9)(10)

[0024] Wherein, formula (4) represents that a user can only use one subchannel; formula (5) represents that one subchannel can only be allocated to one user for use; formula (6) represents that the number of subchannels of a user to each server cannot be greater than the total number of subchannels, formula (7) represents that the MEC server allocates positive computing resources for each user; formula (8) represents that the computing resources allocated to the user cannot exceed the maximum computing capacity of the MEC server; formula (9) represents that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server; formula (10) represents that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server.

[0025] Further, in step three, the optimization model of task offloading with fixed resource allocation is solved: the optimal offloading algorithm is used to solve the task offloading problem with fixed resource allocation, and the optimal offloading strategy is obtained. Therefore, the user set in the non-overlapping area within the coverage range of adjacent base stations can be represented as U nc The user set in the overlapping area within the coverage range of adjacent base stations can be represented as U c Since the user {u|u∈U nc} either calculates locally or calculates on a unique MEC server, only the cost function of the user's local calculation and the cost function of the unique MEC server calculation need to be compared, if the calculation task of the user {u|u∈U nc} will be calculated on the MEC server, otherwise, it will be calculated locally. As for the user {u|u∈U c}, they need to consider the need to calculate locally and select the MEC server at the same time, and the selectable MEC server set of each overlapping area user is {S u |u∈U c}, then the optimal MEC offloading selection strategy optimization problem is as follows:

[0026]

[0027] It can be seen from formula (10) that the cost function of MEC server calculation is related to the signal-to-noise ratio , so the above problem can be transformed into:

[0028]

[0029] Through the above algorithm, the optimal offloading server s * of the user {u|u∈U c} can be found, and and A comparison can be made to obtain the best offloading decision of the user. The user offloaded to the MEC server is put into set U mec , while the user offloaded to the local is put into set U loc .

[0030] Further, in step four, the optimal resource allocation problem model corresponding to the optimization task offloading problem is solved: for the optimal resource allocation problem corresponding to the optimization task offloading problem, it is noted from equation (13) that the bandwidth allocation b and the subchannel allocation X are coupled with each other, while the computing resource allocation f is decoupled from the other two variables. By using this feature, equation (13) can be decoupled into two independent problems, i.e., the bandwidth allocation and subchannel joint allocation problem and the computing resource allocation problem, and the two problems are solved respectively.

[0031] First, in the user computing resource allocation problem, the computing resource allocation problem can be represented by optimizing the third term of equation (13) as follows:

[0032]

[0033] s.t(8)(9)

[0034] wherein equation (8) represents that the computing resource allocated to the user cannot exceed the maximum computing capacity of the MEC server; and equation (9) represents that the bandwidth resource of each task cannot exceed the total bandwidth resource of each MEC server;

[0035] Note that the constraints in equations (8) and (9) are linear. The objective function in equation (16) is represented as g(f us ), and the second derivative of g(f us ) is calculated as follows:

[0036]

[0037] Therefore, the objective function is a convex function with respect to f us , and the above problem is a convex optimization problem, which can be solved by using the Karush-Kuhn-Tucker (KKT) condition. The optimal computing resource allocation f and the corresponding optimal objective function g(f * ) of problem P3 are given as follows:

[0038]

[0039] By optimizing the first and second terms of equation (13), let then the joint subchannel allocation and bandwidth allocation optimization problem is specifically represented as follows:

[0040]

[0041] s.t (4) (5) (6) (7) (10)

[0042] where, formula (4) represents that a user can only use one subchannel; formula (5) represents that one subchannel can only be assigned to one user for use; formula (6) represents that the number of subchannels of a user to each server cannot be greater than the total number of subchannels, formula (7) represents that the MEC server allocates positive computing resources for each user; formula (10) represents that the bandwidth resource of each task cannot exceed the total bandwidth resource of each MEC server.

[0043] The joint subchannel allocation and bandwidth allocation problem is very complex because it contains two coupled optimization variables X and b. The optimization problem is decomposed into two sub-problems of subchannel allocation and bandwidth resource allocation for offloading users to MEC servers. First, fix the subchannel allocation X of offloading users to MEC servers * , then solve the bandwidth resource allocation problem:

[0044]

[0045] s.t (10) (11)

[0046] For the bandwidth allocation problem, since the subchannel allocation X is known At the same time, a user can only occupy one subchannel, so formula (22) can be transformed into:

[0047]

[0048] s.t (10) (11)

[0049] It can be seen that the objective function in formula (23) is a convex function. The constraints for calculating the bandwidth allocation are linear, so the problem P5 is a convex optimization problem, which can also be obtained by Lagrange dual technology, and satisfy the conditions using KKT, then the Lagrange function can be written as:

[0050]

[0051] Finally, the optimal bandwidth resource allocation of problem P5 is obtained :

[0052]

[0053] where

[0054] To simplify its channel model, it is limited that only one user can be in each subchannel, and each user can only occupy one subchannel when receiving a signal. Therefore, the subchannel allocation problem can be represented as:

[0055]

[0056] s.t(4)(5)(6)(7)(11)

[0057] wherein, formula (4) represents that one user can only use one subchannel; formula (5) represents that one subchannel can only be allocated to one user to use; formula (6) represents that the number of subchannels of a user to each server cannot be greater than the total number of subchannels, formula (7) represents that the MEC server allocates positive computing resources for each user; and formula (11) represents the signal-to-noise ratio of a user u to a base station s on a subchannel j.

