Game-theoretic approach for joint optimization of offloading decision and resource allocation in cloud-edge collaborative computing

Abstract

The present invention discloses a game method for the joint optimization of offloading decisions and resource allocation in cloud-edge collaborative computing, and the steps are: constructing a cloud-edge collaborative computing environment model; defining a performance model of a cloud-edge collaborative computing platform; establishing a multi-constraint optimization problem with task offloading ratio and maximum configuration resources of edge servers as constraints, and response time of user equipment and edge servers as optimization targets; solving the optimization problem according to Lagrange multiplier method, KKT condition and numerical method, and finding the optimal computing offloading strategy of user equipment, the optimal computing resource configuration of edge servers and the optimal computing offloading strategy; using game theory methods to solve the joint optimization problem of computing offloading and resource allocation, so as to stabilize a fiercely competitive cloud-edge collaborative computing environment and finally reach a Nash equilibrium state; the overall performance of the cloud-edge collaborative computing system can be improved, and the average task response time of user equipment and edge servers can be optimized at the same time.

Description

Technical Field

[0001] The present invention belongs to the field of mobile communication technology, and in particular relates to a game method for joint optimization of offloading decisions and resource allocation in cloud-edge collaborative computing. Background Art

[0002] With the development of mobile communication technology and the popularity of smart terminals, various mobile applications are widely used in social, business transactions and modern entertainment activities. The limitations of mobile devices in terms of space, weight, battery capacity and heat dissipation have led to restrictions on their computing power, communication resources, storage space and battery life. It is a huge challenge to process computationally intensive and delay-sensitive applications in a short time. These problems seriously affect the operating efficiency of applications on user devices and the user experience.

[0003] In this context, multi-access edge computing and computation offloading technologies have been proposed as mainstream computing paradigms. Multi-access edge computing refers to providing low-latency and high-bandwidth network services to user equipment (UEs) by deploying edge servers (also known as mobile edge clouds, MECs) at the edge of mobile networks, effectively solving the problem of high-latency communication. As one of the key technologies in multi-access edge computing, computation offloading refers to a mainstream technology in which UEs offload part or all of their tasks to MECs for processing, which can not only solve the deficiencies of user equipment in terms of resource storage and computing performance, but also extend battery life. However, compared with cloud data centers (DCs), the computing power and storage resource scale of MECs are much smaller, making it difficult to meet the needs of all terminals. Therefore, cloud-edge collaborative computing is proposed to balance high responsiveness and abundant resources, where edge computing provides low-latency computing services and cloud computing provides powerful computing resources; the cloud-edge collaborative computing framework is more efficient in processing computationally intensive and latency-sensitive tasks, achieving high-performance, low-latency services. In this cloud-edge collaborative computing environment, UEs offload computing-intensive tasks to MECs according to their own needs to minimize task response time, while MECs need to decide whether to offload part or all of the tasks to DC processing to minimize the response time of all received tasks.

[0004] Cloud-Edge Collaborative Computing provides a new solution to improve the quality of experience of user devices. Cloud-Edge Collaborative Computing is to introduce DC to assist computing in a multi-access edge computing environment, where MEC provides low-latency computing services and DC provides abundant computing resources. In such an environment, multiple heterogeneous UEs compete for the computing resources of multiple MECs to maximize their own interests (such as minimizing task delays). In general, UEs are competitive and selfish when using edge / cloud resources, which means that offloading decisions need to be optimized for each terminal to improve its performance. On the other hand, for MECs, in order to minimize task processing delays, it is necessary to reasonably allocate its computing resources to process tasks from terminals; in addition, when MECs resources are difficult to meet task requirements, MECs need to further decide whether to offload all or part of the task to DC for processing.

[0005] The introduction of DC also brings new challenges to the problem of computing offloading. UEs will form a more complex computing offloading decision space, while MECs will form a more complex computing offloading decision space and resource allocation decision space. Decisions involving both the user device layer and the edge server layer will inevitably lead to the complexity of the entire cloud-edge collaborative computing system, greatly increasing the overall difficulty of solving the problem.

[0006] The prior art also has the following disadvantages:

[0007] 1. Inapplicability of single MEC multi-access edge computing environment: When edge servers build a multi-access edge computing architecture, multi-access edge computing can provide ultra-low latency and ultra-high bandwidth services and is suitable for many computing-intensive services. It can greatly reduce task processing latency, achieve efficient communication of computing tasks, and improve UE service quality experience; in addition, MEC is deployed close to users or information sources, which can significantly reduce network latency of business response and reduce the possibility of network congestion in the core network. However, the computing resources of MEC are much smaller than those of DC. For example, if only a single edge server is deployed at the edge of the network, it is obviously more suitable for small application scenarios (such as sparsely populated areas such as suburbs), and there is a problem that it cannot fully meet the needs of all mobile users. This is extremely unsuitable for modern large-scale application scenarios. In other words, the multi-access edge computing environment deploying a single MEC is short of computing resources, communication resources, and storage resources, and does not support large-scale applications in modern society.

[0008] 2. Disadvantages of multi-MECs multi-access edge computing environment: Deploying a large number of MECs in a multi-access edge computing environment solves the resource shortage problem of a single MEC server. However, with the progress and development of the times, people's requirements for portable services have become more complex. Mobile applications have become more energy-consuming and have an increasing demand for computing resources (for example: multiplayer online games, large-scale image processing, personal assistants, etc.); compared with resource-rich DCs, even if multiple MECs are deployed, they cannot handle a large number of computing-intensive applications, and their flexibility is greatly reduced. There are still some problems and challenges in achieving large-scale applications.

