A collaborative task offloading method based on alternating direction multiplier method in intelligent video surveillance system

Abstract

The present invention relates to a collaborative task unloading method based on an alternating direction multiplier method in an intelligent video surveillance system, and belongs to the technical field of task unloading. The method first considers the vertical collaboration between local devices, edge servers and cloud centers, as well as the horizontal collaboration between edge servers, and designs a three-layer video processing computing architecture; then, based on the three-layer video processing computing architecture, a wired communication model is established, and a computing model for the device task processing process is established based on queuing theory; then, an optimization problem of minimizing task processing time is formulated, and the binary variable product terms in the optimization problem are converted based on the reconstruction linearization technology; finally, based on the alternating direction multiplier method and the convex difference programming method, the converted optimization problem is solved, and a task unloading decision plan is obtained; compared with other unloading algorithms, the method can make full use of system resources and effectively reduce task processing time.

Description

Technical Field

[0001] The invention relates to a collaborative task unloading method based on an alternating direction multiplier method in an intelligent video monitoring system, belonging to the technical field of task unloading. Background Art

[0002] In recent years, the improvement of camera performance has affected the development of video surveillance, mobile robots, quality control and other fields. According to a study by Seagate Technology LLC, by 2023, the amount of data generated by global video surveillance systems will reach 35,000PB per day, which poses a huge challenge to the system in handling complex computing tasks.

[0003] Due to the needs of video surveillance applications, cameras are designed as intelligent devices with certain computing capabilities, which can capture facial images from a steady stream of video data and perform face recognition tasks. However, when the facial image is too complex, the camera with limited computing resources cannot handle the computational tasks with high complexity. In addition, using only cameras to meet the computing requirements will make the deployment cost of the system very high. One solution is to offload the computing tasks to the cloud center, because the cloud center has sufficient computing resources to cope with various complex task scenarios. However, in general, the distance between the cloud center and the camera is very far, which is not suitable for computing-intensive tasks that require low latency. Furthermore, the transmission of a large amount of data in the network will cause network congestion, and the huge transmission delay cannot be accepted by users.

[0004] In order to improve the real-time performance of video surveillance systems and reduce the overhead of network transmission, cloud computing-based technologies have been replaced by edge computing. Since the distance between the camera and the edge server is short, the computing tasks can be processed by the camera or the edge server, which effectively reduces the transmission delay from the camera to the cloud center. Nowadays, the camera-edge-cloud three-layer architecture has been regarded as an effective video surveillance system architecture for solving large-scale video analysis tasks. Among them, an edge server is responsible for processing computing tasks from multiple cameras connected to it. Intuitively, low-latency tasks can be processed on the local camera or offloaded to a nearby edge server to obtain a smaller transmission delay. Computationally sensitive tasks can be offloaded to a cloud center with sufficient computing resources to obtain higher accuracy. The three-layer computing architecture provides devices with multiple offloading options, and different offloading decisions largely affect system performance. Therefore, the correct offloading decision is crucial to the performance improvement of video surveillance systems.

[0005] However, there are still many deficiencies in the existing task offloading methods in three-layer computing networks. Most of the work mainly emphasizes the vertical collaboration across layers, without considering the horizontal collaboration between edge servers. Among them, each edge server is regarded as an isolated computing node, which processes the received tasks independently. However, it can be noted that some edge servers are overloaded and have a long delay in processing tasks, while other edge servers are lightly loaded and have a serious surplus of computing resources. Therefore, the horizontal collaboration between edge servers enables those busy edge nodes to forward their tasks to edge nodes with surplus computing resources, thereby balancing the computing load and improving the resource utilization of the system. In addition, some work mainly studies the horizontal collaboration between edge servers, while ignoring the vertical collaboration between local devices, edge servers, and cloud centers. Summary of the invention

[0006] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a collaborative task offloading method based on the alternating direction multiplier method in an intelligent video surveillance system, which takes into account the vertical collaboration among local devices, edge servers and cloud centers, as well as the horizontal collaboration among edge servers, and makes full use of system resources to maximize the optimization of task processing time.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] S1. Considering the vertical collaboration between local devices, edge servers and cloud centers, as well as the horizontal collaboration between edge servers, a three-layer video processing computing architecture is established;

[0009] S2. Based on the three-layer video processing computing architecture, a wired communication model is established, and an M / M / 1 queuing computing model is established for the device task processing process based on queuing theory;

[0010] S3, formulating an optimization problem for minimizing task processing time based on the communication model and the computing model, and transforming binary variable product terms in the optimization problem based on a reconstruction linearization technique;

[0011] S4. Based on the alternating direction multiplier method and convex difference programming method, the converted optimization problem is solved and the task offloading decision plan is obtained.