[0058] Further, in step four, for the subchannel allocation problem, the application proposes a heuristic subchannel allocation algorithm to obtain the optimal solution of subchannel allocation, so as to minimize the total system overhead.

[0059] In the algorithm, the variable is obtained by solving the problem P5 in a distributed manner. Define j (u) as the set of subchannels allocated to the user u, as the set of subchannels not allocated to the user u, and s (j) as the set of users to which the subchannel j has been allocated within the coverage range of the base station s, as the set of users to which the subchannel has not been allocated within the coverage range of the base station s. The specific steps of the heuristic channel allocation algorithm are as follows:

[0060] Step 4.1: initialize j (u) and Ω s (j) and the subchannel allocation matrix X, the transmission power p u , and the channel gain

[0061] Step 4.2: calculate the optimal solution U(X best ) of the initial subchannel allocation according to the initialization parameters by formula (27);

[0062] Step 4.3: determine whether is empty, if it is empty, all users have been allocated the optimal subchannel, otherwise proceed to step 4.4;

[0063] Step 4.4: determine the set of subchannels that can be allocated to the user and find the optimal solution U(X temp ) of the optimal subchannel allocation scheme in the set by formula (27);

[0064] Step 4.5: if U(Xtemp ) < U(X best ), update the set Φ j (u) and the subchannel allocation table, and let U(X best ) = U(X temp );

[0065] Step 4.6: go back to step 4.3 until is empty.

[0066] Further, the step five, set the step length of iteration update, using the algorithm in S3 and S4, through the information parameters of tasks and the configuration information of users, solve the optimal task offloading strategy and the optimal frequency resource allocation, update the bandwidth resource allocation and subchannel allocation of users, the specific steps are as follows:

[0067] Step 5.1: initialize the bandwidth resource b, the computing resource f, the subchannel allocation X and the offloading decision y of all users.

[0068] Step 5.2: determine whether the user is to be calculated locally or in the MEC server through the optimal offloading decision algorithm, and express the final offloading decision as y * .

[0069] Step 5.3: according to the offloading decision y * solved, solve the optimal computing resource allocation f mec of the user set U * offloaded to the MEC server through the Lagrange dual technology.

[0070] Step 5.4: since the optimization variables subchannel X and bandwidth b are coupled with each other, fix the optimization variable subchannel X, then solve the optimal bandwidth b * using the Lagrange dual method, and then bring b * into the heuristic channel allocation algorithm to solve the optimal subchannel allocation X * .

[0071] Step 5.5: repeat step 5.4 until the absolute value of the result of the current time calculated by formula (27) minus the calculation result of the last time is less than the set threshold, then X * and b * of the current time are the optimal X * and b * .

[0072] Preferably, in step six, the convergence condition is as follows: the absolute value of the system overhead of the current time minus the system overhead of the last time is less than the set threshold.

[0073] The application further discloses a distributed task offloading and resource allocation system of a multi-user multi-MEC wireless network, which is used for executing the method and comprises the following modules.

[0074] An initialization module: each node obtains basic configuration information of the network through information interaction;

[0075] An optimization model establishment module: a joint optimization model of offloading decision and resource allocation is established according to task offloading constraints and user resource allocation constraints, and the original optimization problem is decomposed into a task offloading problem with fixed resource allocation and an optimal resource allocation problem corresponding to the optimization task offloading problem, with the goal of minimizing the total system cost.

[0076] An optimal offloading strategy acquisition module: an optimal offloading algorithm is used to solve the task offloading problem with fixed resource allocation, and an optimal offloading strategy is obtained.

[0077] A problem solving module: the optimal resource allocation includes bandwidth resource allocation, frequency resource allocation and subchannel allocation, so the optimal resource allocation problem corresponding to the optimization task offloading problem is divided into a frequency resource allocation problem and a bandwidth resource and subchannel joint allocation problem; the optimal solution of the frequency resource allocation problem is obtained by using the Lagrange dual method; the bandwidth resource and subchannel joint allocation problem is divided into a fixed subchannel optimal bandwidth allocation problem and an optimal subchannel allocation problem of optimal bandwidth allocation; the optimal solution of the fixed subchannel optimal bandwidth allocation problem is obtained by using the Lagrange dual method, and the optimal subchannel allocation problem of optimal bandwidth allocation is solved by using a heuristic subchannel allocation algorithm.

[0078] An updating module: the step length of iterative updating is set, and the bandwidth resource allocation and subchannel allocation of the user are updated by using the Lagrange dual method and the heuristic subchannel allocation algorithm in step four, through the information parameters of the task and the configuration information of the user.

[0079] An iteration module: the updating module is repeatedly executed according to the time slot until the total system cost converges.

[0080] The application has the following advantages:

[0081] (1) The application realizes a distributed task offloading and resource allocation method of a multi-user multi-MEC wireless network; and experiments show that the algorithm proposed in the application can converge within 10 iterations.

