Distributed task unloading and resource allocation method and system for multi-user multi-MEC wireless network

Abstract

The invention discloses a distributed task unloading and resource allocation method and system for a multi-user multi-MEC wireless network. The method comprises the following steps: S1, initializing; s2, establishing an optimization model; s3, for the task unloading problem with fixed resource allocation, the proposed optimal unloading algorithm is used to solve the task unloading problem, and an optimal unloading strategy is obtained; s4, dividing the optimal resource allocation problem into a frequency resource allocation problem and a bandwidth resource and sub-channel joint allocation problem, solving an optimal solution for frequency resource allocation through a Lagrange duality method, and solving an optimal solution for bandwidth resource and sub-channel joint allocation problem through the Lagrange duality method; the problem is decomposed into a fixed sub-channel optimal bandwidth allocation solving problem and an optimal sub-channel allocation solving problem, the fixed sub-channel optimal bandwidth allocation solving problem is obtained, and meanwhile the optimal sub-channel allocation solving problem is solved through the optimal bandwidth allocation solving problem; s5, updating bandwidth resource allocation and sub-channel allocation of the user; and S6, repeating the step S5 according to the time slot until the total overhead of the system is converged.

Description

Technical Field

[0001] The present invention belongs to the technical field of mobile edge computing networks, and in particular relates to a distributed task offloading and resource allocation method and system for a multi-user multi-MEC wireless network. Background Art

[0002] With the rapid development of mobile applications and the Internet of Things, cloud infrastructure and wireless access networks have been asked to meet ultra-low latency, user experience continuity, and high reliability requirements. These stringent requirements have driven the need for highly localized services at the edge of the network close to end users. Based on this, the concept of mobile edge computing has emerged. Mobile edge computing improves the computing power at the edge of the network by deploying high-performance servers closer to users, solves the problem of limited mobile device resources and excessive cloud computing network load pressure, and can achieve ultra-low latency and ultra-low energy consumption requirements.

[0003] However, due to the communication required between user devices and MEC servers in the uplink wireless channel, task offloading incurs additional overhead in terms of latency and energy consumption. In addition, in systems with a large number of offloading users, the limited computing resources at the MEC server significantly affect the task execution delay. Therefore, offloading decisions and execution resource allocation become key issues in achieving efficient computing offloading. Previously, this problem has been partially solved by optimizing offloading decisions, communication resources or computing resources, but all of them have been focused on systems with a single MEC server. Based on the defects existing in the above-mentioned prior art, the present invention discloses a distributed task offloading and resource allocation method and system for a multi-user multi-MEC wireless network, and the invention relates to a channel allocation algorithm based on the Lagrangian duality method and a heuristic. Summary of the invention

[0004] The present invention discloses a distributed task offloading and resource allocation method and system for a multi-user multi-MEC wireless network. In a wireless network of multi-user multi-MEC servers, the present invention takes the user's offloading decision, bandwidth resources, sub-channel allocation and server computing resources as constraints, minimizes the system overhead (the weighted sum of the total system delay and the total system energy consumption) as the target modeling, and proposes an algorithm for joint computing offloading and resource allocation, which divides the original problem into a task offloading problem with fixed user bandwidth resources, sub-channel allocation and server computing resources and a resource allocation problem with an optimal value function corresponding to the optimized offloading problem. The present invention proposes an optimal offloading algorithm to solve the offloading problem, uses the Lagrangian duality technique to solve the resource allocation problem, and solves the sub-channel allocation problem based on a heuristic sub-channel allocation algorithm. Finally, a distributed approximate optimization algorithm is proposed to solve the global optimal solution.

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

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

[0007] Step 1: Initialization phase: Each node obtains basic configuration information of the network through information exchange;

[0008] Step 2: Establish an optimization model: With the goal of minimizing the total system overhead, a joint optimization model of offloading decision and resource allocation is established based on the task offloading constraints and user resource allocation constraints. 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.

[0009] Step 3: For the task offloading problem with fixed resource allocation, the optimal offloading algorithm is used to solve the task offloading problem and obtain the optimal offloading strategy;

[0010] Step 4: 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 sub-channel allocation. Therefore, 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 sub-channel joint allocation problem. The optimal solution for the frequency resource allocation can be obtained by the Lagrange dual method. For the bandwidth resource and sub-channel joint allocation problem, this problem is decomposed into a fixed sub-channel solution for the optimal bandwidth allocation problem and an optimized bandwidth allocation solution for the optimal sub-channel allocation problem. The Lagrange dual technology is used to obtain the optimal solution for the fixed sub-channel solution for the optimal bandwidth allocation problem. At the same time, the heuristic sub-channel allocation algorithm is used to solve the optimal sub-channel allocation problem for the optimized bandwidth allocation.

[0011] Step 5: Set the step size of the iterative update, and use the Lagrange dual method and heuristic sub-channel allocation algorithm in step 4 to update the user's bandwidth resource allocation and sub-channel allocation through the task information parameters and the user's configuration information;

[0012] Step 6: Repeat step 5 by time slot until the total system overhead converges.