[0009] 3. Disadvantages of the existing cloud-assisted edge computing environment: In order to solve the above problems, a large number of existing studies have introduced DC into a multi-access edge computing environment, namely, a cloud-edge collaborative computing environment. In this environment, UEs can offload computing tasks to MECs or DCs based on factors such as system utilization and task characteristics. The flexibility of such an edge computing environment is greatly enhanced, but the offloading decision of UEs is more complicated. Many scholars have ignored this important issue; in the offloading decision process of UEs, they are more concerned about how to make simple decisions to meet the task delay requirements, that is, without deciding whether to offload to MECs or DC, they can directly offload to MECs for processing, and MECs decide whether to offload part or all to DC. It does not fully consider whether MEC has its own task delay requirements when processing tasks. From the perspective of MECs, MECs need to decide whether to offload all or part of the received tasks to DC for processing, so as to return the execution results as soon as possible (minimize its task processing delay). Few scholars have considered such a two-stage game, which considers both the average response time of tasks generated on UEs and the average response time of all tasks in MECs, with the optimization goal of minimizing the response time of tasks of each UE and MEC.

[0010] Therefore, the present invention proposes an effective two-layer game method to solve the above problems in order to stabilize the competitive cloud-edge collaborative computing environment. Summary of the invention

[0011] The purpose of an embodiment of the present invention is to provide a game method for jointly optimizing offloading decisions and resource allocation in cloud-edge collaborative computing, which can improve the overall performance of the cloud-edge collaborative computing system and optimize the average task response time of user devices and edge servers.

[0012] In order to solve the above technical problems, the technical solution adopted by the present invention is a game method for joint optimization of offloading decision and resource allocation in cloud-edge collaborative computing, which includes the following steps:

[0013] S1, build a cloud-edge collaborative computing environment model;

[0014] S2, defines the performance model of the cloud-edge collaborative computing platform;

[0015] S3, taking the task offloading ratio and the maximum configuration resources of the edge server as constraints, and the response time of the user device and the edge server as the optimization target, a multi-constraint optimization problem is established;

[0016] S4, solves the optimization problem according to the Lagrange multiplier method, KKT conditions and numerical method to find the optimal computing offloading strategy for user devices, the optimal computing resource configuration for edge servers and the optimal computing offloading strategy.

[0017] The beneficial effects of the present invention are:

[0018] (1) A game theory approach is used to solve the joint optimization problem of computing offloading and resource allocation in order to stabilize a fiercely competitive cloud-edge collaborative computing environment and ultimately reach a Nash equilibrium state. The game framework consists of two layers of games. The first layer is the game for obtaining the optimal computing offloading strategy for UE, and the second layer is the game for obtaining the optimal computing offloading strategy and optimal resource allocation strategy for MEC.

[0019] (2) In such an environment, not only the average response time of tasks generated on the UE is considered, but also the average response time of all tasks in the MEC. That is, the optimization goal is to take into account both UEs and MECs at the same time and strive to minimize the response time of both.

[0020] (3) It takes into account the scenario of cloud-coordinated multi-access edge computing, which is suitable for large-scale applications (capable of processing a large number of computing-intensive applications) and has higher flexibility and practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0022] Figure 1 is a flow chart of the method of the present invention.

[0023] Figure 2 yes With λ i,j Changes in the graph.

[0024] Figure 3 It is the flowchart of Algorithm 1.

[0025] Figure 4 is λ i,j Follow Changes in the graph.

[0026] Figure 5 It is the flowchart of Algorithm 2.

[0027] Figure 6 yes Follow i,j Changes in the graph.

[0028] Figure 7 is the flowchart of Algorithm 3.

[0029] Figure 8 Yes i,j Follow Changes in the graph.

[0030] Fig. 9 is the flowchart of Algorithm 4.

[0031] Fig.10 yes Follow Change graph.

[0032] Fig.11 is the flowchart of Algorithm 5.

[0033] Fig.12 is the flowchart of Algorithm 6.

[0034] Fig.13 is the flowchart of Algorithm 7. DETAILED DESCRIPTION

[0035] 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.

[0036] In order to build an efficient mobile edge computing platform, the present invention proposes a game method for the joint optimization of offloading decisions and resource allocation in cloud-edge collaborative computing. In an edge computing environment with multiple user devices, multiple edge servers and a cloud data center, the present invention solves the optimal computing offloading strategy of the user device based on the game theory method to minimize the response time of the tasks generated by the user device, and simultaneously solves the optimal computing resource configuration and the optimal computing offloading strategy of the edge server to minimize the response time of all tasks received by the edge server.

[0037] Process such as Figure 1 As shown, including:

[0038] S1, build a cloud-edge collaborative computing environment model;

[0039] S2, defines the performance model of the cloud-edge collaborative computing platform;

[0040] S3, taking the task offloading ratio and the maximum configuration resources of the edge server as constraints, and the response time of the user device and the edge server as the optimization target, a multi-constraint optimization problem is established;

[0041] S4, solves the optimization problem according to the Lagrange multiplier method, KKT conditions and numerical method to find the optimal computing offloading strategy for user devices, the optimal computing resource configuration for edge servers and the optimal computing offloading strategy.

[0042] Simply put, this invention conducts system modeling, quantifies various evaluation indicators and constraints, and uses convex optimization methods to solve the computational offloading optimization problem based on the studied multi-UEs, multi-MECs, and cloud-edge collaborative computing scenarios and minimizing the average task response time of UEs and MECs as the optimization goal.

[0043] The specific steps include:

[0044] 1. Building a cloud-edge collaborative computing environment model

[0045] Firstly, the cloud-edge collaborative computing framework is described as a three-layer network architecture, in which the first layer consists of multiple heterogeneous UEs, the second layer consists of multiple MECs and the third layer consists of a remote DC. According to such a network architecture, a two-stage game (two-layer game) method is proposed. The first stage is the game interaction between user equipment UEs and mobile edge cloud MECs, and the second stage is the game interaction between mobile edge cloud MECs and cloud data center DC. Finally, a highly competitive cloud-edge collaborative computing environment is stabilized. Based on this, the performance model of the three-layer network architecture is further defined, which involves the mathematical models of user equipment, edge servers and cloud data centers.