[0082] (2) The most prominent advantage of the present application is to divide the original problem into a task offloading problem with bandwidth resources, sub-channel allocation and server computing resources of fixed users and a resource allocation problem with an optimal value function corresponding to the optimization offloading problem. The present application proposes an optimal offloading algorithm to solve the offloading problem, uses the Lagrange dual technique to solve the resource allocation problem, and a heuristic-based sub-channel allocation algorithm to solve the sub-channel allocation problem, and finally proposes a distributed approximate optimization algorithm to solve the global optimal solution, greatly reducing the computational complexity. BRIEF DESCRIPTION OF DRAWINGS

[0083] Figure 1 A flow chart of a distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network according to a preferred embodiment of the present application.

[0084] Figure 2 A system model diagram for a multi-user multi-MEC server.

[0085] Figure 3 A graph of the total overhead of the system under different transmit powers versus the number of iterations.

[0086] Figure 4 A system block diagram of a distributed task offloading and resource allocation system for a multi-user multi-MEC wireless network according to a preferred embodiment of the present application. DETAILED DESCRIPTION

[0087] The embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0088] As shown in Figures 1-2 , the distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network according to the present embodiment includes the following steps:

[0089] Step one, initialization phase: each node obtains the basic configuration information of the network through information interaction, including topology information, transmit power, link distance, task data size of user equipment, local computing resources and MEC computing resources, etc.

[0090] The present embodiment considers a multi-user, multi-MEC server system, each cell is equipped with a base station, each base station is equipped with a MEC server, and each user can choose to offload computing tasks to the MEC server at the base station within its coverage. Users in the overlapping area of the base station coverage can choose to offload tasks on any one of the MEC servers. The set of users and MEC servers in the system are denoted as U = {1, 2,..., u} and S = {1, 2,..., s}, respectively. The present embodiment considers that each user u e U has one computing task at a time, denoted as V u, which is atomic and cannot be divided into sub-tasks. Each computing task V u is represented by two parameters {d u , c u}, where d u represents the amount of data required for the u-th user to transfer from the local device to the MEC server, in bits, and c u represents the number of CPU cycles required for the u-th user to complete the task. Each task can be executed locally on the user device or offloaded to the MEC server. Therefore, the task offloading decision for user u to base station s can be represented as y us = {0, 1}, where "0" indicates that the task is executed locally and "1" indicates that the task is executed on the MEC server. The set of task offloading variables for all users is represented as y = {y us | u e U, s e S}.

[0091] Step two, establish an optimization model: to minimize the total system overhead as the goal, according to the task offloading constraints and user resource allocation constraints, establish the joint optimization model of offloading decision and resource allocation, and decompose the original optimization problem into the task offloading problem with fixed resource allocation and the optimal resource allocation problem corresponding to the optimization task offloading problem.

[0092] Let denote the local computing capacity of user u, in CPU cycles / s. Therefore, if user u executes its task locally, the task completion time is represented as:

[0093]

[0094] To calculate the energy consumption of the user device when executing the task locally, the widely adopted energy consumption model per computing cycle is used, ε = κf 2 , where κ is the energy coefficient depending on the chip architecture and f is the CPU frequency. Therefore, when user u executes its task V u locally, the energy consumption of user u can be represented as:

[0095]

[0096] Therefore, the cost function of user local computing can be represented as

[0097]

[0098] where and are the weighted parameter values of latency and energy consumption, respectively,

[0099] ​Consider a system with OFDMA as the multiple access scheme in the uplink, where the bandwidth is divided into J sub-channels, then the set of user bandwidth resource allocation is expressed as in, represents the transmission bandwidth of user u uploading the task to server s on the jth subchannel. Channel allocation can be achieved using a U×J-dimensional binary channel allocation matrix X∈R U×J It is represented by , which is defined as follows: For any user u∈U and any channel j∈J, if user u uploads data to server s through subchannel j, then the element of the channel allocation matrix otherwise, The u-th row of X us represents the channel allocation vector for user u to upload data to server s. Since each user can only be assigned one subchannel, X us It can only contain one element "1", and the rest of the elements are "0". s ={u∈U|y us =1}, Denote the set of users who offload their tasks to server s, and let U mec =∪ s∈S U s Denotes the set of users whose tasks are offloaded to the MEC server, U loc Represents the set of users who execute tasks locally.

[0100] In addition, Denote it as the uplink channel gain between user u and base station s on subchannel j. Let p u User u is sending his task data d u The transmission power when uploading to the base station. Since users transmitting to the same base station use different subchannels, the interference within the uplink cell is well alleviated; however, these users are still affected by the inter-cell interference. In this case, the signal-to-noise ratio from user u to base station s on subchannel j is for:

[0101]

[0102] Since each user transmits on only one subchannel, the achievable rate when user u sends data to base station s using the jth subchannel is expressed as:

[0103]

[0104] User u sends its task data d in the uplink u The transmission time can be expressed as:

[0105]

[0106] The energy consumption of user u offloading tasks to base station s is:

[0107]