[0012] The beneficial effects of the present invention are as follows: based on a three-layer video processing computing architecture, the proximal service advantages of edge computing are utilized to pre-process large-scale monitoring data on local devices or edge servers, thereby realizing the system's fastest response to task requests; utilizing a wired communication model and an M / M / 1 queuing model, an optimization problem for minimizing system delay is established, and a reconstruction linearization technique is used to transform the non-convex objective function in the optimization problem into a convex function, which is more conducive to solving; by adopting a distributed parallel optimization algorithm - the alternating direction multiplier method, and using a successive convex approximation algorithm to update the global unloading decision variables, the unloading position of the video analysis task is obtained, thereby realizing system load balancing and reducing system delay. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0014] Figure 1 This is a flow chart of a collaborative task unloading method based on an alternating direction multiplier method in an intelligent video surveillance system according to an embodiment of the present invention;

[0015] Figure 2 The three-layer video processing computing architecture system model in step S1 of the embodiment of the present invention;

[0016] Figure 3 This is a comparison chart of task processing time of several solutions under different numbers of edge servers in step S4 of an embodiment of the present invention;

[0017] Figure 4 This is a comparison chart of task processing time of several solutions in different computing scenarios in step S4 of an embodiment of the present invention;

[0018] Figure 5 This is a comparison chart of task processing time of several solutions under different local computing capabilities of devices in step S4 of an embodiment of the present invention;

[0019] Figure 6 The present invention is a comparison chart of task processing time of several schemes under different edge server computing capabilities in step S4 of the embodiment. DETAILED DESCRIPTION

[0020] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0021] Figure 1FIG. 1 is a flow chart of a collaborative task unloading method based on an alternating direction multiplier method in an intelligent video surveillance system according to an embodiment of the present invention. Figure 1 As shown, the method includes:

[0022] S1. Considering the vertical collaboration between local devices, edge servers and cloud centers, as well as the horizontal collaboration between edge servers, a three-layer video processing computing architecture is established;

[0023] S2. Based on the three-layer video processing computing architecture, a wired communication model is established, and an M / M / 1 queuing computing model is established for the device task processing process based on queuing theory;

[0024] S3, formulating an optimization problem for minimizing task processing time based on the communication model and the computing model, and transforming binary variable product terms in the optimization problem based on a reconstruction linearization technique;

[0025] S4. Based on the alternating direction multiplier method and convex difference programming method, the converted optimization problem is solved and the task offloading decision plan is obtained.

[0026] The three-layer video processing computing architecture system model described in the present invention is as follows Figure 2 As shown, the device layer consists of a set of monitoring devices, and the device set is represented as The edge layer consists of a set of edge servers. The edge server set is represented as The cloud layer consists of a cloud center CS.

[0027] equipment The computational tasks generated in unit time are expressed as Where L k represents the task data size, δ k represents the computing resources required to process the task, Represents a delay constraint.

[0028] Use x k ,y k,m ,z k ∈{0,1} represents the task offloading decision of device k. If device k processes the computing task locally, then x k =1, otherwise x k = 0. If device k offloads the task to edge server m, then y k,m =1, otherwise y k,m = 0. If device k offloads the task to the cloud center CS, then z k =1, otherwise z k =0.