[0046] 1. Define the user equipment UE model

[0047] In the cloud-edge collaborative computing environment considered, i represents the i-th user equipment, where 1≤i≤n. It is assumed that each UE needs to offload some computationally intensive tasks to MECs for processing or further forward them to DC for processing to minimize the average response time of the task. For simplicity, u i The task is represented by a tuple {r i ,c i} means, where r i represents the size of the input task data (measured in millions of bits, in Mb), c irepresents the number of CPU cycles required to process 1-bit data (measured by the number of CPU cycles consumed per bit of data, in cycles / bit). It should be noted here that processing 1-bit data may require different CPU cycles because different types of computing tasks on different UEs are considered. In addition, let f i Indicates the CPU frequency of the user equipment, that is, the local computing power, in units of CPU cycles per second, that is, CPUcycles / s. Assuming that the computing data of the task owned by each UE can be arbitrarily divided bit by bit for local processing or offloaded to the edge server for processing, therefore, u i Calculation data of r i can be divided into k+1 parts, respectively by user equipment u i , edge servers 1 ,s 2 ,...,s k Execute processing; the division ratio can be expressed as a vector (λ i,0 ,λ i,1 ,λ i,2 ,...,λ i,k ), where λ i,0 ∈[0,1] is the user device u i The proportion of computational tasks processed locally, λ i,j ∈[0,1] means offloading to edge server s j The proportion of computational tasks processed remotely, λ i,j (where 1≤j≤k) already contains λ i,1 ,λ i,2 The case of λ i,1 ,λ i,2 Respectively represent offloading to edge servers s 1 and 2 The proportion of computing tasks that are processed remotely.

[0048] From this we can get:

[0049] Or expressed as Vector(λ i,0 ,λ i,1 ,λ i,2 ,...,λ i,k ) is the user equipment u i Computation offloading strategy.

[0050] 2. Define the edge server MEC model

[0051] Use s j represents the jth edge server, where 1≤j≤k. Each edge server s jare n user equipments in the geographical area U={u 1 ,u 2 ,...,u n}Provide computing offloading services, s j A set of calculation data is received from n UEs, and the calculation data is represented as a vector (λ 1,j r 1 ,λ 2,j r 2 ,...,λ n,j r n ), where λ i,j r i Indicates that it comes from user device u i Since edge servers have limited computing resources and network bandwidth compared to DCs, they need to further decide whether to fully / partially offload tasks to DCs to minimize the average response time of all tasks on edge servers.

[0052] set up Indicates that from u i The task of uninstalling is about to be further removed from s j The proportion of tasks offloaded to DC, therefore, the vector Actually, edge servers j The computation offloading strategy is That is, for the source from user device u i The calculation data is of data needs to be offloaded to the cloud data center for processing, and the remaining The data is sent by the edge server j Local processing.

[0053] In addition, let F j Indicates j The total computing resources configured (in MHz), f i,j represents the computing power allocated by the edge server to the user device, then the edge server s j The resource allocation strategy can be expressed as a vector (f 1,j ,f 2,j ,...,f n,j ), with the following constraints:

[0054]

[0055] That is, the computing power allocated by the edge server to each user device cannot exceed its own resource capacity.

[0056] 3. Define the cloud data center DC model

[0057] Theoretically, cloud data centers have unlimited computing resources. Therefore, assuming that DC can guarantee that any input data size can be processed within t dc (Unit: s) to complete the execution, t dc is the processing delay of the cloud data center; that is, the processing delay is independent of the data size. In addition, since the DC is usually located in the core of the network, far away from the end user, there is a certain transmission and propagation delay, and the impact of this delay needs to be analyzed. Therefore, the transmission delay and propagation delay when offloading tasks from MEC to DC are considered. Let R dc It represents the average data transmission rate in the WAN, in Mb / s, and d represents the average propagation delay when transmitting data from MEC to DC, in seconds.

[0058] 2. Defining the Performance Model of the Cloud-Edge Collaborative Computing Platform

[0059] 1. Performance model of user equipment UE

[0060] After determining the cloud-edge collaborative computing environment model, a performance model needs to be established to analyze the average response time of tasks generated by UE.

[0061] (1) First, analyze the processing delay of tasks generated on the user device and executed locally; based on the user device model defined above, for user device u i For example, i The local processing size is λ i,0 r i bits of calculation data, so it stays in the user device u i The processing delay of the local task is:

[0062]

[0063] (2) Next, according to the Shannon communication principle, we get the user device u i With edge servers j The wireless communication rate (in bits / s) is:

[0064]

[0065] where b i,j Represents edge servers j For user equipment u i The allocated wireless channel bandwidth is in megahertz (MHz). i,j Represents edge servers j and user device u i The channel gain between the two (determined by environmental factors and the distance between the user device and the edge server), in decibel milliwatts (dBm); N iis the noise power spectral density (determined by environmental factors), measured in decibel milliwatts of noise power per Hz (dBm / Hz), P i,j Indicates user equipment u i With edge servers j The transmission power during wireless communication, measured in Watts.

[0066] (3) Due to u i There is λ i,j r i The calculated data of bits needs to be sent to s j , so u i and j The wireless transmission delay between is:

[0067]

[0068] In addition, since the edge server is close to the user device, the data propagation delay is not considered, that is, the propagation delay of the data signal in the propagation medium is 0.

[0069] (4) Then for edge server s j For example, it is necessary to process the computing data from n user devices, among which, for the data from user device u i The calculation data (size is bits), which is in s j The local processing delay is:

[0070]

[0071] (5) For the cloud data center DC, it receives computing data forwarded from k edge servers. i And by the edge server s j Forwarded calculation data (size is bits), its transmission delay is:

[0072]

[0073] Where d represents the average delay when transmitting data from MEC to DC;

[0074] In summary, the user equipment u i The average task response time is:

[0075]

[0076] 2. Performance Model of Edge Server MEC

[0077] According to the above performance model analysis, we know that in sj The processing delay of all tasks executed on is:

[0078]

[0079] Among them, λ l,j r l With λ i,j r i They have the same meaning, that is, the ranges of l and i are the same, but they are distinguished by different symbols in the same formula.