[0108] Each MEC server at a base station is able to provide computing offloading services to multiple users simultaneously. The computing resources provided by each MEC server, which can be shared among users within the base station coverage, are denoted by f s . The computing resource allocation policy is defined as f = {f us | u e U, s e S}, where f us > 0 is the computing resource allocated by base station s to the tasks V s offloaded from user u e U u . Obviously, f us = 0,

[0109] Given the computing resource allocation, the execution time of tasks V u on the MEC server is:

[0110]

[0111] The total latency of user u offloading tasks to base station s is:

[0112]

[0113] The cost function of user edge computing is:

[0114]

[0115] where, and are the weighted parameter values of latency and energy consumption, respectively, The system overhead function Z is defined by the summation of all users on the local and MEC servers. Then, the joint task offloading and resource allocation problem is described as a system overhead minimization problem P0 can be represented as:

[0116]

[0117] where y represents the set of users' binary offloading decisions, X represents the user sub-channel allocation matrix, b represents the set of bandwidth resources allocated by the MEC servers to the users, and f represents the set of computing resources allocated by the MEC servers to the users. Equation (12) represents the user's task offloading decision; equation (13) represents that each task can be executed locally or offloaded to at most one MEC server; equation (14) represents the selection of sub-channel allocation; equation (15) represents that one user can only use one sub-channel; equation (16) represents that one sub-channel can only be allocated to one user for use; equation (17) represents that the number of sub-channels of a user to each server cannot be greater than the total number of sub-channels, and equation (18) represents that the MEC servers allocate positive computing resources to each user; equation (19) represents that the computing resources allocated to the user cannot exceed the maximum computing capacity of the MEC server; and equation (20) represents that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server. Equation (21) represents the signal-to-noise ratio of the user u to the base station s on the sub-channel j.

[0118] Since the optimization problem P0 is a mixed integer programming problem with binary variables, and the multi-dimensional variables are coupled, it is difficult to directly solve the problem by using traditional optimization methods. In order to solve the problem P0, the original optimization problem is divided into two sub-problems, i.e., the original optimization problem is decomposed into a task offloading problem P1 with fixed resource allocation and an optimal resource allocation problem P2 corresponding to the optimization task offloading problem, and the optimal solution of the original problem is finally obtained by solving the decomposed problems.

[0119] Step three, in the task offloading problem with fixed resource allocation, the original optimization problem P0 is converted into problem P1 by fixing the remaining optimization variables except the set of task offloading decisions y, which is specifically represented as:

[0120]

[0121] s.t(12)(13)

[0122] The optimal offloading strategy y obtained by solving problem P1 * Substituting equation (11) into equation (22), the minimization of the total system cost is represented as:

[0123]

[0124] Since the users of local computing do not involve the aspect of resource allocation, equation (23) can be converted into the cost of users offloaded to the MEC server, and therefore the optimal resource allocation problem P2 corresponding to the optimization task offloading problem is represented as:

[0125]

[0126] s.t(14)(15)(16)(17)(18)(19)(20)(21)

[0127] Solving the optimization model of task offloading with fixed resource allocation: using the optimal offloading algorithm to solve the task offloading problem with fixed resource allocation, and obtaining the optimal offloading strategy. Therefore, for the user set in the non-overlapping area within the coverage range of adjacent base stations, it can be expressed as U nc For the user set in the overlapping area within the coverage range of adjacent base stations, it can be expressed as U c Since the user {u|u∈U nc} either calculates locally or calculates on the unique MEC server, only the cost function of the user local calculation and the cost function of the unique MEC server calculation need to be compared, if the calculation task of the user {u|u∈U nc} will be calculated on the MEC server, otherwise, it will be calculated locally. And for the user {u|u∈U c}, they need to consider the need for local calculation and MEC server selection at the same time, the optional MEC server set of each overlapping area user is {S u |u∈U c}, then the optimal MEC offloading selection strategy optimization problem is as follows:

[0128]

[0129] It can be seen from equation (10) that the cost function of MEC server calculation is related to the signal-to-noise ratio , therefore the above problem can be transformed into:

[0130]

[0131] Through the above algorithm, the optimal offloading server s c of the user {u|u∈U *} can be found, and by comparing and , the best offloading decision of the user can be obtained. Finally, the users offloaded to the MEC server are put into the set U mec , and the users offloaded to the local are put into the set U loc .

[0132] Step four, solving the optimal resource allocation problem corresponding to the optimization task offloading problem: for the optimal resource allocation problem corresponding to the optimization task offloading problem, it is noted from equation (24) that the bandwidth allocation b and the subchannel allocation X are coupled with each other, while the computing resource allocation f is decoupled with the other two variables. By using this property, equation (24) can be decoupled into two independent problems, i.e., the bandwidth allocation and subchannel joint allocation problem and the computing resource allocation problem, and the two problems are solved respectively.