[0013] Furthermore, in step 1, each node obtains basic configuration information of the network through information exchange, 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. Furthermore, the optimization model established in step 2 is:

[0014]

[0015] Where y represents the set of binary offloading decisions of the user, X represents the user subchannel allocation matrix, b represents the set of bandwidth resources allocated to the user by the MEC server, and f represents the set of computing resources allocated to the user by the MEC server. Formula (2) represents the task offloading decision of the user; Formula (3) represents that each task can be executed locally or offloaded to at most one MEC server; Formula (4) represents the selection of subchannel allocation; Formula (5) represents that a user can only use one subchannel; Formula (6) represents that a subchannel can only be allocated to one user; Formula (7) represents that the number of subchannels from the user to each server cannot be greater than the total number of subchannels; Formula (8) represents that the MEC server allocates positive computing resources to each user; Formula (9) represents that the computing resources allocated to the user cannot exceed the maximum computing capacity of the MEC server; 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 the transmission from user u to base station s on subchannel j.

[0016] Furthermore, in order to solve problem P0, the present invention divides the original optimization problem into two sub-problems, that is, decomposing the original optimization problem into a task offloading problem P1 with fixed resource allocation and an optimal resource allocation problem P2 corresponding to the optimized task offloading problem, and by solving the decomposed problem, the optimal solution to the original problem is finally obtained.

[0017] In step 3, in the task offloading problem with fixed resource allocation, the original optimization problem P0 is transformed into problem P1 by fixing the remaining optimization variables except the task offloading decision set y, which is specifically expressed as:

[0018]

[0019] st(2)(3)

[0020] Among them, formula (2) means that each task can be executed locally or offloaded to at most one MEC server; formula (3) represents the selection of subchannel allocation.

[0021] Solve the problem P1 to obtain the optimal unloading strategy y * Substituting into equation (1), since local computing users are not involved in resource allocation, the optimal resource allocation problem P2 corresponding to the optimization task offloading problem is expressed as:

[0022]

[0023] st(4)(5)(6)(7)(8)(9)(10)

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

[0025] Furthermore, in step 3, the optimization model of task offloading with fixed resource allocation is solved: for the task offloading problem with fixed resource allocation, the optimal offloading algorithm is used to solve the task offloading problem and obtain the optimal offloading strategy. Therefore, the set of users in non-overlapping areas within the coverage of adjacent base stations can be expressed as U nc , the user set in the overlapping area within the coverage of adjacent base stations can be expressed as U c , since user {u|u∈U nc} Either the calculation is performed locally or on a single MEC server, so only the cost function calculated locally by the user is required and the cost function calculated by the only MEC server For comparison, if User {u|u∈U nc The computing task of {u|u∈U c}, they need to consider both the need for local computing and the need for selecting MEC servers. The set of optional MEC servers for each overlapping user is {S u |u∈U c}, then the optimization problem of the best MEC offloading selection strategy is as follows:

[0026]

[0027] From formula (10), we can see that the cost function calculated by the MEC server is SNR Therefore, the above problem can be transformed into:

[0028]

[0029] Through the above algorithm, we can find the user {u|u∈U c}Optimal Offload Servers * ,Will and By comparing, we can get the best offloading decision for users. Finally, users who are offloaded to MEC servers are put into the set U mec The user who uninstalls it locally puts it in the collection U loc middle.

[0030] Furthermore, in the step 4, 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 can be noted from formula (13) that the bandwidth allocation b and the subchannel allocation X are coupled with each other, while the computing resource allocation f and the other two variables are decoupled from each other. By using this feature, formula (13) can be decoupled into two independent problems, namely, the bandwidth allocation and subchannel joint allocation problem and the computing resource allocation problem, and these two problems can be solved separately.

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

[0032]

[0033] st(8)(9)

[0034] Among them, formula (8) indicates that the computing resources allocated to users cannot exceed the maximum computing capacity of the MEC server; formula (9) indicates that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server;

[0035] Note that the constraints in (8) and (9) are linear. The objective function in (16) is expressed as g(f us ), by calculating g(f us )’s second-order derivative:

[0036]

[0037] So the objective function is about f us The above problem is a convex optimization problem and can be solved using the Karush-Kuhn-Tucker (KKT) condition. The optimal computing resource allocation for problem P3 is given respectively. and the corresponding optimal objective function g(f * ),as follows:

[0038]

[0039] By optimizing the first and second terms of formula (13), let The joint subchannel allocation and bandwidth allocation optimization problem is specifically expressed as:

[0040]

[0041] st(4)(5)(6)(7)(10)

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

[0043] The joint subchannel allocation and bandwidth allocation problem is very complex because it involves two coupled optimization variables X and b. The optimization problem is decomposed into two sub-problems: subchannel allocation to MEC server users and bandwidth resource allocation. First, the subchannel allocation X offloaded to MEC server users is fixed. * , and then solve the bandwidth resource allocation problem:

[0044]

[0045] st(10)(11)