[0080] At the same time, we can know that the delay of the computing task offloaded to the DC for processing is:

[0081]

[0082] Therefore, the edge servers j The average task response time is given by the following formula (2):

[0083]

[0084] 3. Taking the task offloading ratio and the maximum configuration resources of the edge server as constraints, and the average response time of the user device and the edge server as the optimization target, a multi-constraint optimization problem is established.

[0085] The problem to be solved by the present invention can be modeled as follows: Given n user equipments (UEs) u 1 ,u 2 ,...,u n and its parameter r i ,c i ,f i ,N i ,λ i,j ,P i,j ,h i,j , k edge servers (MECs)s 1 ,s 2 ,...,s k and its parameter B j ,F j ,b i,j ,f i,j , B j Edge servers j The total bandwidth resources (in MHz), a cloud data center (DC) and its parameters R dc ,t dc ,d. For user devices, they need to find a set of optimal computing offloading strategies λ i =(λ i,0 ,λ i,1 ,λ i,2,...,λ i,j ), so that its average task response time t i Minimize; for edge servers, they need to find a set of optimal resource allocation solutions f j =(f 1,j ,f 2,j ,...,f n,j ) and a set of optimal computation offloading strategies Make its average task response time T j Minimize, subject to the following constraints:

[0086] (1)λ i,j ∈[0,1], and λ i,0 +λ i,1 +λ i,2 +...+λ i,j =1, for all 1≤i≤n (task offloading ratio constraint);

[0087] (2) for all 1≤i≤n and 1≤j≤k (task offloading ratio constraint);

[0088] (3)f i,j ∈[0,F j ], for all 1≤j≤k (edge ​​server maximum configuration resource constraint).

[0089] 4. Prove the existence of Nash equilibrium

[0090] 1. Prove the existence of Nash equilibrium of UE computing offloading strategy game

[0091] According to non-cooperative game theory and formula (1), we know that t i About Lambda i,0 The first-order derivative of is:

[0092]

[0093] And, t i About Lambda i,j The first-order derivative of is:

[0094]

[0095] And 1≤j≤k, 1≤i≤n.

[0096] Then according to formulas (3) and (4), the second-order derivative can be obtained:

[0097]

[0098] and

[0099]

[0100] as well as

[0101]

[0102] So its Hessian matrix

[0103]

[0104] λ i Indicates user UE i The strategy, λ -i Indicates that except UE i The second-order partial derivative of the Hessian matrix is ​​a diagonal matrix whose elements on the main diagonal are positive. In other words, the Hessian matrix is ​​positive definite. Therefore, the objective function is convex and has an optimal solution.

[0105] 2. Prove the existence of Nash equilibrium in MEC resource allocation game

[0106] According to non-cooperative game theory and formula (2), we know that T j About f i,j The first-order derivative of is:

[0107]

[0108] Then according to (5), we can get its second-order derivative:

[0109]

[0110] as well as

[0111]

[0112] Therefore, its Hessian matrix is positive definite. j Represents edge servers j The resource allocation strategy, f -j Indicates the addition of s j Resource allocation strategy for servers other than .

[0113] 3. Prove the existence of Nash equilibrium of MEC computing offloading strategy game

[0114] According to non-cooperative game theory and formula (2), we know that T j about The first-order derivative of is:

[0115]

[0116] Then we get its second-order derivative:

[0117]

[0118] as well as

[0119]

[0120] Therefore, its Hessian matrix It is positive. Represents edge servers j The computation offloading strategy is Indicates the addition of s j Computation offloading strategy for servers other than .

[0121] 4. Prove the existence of Nash equilibrium of MEC joint computing offloading and resource allocation strategy game

[0122] For the joint computing offloading and resource allocation strategy game of MEC, according to the above analysis, it can be seen that the Hessian matrix of the joint game is

[0123]

[0124] in,

[0125]

[0126] And, there are

[0127]

[0128] Therefore, the Hessian matrix is ​​positive definite.

[0129] 5. Solve the optimization problem based on the Lagrange multiplier method, KKT conditions and numerical method to find the optimal computing offloading strategy for user devices and the optimal computing resource configuration solution and optimal computing offloading strategy for edge servers

[0130] It is challenging to simultaneously obtain the optimal computational offloading strategy for user devices and the optimal resource configuration and computational offloading strategy for edge servers. Based on the previous environmental model definition and performance model definition, the Lagrange multiplier method and numerical methods are used to solve the above problems.

[0131] 1. Find the optimal response of user equipment

[0132] For user devices, the optimal response is to find a set of computation offloading strategies λ i =(λ i,0 ,λ i,1 ,λ i,2 ,...,λ i,j ) to minimize the average task response time t i Under the constraint λ i,0+λ i,1 +λ i,2 +...+λ i,j =1, this is actually a convex optimization problem, which can be solved by the Lagrange multiplier method.

[0133] First, according to the Lagrange multiplier method, the constraint λ i,0 +λ i,1 +λ i,2 +...+λ i,j = 1 is reconstructed into function F(λ i,0 ,λ i,1 ,...,λ i,j )=λ i,0 +λ i,1 +...+λ i,j -1, and then combine the objective function and constraint function to construct the following Lagrangian function:

[0134]

[0135] in, is the Lagrange multiplier.

[0136] After simplification, we get:

[0137]

[0138] According to the above formula, it is found that when a hour, is λ i,j An increasing function of . Figure 2 A specific example is given to illustrate this point.

[0139] Therefore, we can use the classical dichotomy method to find the optimal search interval (λ i,j ∈[0,1]) to find a λ i,j , so that The specific process is as follows Figure 3 As shown in Algorithm 1, it should be noted that the algorithm terminates when the search interval is less than ε = 10 -12 (This ε is the precision value).

[0140] Algorithm 1 includes the following steps:

[0141] S1.1, receiving relevant parameters, including the provided The relevant parameters have been listed in detail in Section 3 and will not be repeated here.