[0133] First, in the user computing resource allocation problem, by optimizing the third term of equation (24), the computing resource allocation problem can be expressed as:

[0134]

[0135] s.t(18)(19)

[0136] Note that the constraints in equations (18) and (19) are linear. The objective function in equation (27) is denoted as g(f us ), and the second derivative of g(f us ) is calculated as:

[0137]

[0138] Therefore, the objective function is a convex function with respect to f us , and the above problem is a convex optimization problem, which can be solved using the Karush-Kuhn-Tucker (KKT) condition. The optimal computing resource allocation and the corresponding optimal objective function g(f * ) of problem P3 are given as follows:

[0139]

[0140] By optimizing the first and second terms of equation (24), let then the joint subchannel allocation and bandwidth allocation optimization problem is specifically expressed as:

[0141]

[0142] s.t(4)(5)(6)(7)(20)

[0143] The joint subchannel allocation and bandwidth allocation problem is very complex because it contains two coupled optimization variables X and b. This optimization problem is decomposed into two subproblems, i.e., the subchannel allocation of the user offloaded to the MEC server and the bandwidth resource allocation. First, fix the subchannel allocation X * of the user offloaded to the MEC server, and then solve the bandwidth resource allocation problem:

[0144]

[0145] s.t(20)(21)

[0146] For the bandwidth allocation problem, since the subchannel allocation Meanwhile, one user can only occupy one subchannel, so the equation (33) can be transformed into:

[0147]

[0148] s.t(20)(21)

[0149] It can be seen that the objective function in equation (34) is a convex function. The constraints of calculating bandwidth allocation are linear, so the problem P5 is a convex optimization problem, which can also be obtained by Lagrange dual technology, and satisfy the conditions of using KKT, then the Lagrange function can be written as:

[0150]

[0151] Finally, the optimal bandwidth resource allocation of problem P5 is obtained :

[0152]

[0153] Where

[0154] In order to simplify its channel model, it is limited that only one user can be in each subchannel, and each user can only occupy one subchannel when receiving signals. Therefore, the subchannel allocation problem can be represented as:

[0155]

[0156] s.t(4)(5)(6)(7)(21)

[0157] For the subchannel allocation problem, the present application proposes a heuristic subchannel allocation algorithm to obtain the optimal solution of subchannel allocation to minimize the total system overhead.

[0158] In this algorithm, the variable is obtained by solving the problem P5 in a distributed manner. Define j (u) as the set of subchannels allocated to user u, as the set of subchannels not allocated to user u, Ω s (j) as the set of users allocated subchannel j in the coverage range of base station s, as the set of users not allocated subchannel in the coverage range of base station s. The specific steps of the heuristic channel allocation algorithm are:

[0159] Step 4.1: Initialization of Φ j (u), Ω s (j), subchannel allocation matrix X, transmission power p u , channel gain

[0160] Step 4.2: Calculate the optimal solution U(X best ) of the initial subchannel allocation according to the initialization parameters by formula (38);

[0161] Step 4.3: Determine whether it is empty, if it is empty, all users have been allocated subchannels, otherwise proceed to step 4.4;

[0162] Step 4.4: Determine the set of subchannels that users can allocate and find the optimal solution U(X temp ) of the optimal subchannel allocation scheme in the set by formula (38);

[0163] Step 4.5: If U(X temp ) < U(X best ), update the set Φ j (u) and the subchannel allocation table, and let U(X best ) = U(X temp );

[0164] Step 4.6: Return to step 4.3 until is empty.

[0165] Step five, variable update phase: set the step size of iterative update, use the algorithms in S3 and S4, through the information parameters of tasks and the configuration information of users, update the task offloading strategy of users, bandwidth resource allocation, frequency resource allocation and subchannel allocation, the specific steps are as follows:

[0166] Step 5.1: Initialize the bandwidth resource b, computing resource f, subchannel allocation X and offloading decision y of all users.

[0167] Step 5.2: Determine whether the user calculates locally or on the MEC server through the optimal offloading decision algorithm, and express the final offloading decision as y * .

[0168] Step 5.3: According to the obtained offloading decision y * , solve the set U mecOptimal computation resource allocation f * .

[0169] Step 5.4: Since the optimization variables subchannel X and bandwidth b are coupled with each other, by fixing the optimization variable subchannel X, then using Lagrange dual method to solve the optimal bandwidth b * , then b * is brought into the optimal subchannel allocation X * solved by heuristic channel allocation algorithm.

[0170] Step 5.5: Repeat step 5.4 until the absolute value of the result calculated by formula (27) at the current time minus the calculation result at the last time is less than the set threshold, then the X * and b * at the current time are the optimal X * and b * .

[0171] Step six, repeat step five by time slot until the system total cost converges. The convergence condition is as follows: the absolute value of the system cost at the current time minus the system cost at the last time is less than the set threshold.

[0172] Figure 3 Fig. 2 is a diagram showing the change of the system total cost with the iteration number when the transmit power of the user equipment is 18dBm, 20dBm and 22dBm respectively. As can be clearly seen from Figure 3 , the algorithm proposed in the present application can converge within 10 iterations, indicating that the algorithm involved in the present application has the characteristic of fast convergence. When the transmit power increases, the system cost gradually increases, because the increase of the transmit power will affect the increase of the transmission energy consumption from the user to the server, and further cause the increase of the system total cost. When the transmit power is 18dBm and 20dBm respectively, the system total cost is reduced by 21% and 13% respectively compared with that when the transmit power is 22dBm, so reducing the transmit power helps to reduce the system cost.

