Computing power network bandwidth investment decision-making method based on game analysis

Abstract

The invention discloses a computing power network bandwidth investment decision-making method based on game analysis, and belongs to the field of information management and information systems. The invention provides a government-enterprise double-layer planning modeling and solving framework for solving the problems of how to invest data transmission bandwidth of a computing power network under limited budget by a government in computing power infrastructure investment construction and realize system cost minimization and how to obtain balanced computing power of an enterprise in a multi-node computing power environment. According to the method, enterprise nodes, edge computing nodes and a center computing center are constructed into a computing power service network, a cost function system including data transmission, processing and computing links is established, and a network topology structure is simplified in a mode of mapping node cost into edge weights. In the lower layer, depicting computing power balance conditions of the enterprise under different path selections by using a variational inequality; on the upper layer, bandwidth-investment function constraint is introduced, and the total cost of the system is optimized through government budget. Through a double-layer iterative algorithm combining gradient projection and a successive average method, synchronous convergence of investment distribution and flow balance is realized. According to the method, the configuration efficiency of computing power resource investment can be effectively improved, the allocation structure of bandwidth funds is optimized, the coordinated improvement of investment income and system performance is realized, and a scientific quantitative support is provided for investment planning and decision making of computing power infrastructures.

Description

TECHNICAL FIELD

[0001] The application provides a computing power network bandwidth investment decision-making method based on game analysis, and belongs to the field of information management and information systems. BACKGROUND

[0002] With the acceleration of global digitization, the fusion application of new generation information technologies such as artificial intelligence, big data, cloud computing and 5G is deepening, and computing power has become a key production factor to promote the high-quality development of digital economy. Computing power infrastructure not only covers computing, storage and network transmission capabilities, but also carries the core computing power demand of intelligent manufacturing, smart government, industrial internet and other scenarios. However, there are still many problems in the construction and operation of computing power network. First, the spatial distribution of computing power resources is extremely uneven, with concentrated computing power and heavy load in the eastern region, and idle resources and low utilization rate in the western region, causing serious regional mismatch. Second, there is a lack of coordination between computing power infrastructure investment and enterprise demand, and market-led decentralized investment is difficult to form a system optimal configuration. Third, there is a significant bandwidth bottleneck and scheduling delay between computing power centers, edge nodes and enterprise terminals, resulting in low cross-domain data flow efficiency and high system operation cost. In terms of resource allocation method, existing researches are mostly limited to static optimization or single-layer scheduling level, and lack of a systematic modeling framework that can reflect the regulatory role of policy investment.

[0003] In view of the above problems, it is urgent to propose a computing power resource optimization method that can comprehensively consider government investment behavior, enterprise computing power demand response and network operation characteristics, so as to realize the dynamic balance and overall efficiency improvement of computing power network under the guidance of policy. Based on this, the application provides a computing power network bandwidth investment decision-making method based on game analysis. The method takes the government as the upper-level decision-making subject, and minimizes the total cost of the system under the investment budget constraint as the target; the enterprise is taken as the lower-level rational response subject, and the principle of minimizing the individual computing power acquisition cost is realized to achieve the balanced allocation of computing power resources. By establishing a bi-level programming model, the dynamic influence relationship of policy investment on bandwidth expansion, node structure and network balance is described, and the lower-level equilibrium condition is described in the form of variational inequality, so as to reveal the interaction mechanism between investment decision and enterprise behavior.