[0142] S1.2, Initialize λ i,j The search interval of

[0143] S1.3, using the binary search method in the search interval λi,j ∈[0,1] to find a λ i,j , so that

[0144] S1.4, find a suitable λ according to the above dichotomy i,j (That is, the i,j satisfy ), and finally output the λ i,j .

[0145] The goal is to find a suitable Make this group of data unloading ratio (λ i,0 ,λ i,1 ,λ i,2 ,...,λ i,j ) satisfies the constraint λ i,0 +λ i,1 +λ i,2 +...+λ i,j =1; find λ i,j yes is an increasing function, so λ i,0 +λ i,1 +λ i,2 +...+λ i,j yes An increasing function, such as Figure 4 .

[0146] So we can find a suitable one based on the classic dichotomy and a group (λ i,0 ,λ i,1 ,λ i,2 ,...,λ i,j ), so that the constraints are established. The specific process is as follows Figure 5 As shown in Algorithm 2.

[0147] Algorithm 2 includes the following steps:

[0148] S2.1, receiving relevant parameters of the i-th UE;

[0149] S2.2, Initialization The search interval of

[0150] S2.3, determine whether the search interval is greater than ε; ε = 10 -12 , is a precision value;

[0151] When greater than, let Equal to the median of the search interval, and then in the current Under the value, call Algorithm 1 to traverse the nodes of k+1 servers and obtain (λ i,0 ,λ i,1 ,λi,2 ,...,λ i,j );Then judge Is it less than 1? If so, adjust the search area to the right half, and then return to the beginning of S2.3 to continue; if not, adjust the search area to the left half, and then return to the beginning of S2.3 to continue;

[0152] S2.4, until the search interval is smaller than ε, directly output and (λ i,0 ,λ i,1 ,λ i,2 ,...,λ i,j ).

[0153] It should be noted that in this algorithm The initial search interval is [0,ub], where ub means The upper bound of the search interval, where ub is solved as follows:

[0154] (1) If j = 0, it is obvious that when λ i,0 =1, ub reaches the maximum value, that is:

[0155] (2) If j≠0, it is obvious that when λ i,j =1, ub reaches the maximum value, that is:

[0156]

[0157] 2. Find the optimal response of the edge server

[0158] For the edge server, the optimal response is to find a set of resource configuration solutions f j =(f 1,j ,f 2,j ,...,f n,j ) in the constraint f 1,j +f 2,j +...+f n,j ≤F j and a set of computation offloading strategies In the constraint In order to minimize the average response time T of its tasks j The above two problems are actually convex optimization problems, which can be solved by the KKT condition for all edge servers with 1≤j≤k.

[0159] (1) Solve the resource allocation plan for edge servers

[0160] First, according to the KKT condition, constrain f 1,j +f 2,j +...+fn,j ≤F j Reconstructed into function g(f 1,j ,f 2,j ,...,f n,j )=f 1,j +f 2,j +...+f n,j -F j , and then combine the objective function and constraint function to construct the following Lagrangian function:

[0161]

[0162] in is the Lagrange multiplier; according to the above formula, we can get:

[0163]

[0164] Then, according to the KKT condition, we can get:

[0165]

[0166] According to the above formula, it is found that when a hour, Yes i,j A decreasing function of . Figure 6 As shown, specific examples are given to illustrate this point.

[0167] Therefore, we can use the classical binary search method to find the optimal search interval (f i,j ∈[0,F j ]) to find an f i,j , so that The specific process is as follows Figure 7 As shown in Algorithm 3.

[0168] Algorithm 3 includes the following steps:

[0169] S3.1, receiving relevant parameters, including the provided

[0170] S3.2, Initialize f i,j The search interval of

[0171] S3.3, using the binary search method in the search interval f i,j ∈[0,F j ] and searched for an f i,j , so that

[0172] S3.4, find a suitable f according to the above dichotomy i,j (i.e. the f i,j satisfy ), and finally output the f i,j .

[0173] Note that, like Algorithm 1, this algorithm terminates when the search interval is smaller than ε.

[0174] The goal is to find a suitable This set of computing resource configuration schemes (f 1,j ,f 2,j ,...,f n,j ) satisfies the constraint f 1,j +f 2,j +...+f n,j ≤F j ; found f i,j yes is a decreasing function, so f 1,j +f 2,j +...+f n,j yes A decreasing function, a specific example is given in Figure 8 .

[0175] So we can use the classic dichotomy to find a suitable and a group (f 1,j ,f 2,j ,...,f n,j ), so that the constraints are established. The specific process is as follows Fig. 9 As shown in Algorithm 4.

[0176] Algorithm 4 includes the following steps:

[0177] S4.1, receiving relevant parameters of the j-th MEC;

[0178] S4.2, Initialization The search interval of

[0179] S4.3, determine whether the search interval [0, ub′] is greater than ε, ub′ represents The upper bound of the search interval, ε = 10 -12 .

[0180] When it is greater than ε, let Equal to the median of the search interval, in the current Under this value, call Algorithm 3 to traverse n user nodes and obtain f 1,j ,f 2,j ,...,f n,j ; Then judge Is it less than F? j If yes, adjust the search interval to the left half, and then return to the beginning of S4.3 to continue; if no, adjust the search interval to the right half, and then return to the beginning of S4.3 to continue;

[0181] When it is less than ε, the output and f 1,j ,f 2,j ,...,f n,j .

[0182] In this algorithm, The initial search interval is [0,ub′], where ub′ represents The upper bound of the search interval is: According to formula (5), we can know that f i,j The smaller it is, the larger ub′ is, so take f i,j =1, then

[0183]

[0184] (2) Solving the computation offloading strategy of edge servers

[0185] For the edge server computation offloading strategy game, there is no constraint on the objective function, so we only need to find Make According to observation, yes An increasing function is given. Specifically, an example is given. Fig.10 :

[0186] Therefore, an algorithm based on the binary search method is proposed5. Found make Finally, we get a set of calculation offloading strategies

[0187] The specific process is as follows Fig.11 shown.