[0173] As shown in Figure 4 , the embodiment discloses a distributed task offloading and resource allocation system of a multi-user multi-MEC wireless network, for executing the above-mentioned method embodiment, which comprises the following modules:

[0174] An initialization module: each node obtains the basic configuration information of the network through information interaction;

[0175] An optimization model establishment module: taking minimizing the system total cost as the target, a joint optimization model of offloading decision and resource allocation is established according to the task offloading constraint and the user resource allocation constraint, and the original optimization problem is decomposed into a task offloading problem with fixed resource allocation and an optimal resource allocation problem corresponding to the optimization task offloading problem;

[0176] optimal unloading strategy obtaining module: using optimal unloading algorithm to solve the task unloading problem for the task unloading problem with fixed resource allocation, and obtaining the optimal unloading strategy;

[0177] problem solving module: for the optimal resource allocation problem corresponding to the optimal task unloading problem, the optimal resource allocation includes bandwidth resource allocation, frequency resource allocation and subchannel allocation, so the optimal resource allocation problem corresponding to the optimal task unloading problem is divided into frequency resource allocation problem, bandwidth resource and subchannel joint allocation problem, the optimal solution is obtained for the frequency resource allocation through Lagrange dual method, and for the bandwidth resource and subchannel joint allocation problem, the problem is divided into fixed subchannel solving optimal bandwidth allocation problem and optimal bandwidth allocation solving optimal subchannel allocation problem, the optimal solution of the fixed subchannel solving optimal bandwidth allocation problem is obtained by using Lagrange dual method, and the heuristic subchannel allocation algorithm is used to solve the optimal bandwidth allocation solving optimal subchannel allocation problem;

[0178] updating module: setting the step length of iterative update, using the Lagrange dual method and the heuristic subchannel allocation algorithm in step four, updating the bandwidth resource allocation and subchannel allocation of the user through the information parameters of the task and the configuration information of the user;

[0179] iteration module: the updating module is repeatedly executed according to the time slot until the total system overhead converges.

[0180] The other contents of the embodiment can refer to the above method embodiment.

[0181] The present application is close to the optimal solution, and compared with the traditional method, the total system overhead is significantly reduced.

[0182] The preferred embodiments and principles of the present application are described in detail above, and for ordinary skilled persons in the art, the specific implementation manner can be changed according to the idea provided by the present application, and these changes should be regarded as the protection scope of the present application.

Claims

1. A method for distributed task offloading and resource allocation in a multi-user multi-MEC wireless network, the method comprising: The method specifically comprises the following steps: Step one, initialization stage: each node obtains the configuration information of the network through information interaction; Step two, establishing an optimization model: taking the minimization of the total system overhead as the target, a joint optimization model of the task offloading decision and the resource allocation is established according to the task offloading constraint and the user resource allocation constraint, and the original optimization problem is decomposed into a task offloading problem with fixed resource allocation and an optimal resource allocation problem corresponding to the optimization task offloading problem; Step three, the optimal offloading algorithm is used to solve the task offloading problem with fixed resource allocation, and the optimal offloading strategy is obtained; Step four, for the optimal resource allocation problem corresponding to the optimization task offloading problem, the optimal resource allocation includes bandwidth resource allocation, frequency resource allocation and subchannel allocation, therefore the optimal resource allocation problem corresponding to the optimization task offloading problem is divided into a frequency resource allocation problem, a bandwidth resource and subchannel joint allocation problem, the optimal solution of the frequency resource allocation is obtained through the Lagrange dual method, and the bandwidth resource and subchannel joint allocation problem is divided into a fixed subchannel to solve the optimal bandwidth allocation problem and an optimal bandwidth allocation to solve the optimal subchannel allocation problem, the optimal solution of the fixed subchannel to solve the optimal bandwidth allocation problem is obtained through the Lagrange dual method, and the optimal bandwidth allocation to solve the optimal subchannel allocation problem is solved through the heuristic subchannel allocation algorithm; Step five, the step length of iterative update is set, the Lagrange dual method and the heuristic subchannel allocation algorithm in step four are used, the bandwidth resource allocation and the subchannel allocation of the user are updated through the information parameters of the tasks and the configuration information of the user; Step six, step five is repeatedly executed according to the time slot until the total system overhead converges; The optimization model in step two is in the form of: where U denotes the set of users, y us denotes the task offloading decision of user u to base station s, denotes the cost function of user local computation, denotes the cost function of user edge computation, S denotes the set of MEC servers, X us denotes the channel allocation vector of user u to upload data to server s, U loc denotes the set of users that execute tasks locally, U mec denotes the set of users that offload their tasks to MEC servers, denotes the element of channel allocation matrix, J denotes sub-channel, f us is the computing resource of base station allocated to the task V u offloaded from user u, U s denotes the set of users that offload tasks to server s, denotes the signal-to-noise ratio, p u denotes the transmission power, denotes the channel gain, y denotes the set of binary offloading decisions of users, X denotes the user sub-channel allocation matrix, b denotes the set of bandwidth resources of MEC servers allocated to users, f denotes the set of computing resources of MEC servers allocated to users; equation (1) denotes the task offloading decision of users; equation (2) denotes that each task can be executed locally or offloaded to at most one MEC server; equation (3) denotes the selection of sub-channel allocation; equation (4) denotes that one user can only use one sub-channel; equation (5) denotes that one sub-channel can only be allocated to one user for use; equation (6) denotes that the number of sub-channels of a user to each server cannot be greater than the total number of sub-channels; equation (7) denotes that the MEC server allocates positive computing resources to each user; equation (8) denotes that the computing resources allocated to a user cannot exceed the maximum computing capacity of the MEC server; equation (9) denotes that the computing resources allocated to a user cannot exceed the maximum computing capacity of the MEC server; equation (10) denotes that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server; equation (11) denotes the signal-to-noise ratio of user u to base station s on sub-channel j for transmission.