[0029] The communication model is introduced below:

[0030] In a dedicated video surveillance network, bandwidth is often sufficient, so the queuing delay of packets in the router is not considered. At the same time, for simplicity, the processing delay of packets in the router is ignored. However, during the transmission process, the task will be affected by the rate at which the router sends packets and the propagation delay of the wired link. Therefore, the transmission delay of the task offloaded from device k to the edge server or cloud center is expressed as follows:

[0031]

[0032] Among them, τ k,m represents the transmission delay from device k to edge server m, m k represents the index of the edge server associated with device k, Indicates edge server m k The task migration delay between the edge server m, and They represent the offloading of tasks from device k to edge server m. k The number of hops and edge servers m k The number of hops that the migration task passes through, d p represents the propagation delay of the wired link, P s Indicates the packet size, P o represents the packet overhead, R d Indicates the data rate sent by the router. represents the ceiling function; Represents a collection of devices; represents the set of edge servers; {CS} represents the set of cloud center CSs;

[0033] The task calculation model is introduced below:

[0034] For equipment λ k =x k δ k Represents its task arrival rate. Based on the M / M / 1 queuing model and the computing power μ of device k k , the average waiting delay of tasks in device k is expressed as follows:

[0035]

[0036] For edge servers Represents its task arrival rate. Based on the M / M / 1 model, and the computing power μ of edge server m m , the average waiting delay of the task offloaded by device k in edge server m is expressed as follows:

[0037]

[0038] For Cloud Center CS, Represents its task arrival rate. Based on the M / M / 1 model and the computing power of the cloud center CS μ CS , the average waiting delay of the task offloaded by device k in the cloud center CS is expressed as follows:

[0039]

[0040] The optimization goal is to minimize the task processing time, including:

[0041] For each device The generated computing tasks have the following processing time:

[0042]

[0043] Then the computational task offloading optimization problem is formulated to minimize the total task processing time, which is expressed as follows:

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] Where, f represents the frame rate of the surveillance video stream, δ c represents the computing resources required to detect a frame of image, δ represents the same computing resources for recognizing a single face. represents the average arrival rate of tasks for device k, Π k ={x k ,y k,1 ,y k,2 ,…,y k,M ,z k} represents the task offloading decision vector of device k, represents the task offloading decision vector of all devices; Formula (6a) indicates that the processing time of the task generated by device k cannot exceed the task deadline Equations (6b), (6c) and (6d) represent the computing resource constraints of the device, edge server and cloud center respectively; Equations (6e) and (6f) indicate that the task of device k is executed at one and only one location.

[0052] Then, the optimization problem is transformed based on the reconstruction linearization technique, including:

[0053] Since the objective function and constraints in problem P1 both contain product terms of binary variables, the objective function and feasible set are non-convex. Therefore, we define two auxiliary variables: and And based on the reconstruction linearization technology, the variables are transformed and expressed as follows:

[0054]

[0055]

[0056] Therefore, formula (6) is rewritten as follows:

[0057]

[0058] Among them, G represents the auxiliary variable corresponding to all devices offloading tasks to the edge server, V represents the auxiliary variable corresponding to all devices offloading tasks to the cloud center CS,

[0059] Formula (6a) is converted to:

[0060]

[0061] Problem P1 is transformed into:

[0062]

[0063] The following describes the distributed offloading algorithm, including:

[0064] definition and x k ,y k,m and z k A local copy of

[0065]

[0066] Formula (6e) can be rewritten as:

[0067]

[0068] Problem P2 is transformed into:

[0069]

[0070] The augmented Lagrangian function has the following representation:

[0071]

[0072] in and They act on the global variable x respectively. k ,y k,m and z k Convergent Lagrange multiplier. ρ>0 is the augmented Lagrange multiplier, which can control the convergence performance of ADMM.

[0073] The ADMM algorithm is used to solve problem P3, which is divided into global variable update, local variable update and dual variable update.

[0074] Global variable updates include:

[0075] Solve the following optimization problem to update the global variables {Π,G,V}:

[0076]

[0077] Where [t] represents the number of iterations, A vector representing local variables for all devices.

[0078] Problem P4 is decomposed into the following three independent sub-problems:

[0079]

[0080] in, Represents the local computation decision vector of the device connected to the edge server m.

[0081]

[0082] in, represents the task migration decision vector of the device connected to the edge server m,

[0083]

[0084] in, It is represented as the decision vector for offloading device tasks to the cloud center.

[0085] For subproblem P1', relax the binary variables in P1' into continuous variables and rewrite the problem as:

[0086]

[0087] in, ζ is the penalty parameter. Therefore, problem P5 is a typical convex difference programming problem, which can be solved using the successive convex approximation algorithm. The specific algorithm is as follows:

[0088]

[0089] For subproblems P2' and P3', since their objective functions and constraints are similar to those of subproblem P1', they can also be transformed into convex difference programming problems and then solved by the successive convex approximation algorithm.