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

[0047]

[0048] st(10)(11)

[0049] It can be seen that the objective function in equation (23) is a convex function. The constraint of computing bandwidth allocation is linear, so problem P5 is a convex optimization problem, which can also be solved by Lagrangian duality technique, and If the conditions for using KKT are met, the Lagrangian function can be written as:

[0050]

[0051] Finally, we get the optimal bandwidth resource allocation for problem P5 for:

[0052]

[0053] in

[0054] To simplify the channel model, each subchannel can only have one user, and each user can only occupy one subchannel when receiving signals. Therefore, the subchannel allocation problem can be expressed as:

[0055]

[0056] st(4)(5)(6)(7)(11)

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

[0058] Furthermore, in step 4, for the sub-channel allocation problem, the present invention proposes a heuristic sub-channel allocation algorithm to obtain the optimal solution of sub-channel allocation to minimize the total system overhead.

[0059] In this algorithm, the variable Obtained by distributively solving problem P5. Define Φ j (u) is the set of subchannels allocated to user u, is the set of subchannels not allocated to user u, Ω s (j) is the set of users who have been allocated subchannel j within the coverage area of ​​base station s, is the set of users that are not assigned subchannels within the coverage of base station s. The specific steps of the heuristic channel allocation algorithm are:

[0060] Step 4.1: Initialize Φ j (u), Ω s (j) Subchannel allocation matrix X, transmission power p u , Channel Gain

[0061] Step 4.2: Calculate the optimal solution U(X) for initialization subchannel allocation based on the initialization parameters through equation (27) best );

[0062] Step 4.3: Judgement Is it empty? If so, all users have been assigned the optimal subchannel. Otherwise, proceed to step 4.4.

[0063] Step 4.4: Determine the set of subchannels that the user can allocate And find the set by calculating formula (27) The optimal solution of the optimal subchannel allocation scheme U(X temp );

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

[0065] Step 4.6: Return to step 4.3 until Is empty.

[0066] Furthermore, in step 5, the step size of iterative update is set, and the algorithm in S3 and S4 is used to solve the optimal task offloading strategy and the optimal frequency resource allocation through the information parameters of the task and the configuration information of the user, and the bandwidth resource allocation and sub-channel allocation of the user are updated. The specific steps are as follows:

[0067] Step 5.1: Initialize bandwidth resources b, computing resources f, subchannel allocations X, and offloading decisions y for all users.

[0068] Step 5.2: Use the optimal offloading decision algorithm to determine whether the user performs calculations locally or on the MEC server, and express the final offloading decision as y * .

[0069] Step 5.3: Based on the obtained unloading decision y * , the Lagrangian duality technique is used to solve the user set U offloaded to the MEC server mec The optimal computing resource allocation f * .

[0070] Step 5.4: Since the optimization variable subchannel X and bandwidth b are coupled to each other, the optimal bandwidth b is solved by fixing the optimization variable subchannel X and then using the Lagrangian dual method * , then b * Bring in the heuristic channel allocation algorithm to solve the optimal sub-channel allocation X * .

[0071] Step 5.5: Repeat step 5.4 until the absolute value of the difference between the result of the current moment calculated by equation (27) and the result of the previous moment is less than the set threshold. Then the X at the current moment is * and b * is the optimal X * and b * .

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

[0073] The present invention also discloses a distributed task offloading and resource allocation system for a multi-user multi-MEC wireless network, which is used to execute the above method and includes the following modules:

[0074] Initialization module: Each node obtains basic configuration information of the network through information interaction;

[0075] Optimization model building module: With the goal of minimizing the total system overhead, a joint optimization model of offloading decision and resource allocation is established according to the 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;

[0076] Optimal offloading strategy acquisition module: For the task offloading problem with fixed resource allocation, the optimal offloading algorithm is used to solve the task offloading problem and obtain the optimal offloading strategy;

[0077] Problem solving module: 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 sub-channel allocation. Therefore, the optimal resource allocation problem corresponding to the optimization task offloading problem is divided into the frequency resource allocation problem and the bandwidth resource and sub-channel joint allocation problem. The optimal solution of the frequency resource allocation is obtained by the Lagrange dual method. For the bandwidth resource and sub-channel joint allocation problem, this problem is decomposed into the problem of solving the optimal bandwidth allocation problem by fixing the sub-channel and the problem of solving the optimal sub-channel allocation problem by optimizing the bandwidth allocation. The Lagrange dual method is used to obtain the optimal solution of the problem of solving the optimal bandwidth allocation problem by fixing the sub-channel. At the same time, the heuristic sub-channel allocation algorithm is used to solve the problem of solving the optimal sub-channel allocation problem by optimizing the bandwidth allocation.

[0078] Update module: Set the step size of iterative update, use the Lagrange dual method and heuristic sub-channel allocation algorithm in step 4, and update the user's bandwidth resource allocation and sub-channel allocation through the task information parameters and user configuration information;

[0079] Iterative module: The update module is executed repeatedly in time slots until the total system overhead converges.