[0004] The invention effectively solves the joint optimization problem of government investment and enterprise balanced response by constructing a double-layer solution framework based on gradient projection and successive average method. This method can quantify the system operation law under different investment intensity and parameter conditions, and reveal the regulatory effect of policy investment on the cost structure, flow distribution and bottleneck link of the computing power network. Compared with the traditional market-oriented single-layer model, the invention can realize the optimal allocation and dynamic equilibrium of computing power resources in a multi-agent game environment, and has both theoretical innovation and engineering implementability. This method can be widely applied to computing power network planning, data center bandwidth expansion decision, regional computing power collaborative scheduling and digital economic infrastructure investment management, and has significant policy guidance significance and application value. SUMMARY TECHNICAL PROBLEM

[0005] The technical problem to be solved by the invention is how to coordinate government investment decision and enterprise computing power demand response under the condition of limited investment budget in the computing power network system with government policy investment participation, and realize the global optimization of bandwidth expansion, node structure optimization and resource allocation. Specifically, under the "cloud-edge-end" collaborative architecture, computing power resources exist significant heterogeneity and spatial imbalance between enterprise nodes, edge computing nodes and central computing power nodes. The cost difference and energy consumption constraint of data in transmission, processing and calculation links lead to the decline of the overall efficiency of the system. The traditional single-layer optimization method cannot simultaneously consider the influence of policy investment on bandwidth structure and the dynamic response mechanism at the enterprise level. The invention aims to build a double-layer programming model that can reflect the interaction between government investment behavior and enterprise balanced selection. By introducing the investment-bandwidth mapping function and variational inequality equilibrium condition, the minimum cost of computing power network system and the dynamic equilibrium allocation of computing power resources are realized, thereby solving the problems of uneven distribution of computing power resources and low system operation efficiency under the policy investment environment. TECHNICAL SCHEME

[0006] The application provides a computing power network bandwidth investment decision-making method based on game analysis. The method takes the government as the upper investment decision-maker and the enterprise as the lower response subject, realizes dynamic optimization of computing power resources and minimization of the total system cost under the "cloud-edge-end" collaborative architecture by establishing a double-layer planning model. Specifically, the method first constructs a computing power service network including enterprise nodes, edge computing nodes and central computing power nodes, models the whole process of data transmission, processing and calculation in the network, and defines the bandwidth, traffic and cost parameters of each link. Then, the government investment behavior is introduced into the bandwidth expansion mechanism, the influence of investment intensity on the network structure and computing power distribution is described by establishing the mapping relationship between investment and bandwidth. Under the budget constraint condition, the optimal investment allocation scheme is determined to make the topology structure and resource allocation of the computing power network optimal. The lower model takes the enterprise as a rational decision-maker, selects the optimal data transmission and calculation path according to the principle of minimizing the computing power acquisition cost under the given bandwidth condition, so as to realize the data flow balance and efficient use of resources in the network. The upper and lower models are solved by mutual nesting and iteration of investment decision-making and balanced response, realizing the dynamic coordination between government investment and enterprise behavior.

[0007] Under the equilibrium condition of the computing power network, the data task allocation of the enterprise is not only affected by the network structure and bandwidth constraint, but also by the computing power resource redistribution effect caused by the government investment behavior. The application establishes a game equilibrium model based on policy investment regulation, the upper layer determines the investment priority and bandwidth expansion strategy of different links with the minimum total system cost as the target, and the lower layer takes the rational selection of the enterprise as the core to achieve the system equilibrium state by dynamically adjusting the data transmission and task allocation. The model is solved by alternating iteration of outer investment optimization and inner flow distribution, and the investment scheme and network flow are updated gradually until they converge at the same time, and the global equilibrium solution of the computing power network is obtained. Through the model, the application can reveal the interaction mechanism between the government investment structure and the enterprise computing power response, realize the adaptive coordination of bandwidth expansion and flow distribution, effectively reduce the operating cost of the computing power network, improve the overall resource utilization, and provide a scientific basis for the investment decision-making and resource scheduling of the computing power infrastructure. 1. Model method 1.1 Problem description