[0090] Local variable updates include:

[0091] After updating the global variables in the (t+1)th iteration, solve the following optimization problem to update the local variables

[0092]

[0093] Among them, the function The following are indicated:

[0094]

[0095] The optimal solution is given by the following formula:

[0096]

[0097]

[0098]

[0099] The dual variable updates include:

[0100] After obtaining the global and local variables, update the dual variables by the following formula:

[0101]

[0102]

[0103]

[0104] The superscript [t] indicates the tth iteration, and the superscript [t+1] indicates the t+1th iteration. Indicates that the global variable x is applied at the t+1th iteration k Convergent multipliers; Indicates that the tth iteration acts on the global variable x k Convergent multipliers; represents the task offloading decision of device k at the t+1th iteration, represents the local copy of the task offloading decision of device k at the t+1th iteration, Indicates that the global variable y is applied at the t+1th iteration k,m Convergent multipliers, Indicates that the tth iteration acts on the global variable y k,m Convergent multipliers, represents the task offloading decision of device k to offload the task to edge server m at the t+1th iteration, represents the local copy of the task offloading decision of device k to offload the task to edge server m at the t+1th iteration, Indicates that the global variable z is applied at the t+1th iteration k Convergent multipliers, Indicates that the tth iteration acts on the global variable z k Convergent multipliers, represents the task offloading decision of device k to offload the task to the cloud center CS at the t+1th iteration, It indicates that at the t+1th iteration, device k offloads the task to the local copy of the task offloading decision of the cloud center CS.

[0105] In summary, the collaborative task offloading algorithm based on the alternating direction multiplier method first decomposes the optimization problem into several sub-problems so that the global variables can be updated in parallel by the edge server and the cloud center in each iteration. Then, the local variables and dual variables are updated in turn to achieve the convergence of the global variables. After the alternating updates of these three steps, an approximate solution to the original problem can be obtained after a finite number of iterations. The specific algorithm is as follows:

[0106]

[0107]

[0108] Next, the effectiveness of the collaborative task offloading method based on the alternating direction multiplier method proposed in the present invention will be verified in combination with specific simulation results.

[0109] Figure 3 A comparison chart of task processing time for several solutions under different numbers of edge servers is given, with a total of 40 monitoring devices. It can be seen that with the increase in the number of edge servers, except for the cloud computing solution, the task processing time of other solutions is getting shorter and shorter. However, the performance improvement of the edge-end collaboration and vertical collaboration solutions is very small. This is because although the number of edge servers has increased, the pressure on the overloaded edge servers has not been reduced, and the performance has not been well improved. The solution proposed in the present invention reduces the load pressure of the edge servers through horizontal collaboration between edge servers, so the processing time of tasks on the edge servers is getting shorter and shorter, and the performance is effectively improved.

[0110] Figure 4 A comparison chart of task processing time of several schemes under different computing scenarios is given. Among them, the task arrival rate of scenario one is [0,30], the task arrival rate of scenario two is [30,45], the task arrival rate of scenario three is [45,60], the task arrival rate of scenario four is [60,90], and the task arrival rate of scenario five is [90,120]. It can be seen that the larger the amount of calculation, the longer the task processing time. When the amount of calculation is small, the task calculation delay is much smaller than the unloading delay of remote transmission to the cloud center. Therefore, compared with the cloud center, the task is more likely to be unloaded to the edge server for processing, which makes the load balancing of the edge layer more important. With the increase of the amount of calculation, the proportion of task calculation delay in the task processing time gradually increases, resulting in more tasks being unloaded to the cloud center for processing, reducing the migration efficiency of tasks between edge servers, and gradually narrowing the gap between the scheme proposed by the present invention and the vertical collaboration scheme. In addition, the increase in the amount of calculation causes all tasks in the edge collaboration scheme to be calculated on the edge server, which makes the load of the edge server too large and the task processing time gradually higher than other schemes.