[0080] The present invention has the following advantages:

[0081] (1) The present invention implements a distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network. Experiments show that the algorithm proposed in the present invention can converge within 10 iterations.

[0082] (2) The most prominent advantage of the present invention is that it divides the original problem into a task offloading problem with fixed users' bandwidth resources, subchannel allocation and server computing resources and a resource allocation problem with an optimal value function corresponding to the optimization offloading problem. The present invention proposes an optimal offloading algorithm to solve the offloading problem, uses the Lagrangian duality technique to solve the resource allocation problem, and solves the subchannel allocation problem based on a heuristic subchannel allocation algorithm. Finally, a distributed approximate optimization algorithm is proposed to solve the global optimal solution, which greatly reduces the computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 The present invention is a flowchart 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 invention.

[0084] Figure 2 This is a system model diagram of multiple users and multiple MEC servers.

[0085] Figure 3 The total overhead of the system changes with the number of iterations under different transmit powers.

[0086] Figure 4 This is a 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 invention. DETAILED DESCRIPTION

[0087] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0088] like Figure 1-2 As shown, this embodiment provides a distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network, including the following steps:

[0089] Step 1, initialization phase: Each node obtains basic configuration information of the network through information exchange, 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.

[0090] This embodiment considers a multi-user, multi-MEC server system, where each cell is equipped with a base station, each base station is equipped with a MEC server, and each user can choose a base station within its coverage to offload computing tasks to the MEC server. For users in overlapping areas within the coverage of the base station, they can choose to offload tasks on any of the MEC servers. The set of users and MEC servers in the system are represented as U = {1, 2, ..., u} and S = {1, 2, ..., s} respectively. This embodiment assumes that each user u∈U has one computing task at a time, represented as V u, which is atomic and cannot be divided into subtasks. Each computation task V u The two parameters {d u ,c u} means, where d u represents the amount of data required for the u-th user to transmit from the local device to the MEC server, in bits, c u represents the number of CPU cycles required for the uth 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 of user u to base station s can be expressed as y us = {0,1}, “0” means the task is executed locally, and “1” means the task is executed on the MEC server. The set of task offloading variables for all users is represented as y = {y us |u∈U,s∈S}.

[0091] Step 2: Establish an optimization model: With the goal of minimizing the total system overhead, a joint optimization model of offloading decision and resource allocation is established based on 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.

[0092] set up represents the local computing power of user u, in CPU cycles / s. Therefore, if user u performs its task locally, the task completion time is expressed as:

[0093]

[0094] In order to calculate the energy consumption of the user device when executing tasks locally, the widely used energy consumption model per computing cycle ε = κf is used. 2 , where κ is the energy coefficient that depends on the chip architecture and f is the CPU frequency. Therefore, when user u executes its task V locally u When the energy consumption of user u is It can be expressed as:

[0095]

[0096] Therefore, the cost function of the user's local calculation can be expressed as

[0097]

[0098] in, and are the weighted parameter values ​​of delay 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 done with 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 uth row of X us represents the channel allocation vector for user u to upload data to server s. Since only one subchannel can be allocated to each user, X us 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 whose tasks are offloaded to server s, and U mec =∪ s∈S U s Represents the set of users whose tasks are offloaded to the MEC server. 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 It is user u who 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 uplink intra-cell interference is well mitigated; however, these users are still affected by 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 the task to base station s is:

[0107]

[0108] The MEC server at each base station can provide computing offload services to multiple users at the same time. The computing resources provided by each MEC server that can be shared among users within the coverage area of ​​the base station are determined by the computing rate f s Denote. The computing resource allocation strategy is defined as f = {f us |u∈U,s∈S}, where f us > 0 is the base station assigned to the slave user u∈U s Unloaded Tasks V u computing resources. Obviously, f us =0,

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

[0110]

[0111] The total delay for user u to offload the task to base station s is:

[0112]

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

[0114]

[0115] in, and are the weighted parameter values ​​of delay and energy consumption respectively, The system overhead function Z is defined by the sum of all users on the local and MEC servers. Then, the joint task offloading and resource allocation problem is formulated as the system overhead minimization problem P0 which can be expressed as:

[0116]

[0117] Where y represents the set of binary offloading decisions of the user, X represents the user subchannel allocation matrix, b represents the set of bandwidth resources allocated to the user by the MEC server, and f represents the set of computing resources allocated to the user by the MEC server. Formula (12) represents the task offloading decision of the user; Formula (13) represents that each task can be executed locally or offloaded to at most one MEC server; Formula (14) represents the selection of subchannel allocation; Formula (15) represents that a user can only use one subchannel; Formula (16) represents that a subchannel can only be allocated to one user; Formula (17) represents that the number of subchannels from the user to each server cannot be greater than the total number of subchannels; Formula (18) represents that the MEC server allocates positive computing resources to each user; Formula (19) represents that the computing resources allocated to the user cannot exceed the maximum computing capacity of the MEC server; Formula (20) represents that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server. Formula (21) represents the signal-to-noise ratio of the transmission from user u to base station s on subchannel 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 solve it directly with traditional optimization methods. In order to solve the problem P0, this paper divides the original optimization problem into two sub-problems, that is, decomposing the original optimization problem into a task offloading problem P1 with fixed resource allocation and an optimal resource allocation problem P2 corresponding to the optimized task offloading problem. By solving the decomposed problems, the optimal solution of the original problem is finally obtained.