[0008] To depict the interaction mechanism between the government and the computing power network, a Stackelberg bi-level programming model is constructed, in which the government investment is the leader and the computing power supply chain network enterprises are the followers. The model aims to improve the construction of computing power network infrastructure, increase bandwidth levels, guide the overall operation efficiency of the computing power network, and maximize the utility of enterprises in the computing power network through policy investment. The model consists of the upper government investment optimization problem and the lower computing power network equilibrium problem, and forms a nested double-layer structure through the mutual feedback of resource allocation and path selection. The double-layer model reflects the interactive game relationship between policymakers and computing power network resource users. The main decision goal of the government is how to allocate the investment to minimize the total cost of the system. Enterprises and other computing power network users dynamically adjust their path selection and task allocation according to the resource changes brought by government investment, thereby affecting the government's evaluation and decision on investment allocation efficiency. Therefore, the model constructed in this study is essentially a nested bi-level optimization framework with the government as the leader and the self-organization operation of the computing power network as the response mechanism, which can effectively simulate the data flow and resource allocation rules under the coordination mechanism of "computing power infrastructure + market behavior".

[0009] In the upper model, we consider that the government invests a certain amount of money D to improve the construction of computing power network infrastructure, and increase the bandwidth B of data transmission in the computing power network ij 、B jk , thereby indirectly affecting the data flow path and enterprise behavior in the computing power network. We assume that the investment cost is a function of the increased bandwidth ΔB ii 、ΔB ik : where β1 and β2 are the coefficients related to the investment cost, and the changed bandwidth is where

[0010] To accurately depict the behavior decision mechanism of the underlying computing power network agents, this study takes the computing power service facilities in the region as the providers of computing services from a systematic perspective, and regards them as a connected computing service network together with demand enterprises. This network includes demand nodes, edge computing nodes, and central computing nodes. Different types of nodes are connected through the network to achieve distributed data processing and collaborative computing. Under this framework, edge computing nodes are responsible for preliminary data processing and integration near the data source, and central computing nodes are responsible for more complex and resource-intensive deep analysis tasks. Specifically, in a regional computing service network composed of m enterprises, n edge computing nodes, and o central computing nodes, data flows between nodes to form a complete data processing and value conversion chain. First, enterprises transmit raw data to adjacent edge computing nodes through optical fibers. As the first processing site for data, edge nodes are responsible for the preliminary fusion, cleaning, and standardization of multi-source heterogeneous data to achieve effective preprocessing of raw data. Subsequently, the data processed by the edge nodes is transmitted to the central computing nodes, where deep modeling, analysis, and mining are completed in a high-performance computing environment to extract knowledge and information with decision-making value. Finally, the processed data products are returned to the original enterprises for production optimization, operational decision-making, and other practical scenarios, forming a closed-loop data-driven enterprise empowerment mechanism.

[0011] During data flow, the operations on different nodes and edges in the network will generate corresponding costs, mainly including: data transmission cost from enterprises to edge computing nodes, processing cost of data fusion and standardization by edge nodes, data transmission cost from edge nodes to central computing nodes, computing resource cost of central nodes, and transmission cost of processed data returning to enterprise end. Through the system modeling of the entire computing service network, the resource allocation behavior and cost trade-off mechanism of various participating agents can be deeply depicted, providing a theoretical basis for the efficient allocation and collaborative development of regional computing resources. The specific network structure is shown in Figure 1 .

[0012] In Figure 1In the shown network, the edge computing center and the center computing node bear the data processing and computing cost, respectively, and these costs are usually attached to the nodes themselves, bringing certain complexity to the optimization modeling. In order to simplify the network structure and more intuitively represent the cost distribution, we use a network transformation method to map the cost on the node to the edge, so that we can more efficiently model and solve in the subsequent analysis and optimization process. Specifically, for each node with cost (i.e. edge computing node and center computing node), we introduce a virtual node and connect it to the original node through a virtual edge. The weight of the virtual edge is equal to the cost on the original node, so that the cost originally attached to the node is transformed into the weight on the edge. After this transformation, the new network structure not only maintains the topological relationship of the data flow, but also makes all the costs in the form of edge weight, thereby improving the model solvability and computational efficiency. The transformed network structure is shown in Figure 2 .