[0188] Algorithm 5 includes the following steps:

[0189] S5.1, receiving relevant parameters of the j-th MEC;

[0190] S5.2, traverse all user nodes and initialize The search interval of

[0191] S5.3, determine whether the search interval is greater than ε;

[0192] When it is greater than, let is equal to the median of the search interval, and then calculate Is it less than 0? If so, adjust the search interval to the right half, and then return to the beginning of S5.3 to continue; if not, adjust the search interval to the left half, and then return to the beginning of S5.3 to continue;

[0193] When less than, the output

[0194] (3) Solve the joint strategy of computing offloading and resource allocation for edge servers

[0195] Due to the MEC computing offloading strategy and resource allocation plan j Together they influence its optimal response. Therefore, an iterative algorithm is developed to find the optimal response of MEC.

[0196] First, initialize the action combination z of this subgame = (z 1 ,z 2 ,...,z k ),in Then, each MEC finds its best response to the current situation by using Algorithm 3-Algorithm 5. When the action combinations of two consecutive rounds are close enough, that is, (Accuracy δ = 10 -5 ), the algorithm terminates, and the final convergent action combination z * =(z 1 * ,z 2 * ,...,z k * ) is returned as a Nash equilibrium; z′ is the action combination of the new round, f i,j '、 It represents the value of computing resources and offloading ratio of edge servers in the new round of z′ state.

[0197] Process such as Fig.12 As shown in Algorithm 6.

[0198] The steps of Algorithm 6 include:

[0199] S6.1, input relevant parameters, including precision δ;

[0200] S6.2, initialize the action combination z of this sub-game = (z 1 ,z 2 ,...,z k );

[0201] S6.3, traverse all server nodes and use Algorithm 3-Algorithm 5 to calculate the new round of action combination z′;

[0202] S6.4, determine whether ||z′-z||≥δ. If so, assign the new round of action combination z′ to the previous round z, then return to the beginning of S6.3 and continue to use Algorithm 3-Algorithm 5 to solve the next round of action combination z′; if not, use this new round of action combination z′ as the final convergent action combination z * Output.

[0203] 3. Solve the total Nash equilibrium

[0204] For the two-layer game model, an iterative algorithm is proposed to find the total Nash equilibrium of the model. The specific process is as follows Fig.13 Algorithm 7 is shown as follows:

[0205] In Algorithm 7, we first initialize the action combination x of the total game = (λ 1 ,λ 2 ,...,λ n ,z 1 ,z 2 ,...,z k ), where x contains the computation offloading strategies of all users and the resource allocation and computation offloading strategies of all servers; then, in each round, each UE finds its best response to the current situation by using Algorithm 1-2; in addition, each MEC also finds its best response to the current situation by using Algorithm 6. When the action combinations of two consecutive rounds are close enough, that is,

[0206]

[0207] The algorithm terminates and the final convergent action combination x * =(λ 1 * ,λ 2 * ,...,λ n * ,z 1 * ,z 2 * ,...,z k * ) is returned as a Nash equilibrium.

[0208] Algorithm 7 includes the following steps:

[0209] S7.1, input relevant parameters, including precision δ;

[0210] S7.2, initialization action combination x=(λ 1 ,λ 2 ,...,λ n ,z 1 ,z 2 ,...,zk );

[0211] S7.3, traverse all user nodes and calculate the best response of each UE's current situation through Algorithm 1-Algorithm 2, that is, find the strategy λ′ of each user 1 ,λ′ 2 ,...,λ′ n .

[0212] S7.4, find the best response of each MEC to the current situation through Algorithm 6, that is, find the resource allocation and computation offloading strategy z′ of each server 1 ,z′ 2 ,...,z′ k .

[0213] S7.5, determine whether ||x′-x||≥δ, if so, then solve x′=(λ′ 1 ,λ′ 2 ,...,λ′ n ,z′ 1 ,z′ 2 ,...,z′ k ) is assigned to the previous round of x=(λ 1 ,λ 2 ,...,λ n ,z 1 ,z 2 ,...,z k ), return to S7.3 and continue the next round of calculation. If not, then the x′=(λ′ 1 ,λ′ 2 ,...,λ′ n ,z′ 1 ,z′ 2 ,...,z′ k ) as the Nash equilibrium solution x * =(λ 1 * ,λ 2 * ,...,λ n * ,z 1 * ,z 2 * ,...,z k * ) output.

[0214] 6. Experimental Results Analysis

[0215] First, we give the initial parameter data and performance data of the cloud-edge collaborative computing environment with 10 UEs, 3 MECs and a single DC (the last two lines are performance data, i.e., our optimization goal), as shown in Table 1 below:

[0216] 1. Experiment on the optimal response algorithm for user equipment

[0217] Table 2 shows the experimental results of finding the optimal user computing offloading strategy for Algorithm 1 and Algorithm 2. Obviously, under stable conditions, compared with the original parameter settings in Table 1, all UEs have increased the amount of computing offloading, and the average response time has been significantly reduced. 1 For example, under the initial calculation offloading strategy, UE 1 The average task response time is t 1 =7.87986. After using Algorithm 1 and Algorithm 2, t 1 =2.52364. That is, compared with the random offloading scheme, the offloading algorithm we proposed can reduce the average task response time by 67.97%.

[0218] Table 1 Initial parameters and performance data

[0219]

[0220] Table 2 Experimental results of algorithms 1 and 2

[0221]

[0222] 2. Experiment on solving the optimal response algorithm of edge servers

[0223] (1) Solve the resource allocation plan for edge servers

[0224] Table 3 shows the experimental results of Algorithm 3 and Algorithm 4 for finding the optimal resource configuration scheme for the server. Obviously, under stable conditions, all MECs have adjusted their resource configuration strategies compared with the original parameter settings in Table 1. For UEs with small computing offload, MEC allocates fewer resources; for UEs with large computing offload, MEC allocates more resources. MEC fully utilizes computing resources, thereby significantly reducing the average response time. 1 For example, under the initial resource allocation strategy, MEC 1 The average task response time is T 1 =1.23285. After using Algorithm 3 and Algorithm 4, T 1 =1.16425. That is to say, compared with the random resource allocation scheme, the resource allocation algorithm we proposed can reduce the average task response time by 5.56%.