[0119] Step 3: In the task offloading problem with fixed resource allocation, by fixing the remaining optimization variables except the task offloading decision set y, the original optimization problem P0 is transformed into problem P1, which is specifically expressed as:

[0120]

[0121] st(12)(13)

[0122] Solve the problem P1 to obtain the optimal unloading strategy y * Substituting into equation (11), the minimized system total overhead is expressed as:

[0123]

[0124] Since local computing users do not involve resource allocation, Equation (23) can be converted into the user cost of offloading to the MEC server. Therefore, the optimal resource allocation problem P2 corresponding to the optimization task offloading problem is expressed as:

[0125]

[0126] st(14)(15)(16)(17)(18)(19)(20)(21)

[0127] Solve the optimization model of task offloading with fixed resource allocation: For the task offloading problem with fixed resource allocation, the optimal offloading algorithm is used to solve the task offloading problem and obtain the optimal offloading strategy. Therefore, the set of users in non-overlapping areas within the coverage of adjacent base stations can be expressed as U nc , the user set in the overlapping area within the coverage of adjacent base stations can be expressed as U c , since user {u|u∈U nc} Either the calculation is performed locally or on a single MEC server, so only the cost function calculated locally by the user is required and the cost function calculated by the only MEC server For comparison, if User {u|u∈U nc The computing task of {u|u∈U c}, they need to consider both the need for local computing and the need for selecting MEC servers. The set of optional MEC servers for each overlapping user is {S u |u∈U c}, then the optimization problem of the best MEC offloading selection strategy is as follows:

[0128]

[0129] From formula (10), we can see that the cost function calculated by the MEC server is SNR Therefore, the above problem can be transformed into:

[0130]

[0131] Through the above algorithm, we can find the user {u|u∈U c}Optimal Offload Servers * ,Will and By comparing, we can get the best offloading decision for users. Finally, users who are offloaded to MEC servers are put into the set U mec The user who uninstalls it locally puts it in the collection U loc middle.

[0132] Step 4: Solve 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 can be noted from formula (24) that the bandwidth allocation b and the subchannel allocation X are mutually coupled, while the computing resource allocation f and the other two variables are decoupled from each other. Using this feature, formula (24) can be decoupled into two independent problems, namely, the bandwidth allocation and subchannel joint allocation problem and the computing resource allocation problem, and these two problems can be solved separately.

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

[0134]

[0135] st(18)(19)

[0136] Note that the constraints in (18) and (19) are linear. The objective function in (27) is expressed as g(f us ), by calculating g(f us )’s second-order derivative:

[0137]

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

[0139]

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

[0141]

[0142] st(4)(5)(6)(7)(20)

[0143] The joint subchannel allocation and bandwidth allocation problem is very complex because it involves two coupled optimization variables X and b. The optimization problem is decomposed into two sub-problems: subchannel allocation to MEC server users and bandwidth resource allocation. First, the subchannel allocation X offloaded to MEC server users is fixed. * , and then solve the bandwidth resource allocation problem:

[0144]

[0145] st(20)(21)

[0146] For the bandwidth allocation problem, since the subchannel allocation is known At the same time, a user can only occupy one sub-channel, so equation (33) can be transformed into:

[0147]

[0148] st(20)(21)

[0149] It can be seen that the objective function in equation (34) is a convex function. The constraint for computing bandwidth allocation is linear, so problem P5 is a convex optimization problem, which can also be solved by the Lagrangian dual technique, and If the conditions for using KKT are met, the Lagrangian function can be written as:

[0150]

[0151] Finally, we get the optimal bandwidth resource allocation for problem P5 for:

[0152]

[0153] in

[0154] To simplify the channel model, each subchannel can only have one user, and each user can only occupy one subchannel when receiving signals. Therefore, the subchannel allocation problem can be expressed as:

[0155]

[0156] st(4)(5)(6)(7)(21)

[0157] For the sub-channel allocation problem, the present invention proposes a heuristic sub-channel allocation algorithm to obtain the optimal solution of sub-channel allocation to minimize the total system overhead.

[0158] In this algorithm, the variable Obtained by distributively solving problem P5. Define Φ j (u) is the set of subchannels allocated to user u, is the set of subchannels not allocated to user u, Ω s (j) is the set of users who have been allocated subchannel j within the coverage area of ​​base station s, is the set of users that are not assigned subchannels within the coverage of base station s. The specific steps of the heuristic channel allocation algorithm are:

[0159] Step 4.1: Initialize 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) for initialization subchannel allocation according to the initialization parameters through equation (38) best );

[0161] Step 4.3: Judgement Is it empty? If so, all users have been assigned subchannels. Otherwise, proceed to step 4.4.