[0013] All the parameters, variables and functions involved in the present application are shown in Table 1.

[0014] For the description of various cost functions in the network, it is assumed that the cost functions are continuous. First, from the starting enterprise, the data generated in the daily production and operation of the enterprise is transmitted to the edge computing node through the network, and the transmission cost function is usually represented as the ratio of the amount of data transmitted to the transmission rate: where e1 represents the parameter related to the transmission cost, represents the transmission rate of data between ij, is itself a function of bandwidth and signal-to-noise ratio M: After the data reaches the edge computing node, it enters the processing stage of heterogeneous data. The processing cost can be represented as the ratio of the amount of data to the processing rate: where e2 represents the parameter related to the processing cost, represents the processing rate of data, which is an exogenous variable and may be affected by the industry data collection and processing standards. The amount of data after processing by the edge computing node will change, and the relationship before and after the change can be expressed as: where α jParameters related to the algorithm, hardware used by edge computing node j. The data processed will be transmitted to the central computing center, and the transmission cost of the process is also described using a similar data transmission cost function: wherein e1 represents a parameter related to the transmission cost, represents the transmission rate of data, is the bandwidth and the signal-to-noise ratio M:

[0015] When the data arrives at the central computing node, it enters the data computing stage, where the data is converted into valuable information products through calculation. In order to ensure the generality of the model, the computing cost of the central computing center can be represented as a function of the sum of all data processed by the node: wherein e3, e4 represent parameters related to the data computing cost, represents the data processing rate of the central computing node k, q k and queuing are modeled.

[0016] After the data is processed, it is converted into information. Unlike traditional product supply chain networks, data as an intangible product will change in the amount of information formed through processing. Due to the influence of software algorithms and hardware used in data processing, the calculated data will output different amounts of information. Here we use the following function to represent the relationship between data sent to the central computing center before and after calculation: wherein a k represents a parameter related to the algorithm and hardware used by the central computing center. The calculated information product returns to the original enterprise through a virtual edge, and the transmission cost of this process is also represented as the ratio of the amount of data transmitted to the transmission rate: wherein e1 represents a parameter related to the transmission cost, represents the transmission rate of data, which is the bandwidth B ki and the signal-to-noise ratio M: Thus, data has completed processing and calculation through the computing power network.

[0017] In this bi-level programming problem, the upper level aims to allocate the fund D to different links of bandwidth to minimize the total cost of the whole system. The lower level aims to select the edge and center nodes for each enterprise to maximize the individual utility, so that the whole network reaches equilibrium. The interaction between the upper and lower levels is as follows Figure 3 1.2 Model establishment 1.2.1 Lower level model

[0018] Assume that in a computing power network G, there are m enterprises that need to transmit data to the computing center for calculation. Each enterprise can choose different edge computing nodes and center computing nodes, and these different choices can be combined into multiple different paths. When the computing power network reaches equilibrium, if the data flow of a certain link is greater than 0, the total cost of the path is equal to the minimum cost of all paths, that is, If the transmission data volume of a certain link is equal to 0, then the total cost of the path must be greater than the minimum cost, that is,

[0019] In the process of balanced allocation, data needs to be transmitted and processed through multiple layers of nodes (such as j-layer edge computing nodes and k-layer center computing nodes). Each node will perform a specific nonlinear transformation on the input data, resulting in a regular change in data volume during transmission in the computing power network. Although the total amount of information data received by the terminal may differ from the initial input, the sum of the transformed flow on all paths is still equal to the information obtained after processing the data of each enterprise. This relationship is guaranteed by the defined data volume conversion function rule and becomes the basis for path cost calculation and flow adjustment, ultimately driving the entire allocation system to converge to equilibrium, that is,