2. The method of claim 1, wherein, In step one, the configuration information includes topology information, transmission power, link distance, task data size of user equipment, local computing resource and MEC computing resource.

3. The method of claim 1, wherein, In step three, in the optimization task offloading problem, the original optimization task offloading problem P0 is converted into problem P1 by fixing the remaining optimization variables except the task offloading decision set y, and is specifically expressed as: s.t(2)(3) Wherein, formula (2) indicates that each task can be executed locally or offloaded to at most one MEC server; formula (3) indicates the selection of subchannel allocation; The optimal resource allocation problem P2 corresponding to the optimization task offloading problem is specifically expressed as: s.t(4)(5)(6)(7)(8)(9)(10) Wherein, formula (4) represents that a user can only use one subchannel; formula (5) represents that one subchannel can only be assigned to one user to use; formula (6) represents that the number of subchannels of a user to each server cannot be greater than the total number of subchannels, formula (7) represents that the MEC server allocates positive computing resources for each user; formula (8) represents that the computing resources allocated to the user cannot exceed the maximum computing capacity of the MEC server; formula (9) represents that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server; formula (10) represents that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server.

4. The method of claim 3, wherein, Step three, solving the task offloading problem with fixed resource allocation; using the optimal offloading algorithm for the task offloading problem with fixed resource allocation to solve the task offloading problem, and obtaining the optimal offloading strategy; for the user set in the non-overlapping area within the coverage range of the adjacent base stations, denoted as U nc , for the user set in the overlapping area within the coverage range of the adjacent base stations, denoted as U c , since the user {u|u∈U nc} performs calculation locally or in a unique MEC server, only the cost function of the user local calculation and the cost function of the unique MEC server calculation need to be compared, if the calculation task of the user {u|u∈U nc} will be calculated in the MEC server, otherwise, it will be calculated locally; for the user {u|u∈U c}, considering the local calculation and the selection of the MEC server at the same time, the selectable MEC server set of each overlapping area user is {S u |u∈U c}, and the optimal MEC offloading selection strategy optimization problem is as follows: Cost function computed by the MEC server With signal-to-noise ratio Therefore, the above problem is transformed into: Find the optimal offloading server s for user {u | u ∈ U c} * , compare and , get the best offloading decision of the user; put the user offloaded to the MEC server into set U mec , and put the user offloaded to the local into set U loc .

5. The method of claim 4, wherein, In step four, the optimal resource allocation problem corresponding to the optimization task offloading problem is solved; for the optimal resource allocation problem corresponding to the optimization task offloading problem, it is known from formula (13) that the bandwidth allocation b and the subchannel allocation X are coupled with each other, and the computing resource allocation f is decoupled with the other two variables, and by utilizing this characteristic, formula (13) is decoupled into two independent problems, namely, the bandwidth allocation and subchannel joint allocation problem and the computing resource allocation problem, and the two problems are solved respectively; In the computing resource allocation problem, the computing resource allocation problem is represented as formula (14) by optimizing the third term of formula (13): s.t(8)(9) Wherein, formula (8) represents that the computing resources allocated to the user cannot exceed the maximum computing capacity of the MEC server; formula (9) represents that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server. The constraints in equations (8) and (9) are linear; the objective function in equation (16) is represented as g(f us ) by computing the second derivative of g(f us ): Therefore, the objective function is a convex function about f us , and P3 problem is a convex optimization problem, which is solved by KKT condition; the optimal calculation resource allocation and the corresponding optimal objective function g(f * ) of problem P3 are given as follows: By optimizing the first and second terms of equation (13), we have The joint subchannel and bandwidth allocation optimization problem is then expressed as: s.t(4)(5)(6)(7)(10) Wherein, formula (4) represents that a user can only use one subchannel; formula (5) represents that one subchannel can only be assigned to one user to use; formula (6) represents that the number of subchannels of a user to each server cannot be greater than the total number of subchannels, formula (7) represents that the MEC server allocates positive computing resources for each user; formula (10) represents that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server. where X and b are two coupled optimization variables; decompose the optimization problem into two sub-problems of sub-channel allocation and bandwidth resource allocation for offloaded MEC server users; fix the sub-channel allocation X for offloaded MEC server users * , solve the bandwidth resource allocation problem: s.t(10)(11) For the bandwidth resource allocation problem, the known subchannel allocation Meanwhile, one user can only occupy one subchannel, so formula (22) is transformed into: s.t(10)(11) Wherein, formula (10) represents that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server; formula (11) represents the signal-to-noise ratio of user u to base station s on subchannel j. The objective function in equation (23) is a convex function; the constraints for computing bandwidth allocation are linear, thus problem P5 is a convex optimization problem, which is solved by the Lagrangian dual method, and satisfying the conditions using KKT, the Lagrangian function is written as: obtaining an optimal bandwidth resource allocation for problem P5 for: wherein, Each subchannel is limited to have only one user, and each user can only occupy one subchannel when receiving a signal; therefore, the subchannel allocation problem is represented as formula (15): s.t(4)(5)(6)(7)(11) Wherein, formula (4) represents that a user can only use one subchannel; formula (5) represents that one subchannel can only be assigned to one user to use; formula (6) represents that the number of subchannels of a user to each server cannot be greater than the total number of subchannels; formula (7) represents that the MEC server allocates positive computing resources for each user; formula (11) represents the signal-to-noise ratio of user u to base station s on subchannel j.