[0162] Step 4.4: Determine the set of subchannels that the user can allocate And find the set by calculating formula (38) The optimal solution U(X temp );

[0163] Step 4.5: If U(X temp )<U(X best ), then 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 5, variable update phase: set the step size of the iterative update, use the algorithms in S3 and S4, and update the user's task offloading strategy, bandwidth resource allocation, frequency resource allocation, and sub-channel allocation through the task information parameters and user configuration information. The specific steps are as follows:

[0166] Step 5.1: Initialize bandwidth resources b, computing resources f, subchannel allocations X, and offloading decisions y for all users.

[0167] Step 5.2: Use the optimal offloading decision algorithm to determine whether the user performs calculations locally or on the MEC server, and express the final offloading decision as y * .

[0168] Step 5.3: Based on the obtained unloading decision y * , the Lagrangian duality technique is used to solve the user set U offloaded to the MEC server mecThe optimal computing resource allocation f * .

[0169] Step 5.4: Since the optimization variable subchannel X and bandwidth b are coupled to each other, the optimal bandwidth b is solved by fixing the optimization variable subchannel X and then using the Lagrangian dual method * , then b * Bring in the heuristic channel allocation algorithm to solve the optimal sub-channel allocation X * .

[0170] Step 5.5: Repeat step 5.4 until the absolute value of the difference between the result of the current moment calculated by equation (27) and the result of the previous moment is less than the set threshold. Then the X at the current moment is * and b * is the optimal X * and b * .

[0171] Step 6: Repeat step 5 according to the time slot until the total system overhead converges. The convergence condition is as follows: the absolute value of the system overhead at the current moment minus the system overhead at the previous moment is less than the set threshold.

[0172] Figure 3 The total system overhead varies with the number of iterations when the transmit power of the user equipment is 18dBm, 20dBm and 22dBm respectively. Figure 3 It can be clearly seen that the algorithm proposed in the present invention can converge within 10 iterations, indicating that the algorithm involved in the present invention has the characteristic of fast convergence. When the transmission power increases, the system overhead gradually increases. This is because the increase in transmission power will affect the increase in transmission energy consumption from the user to the server, which in turn leads to an increase in the total system overhead. When the transmission power is 18dBm and 20dBm respectively, the total system overhead decreases by 21% and 13% respectively compared to 22dBm, so reducing the transmission power helps to reduce the system overhead.

[0173] like Figure 4 As shown, this embodiment discloses a distributed task offloading and resource allocation system for a multi-user multi-MEC wireless network, which is used to execute the above method embodiment, and includes the following modules:

[0174] Initialization module: Each node obtains basic configuration information of the network through information interaction;

[0175] Optimization model building module: With the goal of minimizing the total system overhead, a joint optimization model of offloading decision and resource allocation is established according to the 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;

[0176] Optimal offloading strategy acquisition module: For the task offloading problem with fixed resource allocation, the optimal offloading algorithm is used to solve the task offloading problem and obtain the optimal offloading strategy;

[0177] Problem solving module: 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 sub-channel allocation. Therefore, the optimal resource allocation problem corresponding to the optimization task offloading problem is divided into the frequency resource allocation problem and the bandwidth resource and sub-channel joint allocation problem. The optimal solution of the frequency resource allocation is obtained by the Lagrange dual method. For the bandwidth resource and sub-channel joint allocation problem, this problem is decomposed into the problem of solving the optimal bandwidth allocation problem by fixing the sub-channel and the problem of solving the optimal sub-channel allocation problem by optimizing the bandwidth allocation. The Lagrange dual method is used to obtain the optimal solution of the problem of solving the optimal bandwidth allocation problem by fixing the sub-channel. At the same time, the heuristic sub-channel allocation algorithm is used to solve the problem of solving the optimal sub-channel allocation problem by optimizing the bandwidth allocation.

[0178] Update module: Set the step size of iterative update, use the Lagrange dual method and heuristic sub-channel allocation algorithm in step 4, and update the user's bandwidth resource allocation and sub-channel allocation through the task information parameters and user configuration information;

[0179] Iterative module: The update module is executed repeatedly in time slots until the total system overhead converges.

[0180] For other contents of this embodiment, please refer to the above method embodiment.

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

[0182] The preferred embodiments and principles of the present invention are described in detail above. For those skilled in the art, according to the ideas provided by the present invention, there may be changes in the specific implementation methods, and these changes should also be regarded as the protection scope of the present invention.