[0020] Secondly, for the data flow on a certain link x a , it should be equal to the sum of the path flow using this link, that is, the path data volume and the link data volume x a should satisfy the following conditions: the link data volume should be the sum of the path data volume of each (r, s) pair passing through the link, which can be expressed as: At the same time, the total cost of the path and the cost of the link should satisfy the following conditions: the cost of the path should be the sum of the cost of each link it passes through, which can be expressed as:​​​ Where the total cost of the specific path should be equal to the sum of the link cost generated by each link in the data computing service, which is the transmission cost from enterprise to edge computing node, the transmission cost from edge computing node to center computing center, the processing cost of edge computing node and the computing cost of center computing center. We let A1, A2, A3, A4, A5 be the index set corresponding to each layer edge respectively, then A1, A2, A3, A4, A5 represent the link between enterprise and edge computing node, the link on the edge of edge computing node, the link between edge computing node and center computing node, the link on the edge of center computing node and the link from center computing node to enterprise respectively. Different a corresponds to different links, then the cost function c a (x a ) on each link can be expressed as: Finally, the path data volume should satisfy the non-negative constraint, that is

[0021] Based on the above analysis of the cost of computing power network and the process of data flow, we give the equilibrium condition of computing power network: Definition 1 If the following conditions are met, the path flow mode Q* of computing power network reaches the equilibrium state: Where K is the feasible set that satisfies K = {Q* e R +}. Now we give the explanation of the equilibrium condition: if the total cost of enterprise choosing a path to edge computing node and center computing node to complete the calculation is equal to the cost of its shortest path, there will be data flow on this path; on the other hand, if the total cost of enterprise choosing a path to edge computing node and center computing node to complete the calculation exceeds the minimum cost it will take to complete the data calculation, there will be no data flow on this path, because at this time the enterprise can always choose another path to reduce its cost and get greater utility. In addition, the computing power network must satisfy the flow conservation condition, that is, the sum of the data volume on each path between the starting point and the ending point should be equal to the total amount of computing demand.

[0022] Next, we give the variational inequality corresponding to the equilibrium condition in Definition 1: Theorem 1 The data path flow Q* in computing power network can reach the equilibrium state if and only if it satisfies the following variational inequality problem:

[0023] To further study this equilibrium state, if the transportation cost function, the processing cost function and the calculation cost function have symmetric Jacobian matrix and the functions are monotonically non-decreasing, the equilibrium traffic distribution pattern in the computing power network can also be obtained by solving the following convex optimization problem. The following theorem is given: Theorem 2 The equilibrium represented by formula (7) is equivalent to the solution of the nonlinear programming problem represented by formula (8).

[0024] Since the constraints of the model are all linear and the objective function is strictly convex, it is guaranteed that there is only one unique solution to the model, that is, when the equilibrium state is reached, the amount of data allocated to each link is unique. The following proves that the optimization problem in Theorem 2 is the equivalent form of Theorem 1.

[0025] Proof: First, construct the Lagrangian function of formula (10). We let λ rs be the Lagrange multiplier corresponding to the flow conservation constraint, then the original optimization problem can be rewritten as Taking the partial derivative of formula (11) with respect to , we get Therefore, the KKT condition of the Lagrangian function is: If is the optimal solution of formula (10), then there exists a Lagrange multiplier under the equilibrium condition such that: Substituting formula (12) into (13) gives This means that the conditions for the optimal solution of this nonlinear programming problem are exactly the same as the variational inequality form of the computing power network— for all paths from a certain starting point to a certain ending point: if there is data flow, then the total cost of the path is equal, which is the minimum cost through the computing power network; if there is no data flow, the total cost of transmitting data is greater than the minimum cost through the network. Therefore, the equilibrium state described by the variational inequality is the solution of this nonlinear programming problem.

[0026] Q.E.D. 3.2.2 Upper Model

[0027] In the upper layer, the government as the main resource allocator aims to determine the bandwidth B ij , B jkthe optimal investment allocation scheme, so that the total system cost of the computing power network is minimized. It can be expressed in mathematical form as: When the lower-level equilibrium solution is determined, the upper-level model is essentially a convex optimization problem, and the core goal is to determine the optimal investment allocation ii , ΔB ik , under the constraint of the investment budget D total , so that the total system cost C max is minimized.