[0225] Table 3 Experimental results of algorithms 3 and 4

[0226]

[0227] (2) Solving the computation offloading strategy of edge servers

[0228] Table 4 shows the experimental results of algorithm 5 for finding the optimal server computing offloading strategy. Obviously, under stable conditions, compared with the original parameter settings in Table 1, the amount of computing offloading of all MECs is reduced, and the average response time is significantly reduced. 2 For example, under the initial offloading strategy, MEC 2 The average task response time is T 2 =1.21350. After using Algorithm 5, T 2 =0.97795; that is, compared with the random offloading scheme, the offloading algorithm we proposed can reduce the average task response time by 19.41%.

[0229] Table 4 Experimental results of algorithm 5

[0230]

[0231] (3) Solve the joint strategy of computing offloading and resource allocation for edge servers

[0232] Table 5 shows the experimental results of Algorithm 6 for finding the joint strategy of server joint computing offloading and resource allocation. Obviously, in the stable case, compared with the original parameter settings in Table 1, all MECs adjusted the resource allocation strategy and did not perform computing offloading, thus significantly shortening the average response time. 1 For example, under the initial computation offloading and resource allocation strategy, MEC 1 The average task response time is T 1 =1.23285; after Algorithm 6, T 1 =0.89564. That is, compared with the random offloading scheme and resource allocation scheme, the joint computation offloading and resource allocation algorithm we proposed can reduce the average task response time by 27.35%.

[0233] Table 5 Experimental results of Algorithm 6

[0234]

[0235] Each embodiment in this specification is described in a related manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0236] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. Game theory approach for joint optimization of offloading decision and resource allocation in cloud-edge collaborative computing, It is characterized in that The following steps are involved: S1, build a cloud-edge collaborative computing environment model; S2, defines the performance model of the cloud-edge collaborative computing platform; S3, taking the task offloading ratio and the maximum configuration resources of the edge server as constraints, and the response time of the user device and the edge server as the optimization target, a multi-constraint optimization problem is established; S4, solve the optimization problem according to the Lagrange multiplier method, KKT conditions and numerical method, and find the optimal computing offloading strategy for user devices, the optimal computing resource configuration for edge servers and the optimal computing offloading strategy; The S4 comprises the following steps: S41, solving the optimal response of the user equipment; S42, solving the optimal response of the edge server; S43, solve the total Nash equilibrium; The step S41 comprises: First, according to the Lagrange multiplier method, the constraint λ i,0 +λ i,1 +λ i,2 +...+λ i,j = 1 is reconstructed into function F(λ i,0 ,λ i,1 ,...,λ i,j )=λ i,0 +λ i,1 +...+λ i,j -1, and then combine the objective function and constraint function to construct the following Lagrangian function: in, is the Lagrange multiplier, After simplification, we get: When given a hour, is λ i,j An increasing function of , so based on the classical bisection method, find a λ in a given search interval i,j , so that The specific process is as follows: Algorithm 1. Algorithm 1 includes the following steps: S1.1, receiving relevant parameters, including the provided S1.2, Initialize λ i,j The search interval of S1.3, using the binary search method in the search interval λ i,j ∈[0,1] to find a λ i,j , so that S1.4, find a suitable λ according to the above dichotomy i,j , and finally output the λ i,j ; λ i,j yes is an increasing function, so λ i,0 +λ i,1 +λ i,2 +...+λ i,j yes An increasing function; so based on the classical dichotomy method, we find a suitable and a group (λ i,0 ,λ i,1 ,λ i,2 ,...,λ i,j ), so that the constraint condition is established. The specific process is Algorithm 2. Algorithm 2 includes the following steps: S2.1, receiving relevant parameters of the i-th UE; S2.2, Initialization The search interval of S2.3, determine whether the search interval is greater than ε; When greater than, let Equal to the median of the search interval, and then in the current Under the value, call Algorithm 1 to traverse the nodes of k+1 servers and obtain (λ i,0 ,λ i,1 ,λ i,2 ,...,λ i,j );Then judge Is it less than 1? If so, adjust the search area to the right half, and then return to the beginning of S2.3 to continue; if not, adjust the search area to the left half, and then return to the beginning of S2.3 to continue; S2.4, until the search interval is smaller than ε, directly output and (λ i,0 ,λ i,1 ,λ i,2 ,...,λ i,j ); Said The initial search interval is [0,ub], where ub means The upper bound of the search interval, where ub is solved as follows: (1) If j = 0, when λ i,0 =1, ub reaches the maximum value, that is: (2) If j≠0, when λ i,j =1, ub reaches the maximum value, that is: The S42 includes: 1) Solve the resource allocation plan for edge servers First, according to the KKT condition, constrain f 1,j +f 2,j +...+f n,j ≤F j Reconstructed into function g(f 1,j ,f 2,j ,...,f n,j ) = f 1,j +f 2,j +...+f n,j -F j , and then combine the objective function and constraint function to construct the following Lagrangian function: in is the Lagrange multiplier; according to the above formula, we can get: Then, according to the KKT condition, we can get: Find an f in a given search interval based on the classical bisection method i,j , so that The specific process is Algorithm 3. Algorithm 3 includes the following steps: S3.1, receiving relevant parameters, including the provided S3.2, Initialize f i,j The search interval of S3.3, using the binary search method in the search interval f i,j ∈[0,F j ] and searched for an f i,j , so that S3.4, find a suitable f according to the above dichotomy i,j , and finally output the f i,j ; The goal is to find a suitable This set of computing resource configuration schemes (f 1,j ,f 2,j ,...,f n,j ) satisfies the constraint f 1,j +f 2,j +...+f n,j ≤F j ; Use the classic dichotomy method to find a suitable and a group (f 1,j ,f 2,j ,...,f n,j ), so that the constraint condition is established. The specific process is Algorithm 4. Algorithm 4 includes the following steps: S4.1, receiving relevant parameters of the j-th MEC; S4.2, Initialization The search interval of S4.3, determine whether the search interval [0, ub'] is greater than ε, ub' represents The upper bound of the search interval; When it is greater than ε, let Equal to the median of the search interval, in the current Under this value, call Algorithm 3 to traverse n user nodes and obtain f 1,j ,f 2,j ,...,f n,j ; Then judge Is it less than F? j If yes, adjust the search interval to the left half, and then return to the beginning of S4.3 to continue; if no, adjust the search interval to the right half, and then return to the beginning of S4.3 to continue; When it is less than ε, the output and f 1,j ,f 2,j ,...,f n,j ; The initial search interval is [0,ub'], ub' represents The upper bound of the search interval is f according to formula (5). i,j =1, then 2) Solve the computation offloading strategy of edge servers Algorithm 5 based on the binary search method finds make Finally, we get a set of calculation offloading strategies Algorithm 5 includes the following steps: S5.1, receiving relevant parameters of the j-th MEC; S5.2, traverse all user nodes and initialize The search interval of S5.3, determine whether the search interval is greater than ε; When it is greater than, let is equal to the median of the search interval, and then calculate Is it less than 0? If so, adjust the search interval to the right half, and then return to the beginning of S5.3 to continue; if not, adjust the search interval to the left half, and then return to the beginning of S5.3 to continue; When less than, the output 3) Solve the joint strategy of computing offloading and resource allocation of edge servers First, initialize the action combination z of the subgame = (z 1 ,z 2 ,…,z k ),in Then, each MEC finds its best response to the current situation by using Algorithm 3-Algorithm 5. When the action combination of two consecutive rounds is close enough, that is, The algorithm terminates and the final convergent action combination z * =(z 1 * ,z 2 * ,…,z k * ) is returned as a Nash equilibrium; z' is the action combination of the new round, f i,j '、 'Indicates the value of computing resources and offloading ratio of edge servers in the new round of state z; The step S43 comprises: First, initialize the action combination x = (λ 1 ,λ 2 ,…,λ n ,z 1 ,z 2 ,…,z k ), where x contains the computation offloading strategies of all users and the resource allocation and computation offloading strategies of all servers; then, in each round, each UE finds its best response to the current situation; each MEC finds its best response to the current situation. When the action combinations of two consecutive rounds are close enough, that is, The algorithm terminates and the final convergent action combination x * =(λ 1 * ,λ 2 * ,…,λ n * ,z 1 * ,z 2 * ,…,z k * ) is returned as a Nash equilibrium.