Claims

1. A distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network, characterized in that: The method specifically comprises the following steps: Step 1: Initialization phase: Each node obtains basic configuration information of the network through information exchange; Step 2: Establish an optimization model: With the goal of minimizing the total system overhead, a joint optimization model of offloading decision and resource allocation is established according to the 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; Step 3: For the task offloading problem with fixed resource allocation, the optimal offloading algorithm is used to solve the task offloading problem and obtain the optimal offloading strategy; Step 4: 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 sub-channel allocation. Therefore, 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 sub-channel joint allocation problem. For the frequency resource allocation, the optimal solution is obtained by the Lagrange dual method. For the bandwidth resource and sub-channel joint allocation problem, this problem is decomposed into a fixed sub-channel solution to the optimal bandwidth allocation problem and an optimized bandwidth allocation solution to the optimal sub-channel allocation problem. The Lagrange dual method is used to obtain the optimal solution to the fixed sub-channel solution to the optimal bandwidth allocation problem. At the same time, a heuristic sub-channel allocation algorithm is used to solve the optimized bandwidth allocation solution to the optimal sub-channel allocation problem. Step 5: Set the step size of the iterative update, and use the Lagrange dual method and heuristic sub-channel allocation algorithm in step 4 to update the user's bandwidth resource allocation and sub-channel allocation through the task information parameters and the user's configuration information; Step 6: Repeat step 5 according to the time slot until the total system overhead converges.

2. A distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network according to claim 1, characterized in that: In step 1, the basic configuration information includes topology information, transmit power, link distance, task data size of user equipment, local computing resources and MEC computing resources.

3. A distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network according to claim 1 or 2, characterized in that: The optimization model in step 2 is: Where y represents the set of binary offloading decisions of the user, X represents the user subchannel allocation matrix, b represents the set of bandwidth resources allocated to the user by the MEC server, and f represents the set of computing resources allocated to the user by the MEC server; Formula (1) represents the task offloading decision of the user; Formula (2) represents that each task can be executed locally or offloaded to at most one MEC server; Formula (3) represents the selection of subchannel allocation; Formula (4) represents that a user can only use one subchannel; Formula (5) represents that a subchannel can only be allocated to one user; Formula (6) represents that the number of subchannels from the user to each server cannot be greater than the total number of subchannels; Formula (7) represents that the MEC server allocates positive computing resources to 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; Formula (11) represents the signal-to-noise ratio of the transmission from user u to base station s on subchannel j.

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

5. The distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network according to claim 4, characterized in that: Step 3: Solve the task offloading problem with fixed resource allocation. For the task offloading problem with fixed resource allocation, use the optimal offloading algorithm to solve the task offloading problem and obtain the optimal offloading strategy. For the user set in the non-overlapping area within the coverage of adjacent base stations, it is represented as U nc , the set of users in the overlapping area covered by adjacent base stations is represented as U c , since user {u|u∈U nc }Calculation is performed locally or on a single MEC server, so only the cost function calculated locally by the user is needed and the cost function calculated by the only MEC server For comparison, if User {u|u∈U nc The computing task of {u|u∈U c }, considering both local computing and selection of MEC servers, the set of optional MEC servers for each overlapping user is {S u |u∈U c }, then the optimal MEC offloading selection strategy optimization problem is as follows: The cost function calculated by the MEC server can be seen from formula (10): SNR Therefore, the above problem is transformed into: Find user {u|u∈U c }Optimal Offload Servers * ,Will and Compare and get the best offloading decision for users; put users who offload to MEC servers into set U mec The user who uninstalls it locally puts it in the collection U loc middle.

6. A distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network according to claim 5, characterized in that: In step 4, 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 can be seen from formula (13) that the bandwidth allocation b and the subchannel allocation X are mutually coupled, while the computing resource allocation f and the other two variables are decoupled from each other. Using 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 these two problems are solved separately; In the computing resource allocation problem, by optimizing the third term of formula (13), the computing resource allocation problem can be expressed as: st(8)(9) Among them, formula (8) indicates that the computing resources allocated to users cannot exceed the maximum computing capacity of the MEC server; formula (9) indicates that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server; The constraints in (8) and (9) are linear; the objective function in (16) is expressed as g(f us ), by calculating g(f us )’s second-order derivative: Therefore, the objective function is about f us Convex function, P3 problem is a convex optimization problem, which is solved by KKT condition; the optimal computing resource allocation of problem P3 is given respectively and the corresponding optimal objective function g(f * ),as follows: By optimizing the first and second terms of formula (13), let The joint subchannel allocation and bandwidth allocation optimization problem is specifically expressed as: st(4)(5)(6)(7)(10) Among them, formula (4) means that a user can only use one subchannel; formula (5) means that a subchannel can only be allocated to one user; formula (6) means that the number of subchannels from a user to each server cannot be greater than the total number of subchannels; formula (7) means that the MEC server allocates positive computing resources to each user; formula (10) means that the bandwidth resources of each task cannot exceed the total bandwidth resources of each MEC server; Among them, X and b are two coupled optimization variables; the optimization problem is decomposed into two sub-problems: sub-channel allocation to MEC server users and bandwidth resource allocation; the sub-channel allocation X offloaded to MEC server users is fixed. * , solve the bandwidth resource allocation problem: st(10)(11) For the bandwidth resource allocation problem, it is known that the subchannel allocation At the same time, a user can only occupy one sub-channel, so equation (22) is transformed into: st(10)(11) Among them, formula (10) indicates 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 (23) is a convex function; the constraint for computing bandwidth allocation is linear, so problem P5 is a convex optimization problem, which is obtained by the Lagrangian dual method, and If the conditions for using KKT are met, the Lagrangian function can be written as: Get the optimal bandwidth resource allocation for problem P5 for: in, It is limited that there can be only one user in each subchannel, and each user can only occupy one subchannel when receiving signals; therefore, the subchannel allocation problem is expressed as: st(4)(5)(6)(7)(11) Among them, formula (4) means that a user can only use one subchannel; formula (5) means that a subchannel can only be assigned to one user; formula (6) means that the number of subchannels from the user to each server cannot be greater than the total number of subchannels; formula (7) means that the MEC server allocates positive computing resources to each user; formula (11) means the signal-to-noise ratio of the transmission from user u to base station s on subchannel j.