[0111] Figure 5 A comparison chart of task processing time of several schemes under different local computing power of devices is given. It can be observed that the task processing time decreases with the increase of local computing power. Among them, the performance of the edge-end collaboration scheme gradually outperforms cloud computing. This is because in cloud computing, the tasks of some devices in the system may have a large amount of calculation. Although the computing power of the local device has increased, it is still insufficient to process. Therefore, the task still needs to be unloaded to the cloud center with ultra-high delay. However, with the increase of local computing power, tasks are more likely to be processed locally, which reduces the load of the edge server. Therefore, the computing time of the task on the edge server is getting shorter and shorter, and ultra-high transmission delay is not required. In addition, since the tasks are concentrated in the device layer and the edge layer, they will not be unloaded to the cloud center. Therefore, the performance of the vertical collaboration scheme is ultimately consistent with the edge scheme. Finally, with the improvement of local computing power, the performance gap between the scheme proposed by the present invention and the vertical collaboration scheme gradually narrows. This is because the device is more likely to process tasks locally, and will not offload tasks to the edge server, reducing the necessity of collaboration between edge servers.

[0112] Figure 6A comparison chart of task processing time for several solutions under different edge server computing power is given. It can be seen that, except for the cloud computing solution, the greater the computing power of the edge server, the shorter the task processing time. Because cloud computing does not use edge servers, changes in the computing power of edge servers have no effect on this solution. In addition, the task processing time of the solution proposed in the present invention is shorter than the other two solutions. This is because the horizontal collaboration between edge servers can balance the computing load of the edge layer, and each task can obtain sufficient computing resources, thereby reducing the task processing time. As computing power increases, the vertical collaboration solution gradually converges to the edge collaboration solution, because tasks are offloaded to the edge server for processing to obtain shorter processing time.

[0113] A person skilled in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing the relevant hardware through a program, and the program can be stored in a computer-readable storage medium, which can include: ROM, RAM, disk or CD, etc.