6. The method of claim 5, wherein, In step four, for the sub-channel allocation problem, a heuristic sub-channel allocation algorithm is used to obtain the optimal solution of sub-channel allocation. In the heuristic sub-channel allocation algorithm, the variables are obtained by solving the problem P5 distributively; define Φ j (u) is the set of sub-channels allocated to user u, is the set of sub-channels not allocated to user u, Ω s (j) is the set of users allocated with the optimal sub-channel j in the coverage of base station s, is the set of users not allocated with the optimal sub-channel in the coverage of base station s; the specific steps of the heuristic channel allocation algorithm are as follows: Step 4.1: Initialization of Φ j (u), Ω s (j), subchannel allocation matrix X, transmission power p u , channel gain Step 4.2: Calculate the optimal solution U(X of the initialization subchannel allocation according to the initialization parameters by equation (27) best ); Step 4.3: Determine whether it is empty. If it is empty, then all users have been assigned an optimal subchannel. Otherwise, perform step 4.

4. Step 4.4: Determine the set of sub-channels that the user can allocate and find the optimal solution U(X ) of the optimal sub-channel allocation scheme in set temp ) by equation (27). Step 4.5: If U(X temp ) < U(X best ), update the set Φ j (u) and the subchannel allocation table, and let U(X best ) = U(X temp ). Step 4.6: Go back to Step 4.3 until is empty.

7. The method of claim 6, wherein, Step five is specifically as follows: Step 5.1: initialize the bandwidth resources b, the computing resources f, the subchannel allocation X and the offloading decision y of all users; Step 5.2: Decide whether the user computes locally or at the MEC server by the optimal offloading decision algorithm, and represent the final offloading decision as y * ; Step 5.3: According to the derived offloading decision y * , solve the optimal computation resource allocation f mec for the user set U * offloaded to the MEC server by Lagrangian dual method. Step 5.4: Since the optimization variables quantum channel X and bandwidth b are coupled with each other, by fixing the optimization variable quantum channel X, the optimal bandwidth b is solved by using the Lagrangian dual method * , and then b * is brought into the optimal sub-channel allocation X * solved by the heuristic channel allocation algorithm. Step 5.5: Repeat the execution of Step 5.4 until the absolute value of the result of the calculation of the current time instant of formula (27) minus the result of the calculation of the previous time instant is less than a set threshold, then the X * and b * is the optimal X * and b * .

8. The method of claim 1, wherein, In step six, the convergence condition is as follows: the absolute value of the system overhead at the current time minus the system overhead at the last time is less than a set threshold.

9. A distributed task offloading and resource allocation system for multi-user multi-MEC wireless networks for performing the method of any of claims 1-8, characterized in that, The method comprises the following modules: An initialization module: each node obtains network configuration information through information interaction; An optimization model establishment module: a joint optimization model of task offloading decision and resource allocation is established according to task offloading constraints and user resource allocation constraints, and the original optimization problem is decomposed into a task offloading problem with fixed resource allocation and an optimal resource allocation problem corresponding to the optimized task offloading problem; An optimal offloading strategy acquisition module: an optimal offloading algorithm is used to solve the task offloading problem with fixed resource allocation, and an optimal offloading strategy is obtained; A problem solving module: the optimal resource allocation includes bandwidth resource allocation, frequency resource allocation and subchannel allocation, so the optimal resource allocation problem corresponding to the optimized task offloading problem is divided into a frequency resource allocation problem, a bandwidth resource and subchannel joint allocation problem, the optimal solution of the frequency resource allocation problem is obtained through the Lagrange dual method, and the optimal resource allocation problem corresponding to the optimized task offloading problem is divided into a fixed subchannel optimal bandwidth allocation problem and an optimized bandwidth allocation optimal subchannel allocation problem, the optimal solution of the fixed subchannel optimal bandwidth allocation problem is obtained through the Lagrange dual method, and the optimized bandwidth allocation optimal subchannel allocation problem is solved through a heuristic subchannel allocation algorithm; An updating module: the step length of iterative updating is set, the Lagrange dual method and the heuristic subchannel allocation algorithm in step four are used, and the bandwidth resource allocation and the subchannel allocation of the user are updated through the information parameters of the tasks and the configuration information of the user; An iteration module: the updating module is repeatedly executed according to the time slot until the system total overhead converges.

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