7. A distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network according to claim 6, characterized in that: In step 4, for the subchannel allocation problem, a heuristic subchannel allocation algorithm is used to obtain the optimal solution for subchannel allocation. In the heuristic subchannel allocation algorithm, the variable Obtained by distributively solving problem P5; define Φ j (u) is the set of subchannels allocated to user u, is the set of subchannels not allocated to user u, Ω s (j) is the set of users that have been allocated the optimal subchannel j within the coverage area of ​​base station s, is a set of users that are not allocated the optimal subchannel within the coverage of base station s; the specific steps of the heuristic channel allocation algorithm are: Step 4.1: Initialize 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) for initialization subchannel allocation based on the initialization parameters through equation (27) best ); Step 4.3: Judgement Is it empty? If so, all users have been assigned the optimal subchannel. Otherwise, go to step 4.

4. Step 4.4: Determine the set of subchannels that the user can allocate And find the set by calculating formula (27) The optimal solution of the optimal subchannel allocation scheme U(X temp ); Step 4.5: If U(X temp )<U(X best ), then update the set Φ j (u) and the subchannel allocation table, and let U(X best )=U(X temp ); Step 4.6: Return to step 4.3 until Is empty.

8. The distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network according to claim 7, characterized in that: Step 5 The specific steps are as follows: Step 5.1: Initialize bandwidth resources b, computing resources f, subchannel allocation X, and offloading decision y for all users; Step 5.2: Use the optimal offloading decision algorithm to determine whether the user performs computation locally or on the MEC server, and represent the final offloading decision as y * ; Step 5.3: Based on the obtained unloading decision y * , the user set U offloaded to the MEC server is solved by the Lagrangian dual method mec The optimal computing resource allocation f * ; Step 5.4: Since the optimization variable subchannel X and bandwidth b are coupled to each other, the Lagrangian dual method is used to solve the optimal bandwidth b by fixing the optimization variable subchannel X. * , then b * Bring in the heuristic channel allocation algorithm to solve the optimal sub-channel allocation X * ; Step 5.5: Repeat step 5.4 until the absolute value of the difference between the result of the current moment calculated by equation (27) and the result of the previous moment is less than the set threshold. Then the X at the current moment is * and b * is the optimal X * and b * .

9. The distributed task offloading and resource allocation method for a multi-user multi-MEC wireless network according to claim 1, characterized in that: In step six, the convergence condition is as follows: the absolute value of the system overhead at the current moment minus the system overhead at the previous moment is less than a set threshold.

10. A distributed task offloading and resource allocation system for a multi-user multi-MEC wireless network, used to execute the method according to any one of claims 1 to 9, characterized in that: Includes the following modules: Initialization module: Each node obtains basic configuration information of the network through information interaction; Optimization model building module: With the goal of minimizing the total system overhead, a joint optimization model of offloading decision and resource allocation is established according to the 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; Optimal offloading strategy acquisition module: For the task offloading problem with fixed resource allocation, the optimal offloading algorithm is used to solve the task offloading problem and obtain the optimal offloading strategy; Problem solving module: 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 sub-channel allocation. Therefore, the optimal resource allocation problem corresponding to the optimization task offloading problem is divided into the frequency resource allocation problem and the bandwidth resource and sub-channel joint allocation problem. The optimal solution of the frequency resource allocation is obtained by the Lagrange dual method. For the bandwidth resource and sub-channel joint allocation problem, this problem is decomposed into the problem of solving the optimal bandwidth allocation problem by fixing the sub-channel and the problem of solving the optimal sub-channel allocation problem by optimizing the bandwidth allocation. The Lagrange dual method is used to obtain the optimal solution of the problem of solving the optimal bandwidth allocation problem by fixing the sub-channel. At the same time, the heuristic sub-channel allocation algorithm is used to solve the problem of solving the optimal sub-channel allocation problem by optimizing the bandwidth allocation. Update module: Set the step size of iterative update, use the Lagrange dual method and heuristic sub-channel allocation algorithm in step 4, and update the user's bandwidth resource allocation and sub-channel allocation through the task information parameters and user configuration information; Iterative module: The update module is executed repeatedly in time slots until the total system overhead converges.

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