[0114] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A collaborative task unloading method based on alternating direction multiplier method in an intelligent video surveillance system, characterized in that: The method comprises the following steps: S1. Considering the vertical collaboration among local devices, edge servers and cloud centers, and the horizontal collaboration among edge servers, a three-layer video processing computing architecture is established; the three-layer video processing computing architecture includes a device layer, an edge layer and a cloud layer, as follows: the device layer includes a group of monitoring devices, and the device set is represented as The edge layer includes a set of edge servers. The edge server set is represented as The cloud layer includes a cloud center CS; the equipment The computational tasks generated in unit time are expressed as Where L k represents the task data size, δ k represents the computing resources required to process the task, Indicates delay constraint; x k ,y k,m ,z k ∈{0,1} represents the task offloading decision of device k; if device k processes the computing task locally, then x k =1, otherwise x k = 0; if device k offloads the task to edge server m, then y k,m =1, otherwise y k,m = 0; if device k offloads the task to the cloud center CS, then z k =1, otherwise z k =0; S2. Based on the three-layer video processing computing architecture, a wired communication model is established, and an M / M / 1 queuing computing model is established for the device task processing process based on queuing theory; the communication model includes ignoring the processing delay and queuing delay of the data packet in the router, considering the delay of the router sending the data packet and the propagation delay of the wired link, and obtaining the transmission delay representation of the device k offloading task to the edge server or cloud center: Among them, τ k,m represents the transmission delay from the offload task of device k to the edge server m, Indicates that device k offloads tasks to edge server m k The transmission delay, m k represents the index of the edge server associated with device k, Indicates edge server m k The task migration delay between the edge server m, and They represent the offloading of tasks from device k to edge server m. k The number of hops and edge servers m k The number of hops that the migration task passes through, d p represents the propagation delay of the wired link, P s Indicates the packet size, P o represents the packet overhead, R d Indicates the data rate sent by the router. represents the ceiling function; {CS} represents the cloud center CS set; The calculation model includes: For equipment Based on the M / M / 1 queuing model, the average waiting delay of tasks in device k is expressed as: Among them, λ k =x k δ k represents its task arrival rate; μ k Indicates the computing capability of device k; For edge servers Based on the M / M / 1 model, the average waiting delay of the task offloaded by device k in edge server m is expressed as: in, represents its task arrival rate; μ m represents the computing power of edge server m; For the cloud center CS, based on the M / M / 1 model, the average waiting delay of the task offloaded by device k in the cloud center CS is expressed as: in, represents its task arrival rate; μ CS Indicates the computing power of the cloud center CS; S3, formulating an optimization problem for minimizing task processing time based on the communication model and the computing model, and transforming binary variable product terms in the optimization problem based on a reconstruction linearization technique; Optimization problems include: For each device The generated computing task, its task processing time is expressed as: The computational task offloading optimization problem is formulated to minimize the total task processing time, which is expressed as follows: Among them, P1 represents the optimization problem of minimizing the task processing time; f represents the frame rate of the monitoring video stream, δ c represents the computing resources required to detect a frame of image, δ represents the same computing resources for recognizing a single face. represents the average arrival rate of tasks for device k, Π k ={x k ,y k,1 ,y k,2 ,...,y k,M ,z k } represents the task offloading decision vector of device k, represents the task offloading decision vector of all devices; Formula (6a) indicates that the processing time of the task generated by device k cannot exceed the task deadline Formulas (6b), (6c) and (6d) represent the computing resource constraints of the device, edge server and cloud center respectively; Formulas (6e) and (6f) indicate that the task of device k is executed at one and only one location; The transformation process of the optimization problem includes: Define two auxiliary variables and And based on the reconstruction linearization technology, the variables are transformed and expressed as follows: Therefore, formula (6) is rewritten as follows: in, and Formula (6a) is converted to: Problem P1 is transformed into: Among them, P2 represents the optimization problem after transformation; S4. Based on the alternating direction multiplier method and convex difference programming method, solve the converted optimization problem and obtain the task offloading decision plan; Distributed offloading algorithms include: definition and x k ,y k,m and z k A local copy of Formula (6e) can be rewritten as: Problem P2 is transformed into: The augmented Lagrangian function has the following representation: in and They act on the global variable x respectively. k ,y k,m and z k Convergent Lagrange multiplier; ρ>0 is the augmented Lagrange multiplier; The ADMM algorithm is used to solve problem P3, which is divided into global variable update, local variable update and dual variable update; Based on the alternating direction multiplier method and convex difference programming method, the converted optimization problem is solved and the task offloading decision plan is obtained, which includes first decomposing the converted optimization problem into several sub-problems, and secondly, updating the global variables in parallel by the edge server and the cloud center in each iteration; then, updating the local variables and the dual variables in turn to achieve the convergence of the global variables; after the alternating updates of these three steps, after a finite number of iterations, the approximate solution of the original optimization problem is obtained, and the corresponding task offloading decision plan is determined; Global variable updates include: Solve the following optimization problem to update the global variables {Π,G,V}: The superscript [t] indicates the number of iterations. A vector of local variables representing all devices; Problem P4 is decomposed into the following three independent sub-problems: in, represents the local computation decision vector of the device connected to the edge server m; in, represents the task migration decision vector of the device connected to the edge server m, in, It is represented as the decision vector for offloading device tasks to the cloud center. For subproblems P1', P2' and P3', the successive convex approximation algorithm is used to solve them; for subproblem P1', the binary variables are relaxed to continuous variables and transformed into a convex difference programming problem: in, ζ is the penalty parameter; Local variable updates include: After updating the global variables in the (t+1)th iteration, solve the following optimization problem to update the local variables Among them, the function The following are indicated: The optimal solution is given by the following formula: The dual variable updates include: After obtaining the global and local variables, update the dual variables by the following formula: The superscript [t+1] indicates the number of iterations (t+1). Indicates that the global variable x is applied at the t+1th iteration k Convergent multipliers; Indicates that the tth iteration acts on the global variable x k Convergent multipliers; represents the task offloading decision of device k at the t+1th iteration, represents the local copy of the task offloading decision of device k at the t+1th iteration, Indicates that the global variable y is applied at the t+1th iteration k,m Convergent multipliers, Indicates that the tth iteration acts on the global variable y k,m Convergent multipliers, represents the task offloading decision of device k to offload the task to edge server m at the t+1th iteration, represents the local copy of the task offloading decision of device k to offload the task to edge server m at the t+1th iteration, Indicates that the global variable z is applied at the t+1th iteration k Convergent multipliers, Indicates that the tth iteration acts on the global variable z k Convergent multipliers, represents the task offloading decision of device k to offload the task to the cloud center CS at the t+1th iteration, It indicates that at the t+1th iteration, device k offloads the task to the local copy of the task offloading decision of the cloud center CS.

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