2. According to claim 1, the game method for joint optimization of offloading decision and resource allocation in cloud-edge collaborative computing, It is characterized in that In the S1, a three-layer network system is included, the first layer is composed of multiple heterogeneous UE models, the second layer is composed of multiple MEC models, and the third layer is composed of a remote DC model; In the UE model, the vector (λ i,0 ,λ i,1 ,λ i,2 ,…,λ i,k ) is the user device u i The computation offloading strategy, u i Calculation data of r i can be divided into k+1 parts, respectively by user equipment u i , edge servers 1 ,s 2 ,…,s k Execute processing; where λ i,0 ∈[0,1] is the user device u i The proportion of computing tasks processed locally, λ i,j ∈[0,1] means offloading to edge server s j The proportion of computing tasks processed remotely; In the MEC model, each edge server s j are n user equipments in the geographical area U={u 1 ,u 2 ,…,u n }Provide computing offloading services, s j A set of calculation data is received from n UEs, and the calculation data is represented as a vector (λ 1,j r 1 ,λ 2, j r 2 ,…,λ n,j r n ), where λ i,j r i Indicates that it comes from user device u i The total amount of computing data; MEC needs to calculate whether to fully or partially offload the task to DC; F j Indicates j The total computing resources configured, f i,j represents the computing power allocated by the edge server to the user device, then the edge server s j The resource allocation strategy is represented as a vector (f 1,j ,f 2,j ,…,f n,j ), with the following constraints: For all 1≤j≤k; In the DC model, DC guarantees that the dc The execution is completed within t dc is the processing delay in the cloud data center.

3. According to the game method for joint optimization of offloading decision and resource allocation in cloud-edge collaborative computing in claim 1, It is characterized in that S2 includes a performance model of the UE and a performance model of the MEC; Among them, the UE performance model is established to analyze the average response time of the tasks generated by the UE. i The average task response time is: λ i,0 ∈[0,1] is the user device u i The proportion of computing tasks processed locally, r i Indicates the size of the input task data, c i Indicates the number of CPU cycles required to process 1-bit data, f i Indicates the CPU frequency of the user device. Indicates that from u i The task of uninstalling is about to be further removed from s j The proportion of tasks offloaded to DC, λ i,j ∈[0,1] means offloading to edge server s j The proportion of computing tasks processed remotely, R i.j User equipment i With edge servers j The wireless communication rate, f i,j represents the computing power allocated by the edge server to the user device, R dc Represents the average data transmission rate in the wide area network, t dc The processing delay of the cloud data center is, d represents the average propagation delay when transmitting data from MEC to DC; Among them, the performance model of MEC is established to analyze the average response time of tasks generated by MEC, and the edge server s j The average task response time is: λ l,j r l With λ i,j r i Same meaning.

4. According to claim 1, the game method for joint optimization of offloading decision and resource allocation in cloud-edge collaborative computing, It is characterized in that In S3, the constraints followed are: 1), λ i,j ∈[0,1], and λ i,0 +λ i,1 +λ i,2 +...+λ i,j =1, for all 1≤i≤n; 2), For all 1≤i≤n and 1≤j≤k; 3), f i,j ∈[0,F j ], For all 1≤j≤k; Among them, λ i,j ∈[0,1] means offloading to edge server s j The proportion of computing tasks processed remotely, Indicates that from u i The task of uninstalling is about to be further removed from s j The proportion of tasks offloaded to DC, f i,j represents the computing power allocated by the edge server to the user device, F j Indicates j The total computing resources configured.

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