[0028] According to formula (10) and formula (15), a bi-level programming model between the users and the government managers of the computing power network can be constructed: The bi-level programming model described in formula (16) has an upper-level programming as an investment optimization decision problem and a lower-level as a nonlinear programming derived from user equilibrium transformation. Next, this paper will design an algorithm to solve it. 2. Algorithm design

[0029] To solve the proposed bi-level programming model, an alternating iteration algorithm based on outer investment optimization-inner flow equilibrium is designed. This method combines the upper-level investment decision and the lower-level flow distribution organically: the upper level aims to minimize the system potential function and uses the gradient-projection method to update the investment scheme within the budget constraint set; the lower level solves the user equilibrium problem using the successive averaging method under the given link bandwidth conditions to ensure the convergence of the flow distribution. Specifically, the outer algorithm gives the investment vector ΔB in each iteration, updates the effective bandwidth of each link through the bandwidth-investment function, and passes it to the lower layer. The lower layer uses the MSA algorithm to iteratively correct the flow distribution based on this input until the equilibrium condition is met and outputs the equilibrium flow. Subsequently, the upper layer calculates the objective function and its gradient based on the equilibrium flow result, and updates the investment vector through the gradient-projection method, so that it not only meets the budget constraint but also reduces the total system cost. The outer and inner layers are iterated alternately until the investment vector and the flow distribution converge simultaneously, and the global equilibrium solution of the bi-level model is finally obtained.

[0030] The core advantage of this method is that the MSA algorithm in the lower layer can guarantee the convergence of the flow equilibrium under complex network structures, and the gradient-projection method in the upper layer can ensure that the budget constraint is not violated by continuously correcting the investment allocation, thereby realizing the unified solution of investment decision and flow equilibrium. The specific solving steps are as follows:

[0031] Step 1: Initialize parameters: Set the iteration precision ε, the maximum number of iterations k max , and the given basic bandwidth B ii , B ikSet investment budget D, calculate demand vector OD and initial investment amount ΔB(0) by equal division projection method.

[0032] Step two: Calculate link rate: According to the investment-bandwidth mapping relationship, get the data transmission rate on the link corresponding to the investment:

[0033] Step three: lower level equilibrium initialization: Under the condition of given link rate, carry out a full have-no shortest path allocation for each OD pair to get the initial flow vector x(0).

[0034] Step four: lower level equilibrium iteration: in the kth iteration, in turn: (1) Update link cost: c ii (x), c i (x), c jk (x), c k (x), c ki (x). (2) Full have-no allocation: re-allocate the demand of each OD pair with the updated cost as the edge weight to get the new flow vector y (k) . (3) Flow update: update according to the method of successive average (MSA): (4) Convergence test: if The lower level converges, and the equilibrium solution is x*; otherwise, return to this step to continue iteration.

[0035] Step five: calculate the total cost of system operation: According to the equilibrium flow x* returned by the lower level, calculate the upper level objective function to get the total cost of the system:

[0036] Step six: upper level gradient update: Calculate the gradient about ΔB: Gradient descent update:

[0037] Step seven: projection to budget constraint. Project the updated investment vector to the budget set: Ensure that the investment constraint is strictly met.

[0038] Step 8: Outer layer iteration: Repeat steps two through seven until the outer iteration converges or the maximum number of iterations is reached, to obtain the final investment allocation ΔB* and the corresponding equilibrium flow x. * and system cost C total . Beneficial effects:

[0039] This invention focuses on the optimization of computing power networks under policy-driven investment, specifically addressing the challenge of dynamically coordinating government investment with enterprise computing power demand. By constructing a two-layer planning model led by the government and responded to by enterprises, this invention achieves a balanced allocation of computing resources among enterprise nodes, edge computing nodes, and central computing nodes, effectively reducing system operating costs and improving overall resource utilization. Compared to existing computing power scheduling methods that rely solely on market mechanisms or single-layer optimization, this invention introduces an investment-bandwidth mapping and equilibrium feedback mechanism, enabling the system to automatically adjust bandwidth structure and traffic distribution according to different investment intensities, resulting in higher adaptability and decision-making efficiency. The proposed algorithm framework features a clear structure, scalable parameters, and stable convergence performance, making it applicable to computing power networks of different sizes and levels. This method not only significantly improves the investment efficiency of computing power infrastructure but also promotes the coordinated layout of computing power resources across regions, providing government decision-making departments and computing power service operators with a scientific basis for investment planning and resource scheduling, demonstrating significant theoretical value and promising engineering applications. Attached image description: Figure 1 This is a diagram of the original computing power network structure. Figure 2 This is a diagram of the transformed computing power network structure; Figure 3 This is a schematic diagram of the model. Figure 4 Here is the algorithm flowchart; Figure 5 A diagram of the computing power network structure for example; Detailed implementation method:

[0040] We consider a network consisting of 3 enterprises, 2 edge computing nodes, and 2 central computing centers to construct a numerical simulation. The upper-level government, acting as the manager of the computing network system, plans to invest 10 million yuan to increase bandwidth between enterprises and edge computing centers, and between edge computing centers and central computing centers, thereby reducing the overall operating cost of the system. Enterprises, as lower-level decision-makers, autonomously choose the optimal computing power acquisition path and allocation strategy based on their own computing power needs and service costs within the given network environment. The structure of the lower-level network is as follows: Figure 5As shown, the edge nodes are connected to multiple enterprises, respectively, and can provide low-latency, limited computing power services for enterprises; the central computing nodes have higher computing power but larger communication latency. The link bandwidth capacity, transmission cost, and energy consumption parameters are set according to different connection types to reflect the real cloud-edge-end collaborative characteristics.

[0041] In Figure 5 , nodes 1, 2, and 3 are the starting nodes of the network demand and also the terminating nodes of the demand; nodes 4 and 5 represent two different edge computing nodes; and nodes 6 and 7 represent two different central computing centers. It is assumed that enterprises 1, 2, and 3 have (2000 GB, 3000 GB, 2000 GB) of data to be transmitted to the central computing center for computing and processing due to their own computing resource limitations, as shown in Table 2. Table 2: Data computing demand of each enterprise

[0042] It is assumed that the coefficient e1 related to the data transmission cost is 1, the bandwidth B ij between the enterprise and the edge computing node is [30, 30, 40, 40, 40, 40] Gbps (gigabit per second), and the signal-to-noise ratio M is 1000, so the transmission cost between the enterprise and the edge computing node is:

[0043] It is assumed that the coefficient e2 related to the data transmission cost is 0.5, and the coefficient v i related to the data processing of the edge computing node is 100, so the cost of the edge computing node for processing heterogeneous data is:

[0044] After the data is processed by the edge computing node, the data volume may change due to the influence of the data itself and the hardware and software capabilities of the edge computing node. Here, we consider the simplest scenario, assuming that a4 = a5 = 1, and the data volume remains unchanged. The processed data will be transmitted to the central computing center, and the bandwidth B ij between the edge computing node and the central computing center is [40, 30, 20, 30] Gbps, and the signal-to-noise ratio M is 1000, so the data transmission cost from the edge computing node to the central computing node is:

[0045] It is assumed that the data processing capabilities of different central computing centers are the same, and the processing rate of data per unit time is as shown in Table 3:

[0046] Table 3: Processing rate of each central computing center

[0047] Let e3=0.05 and e4=1, then the data computing cost of the center computing center is:

[0048] Similarly, assuming that the coefficient e1 related to the data product transmission cost is 1, the bandwidth B ki =[30, 30, 30, 40, 40, 40] in Gbps, and the signal-to-noise ratio M=1000, then the transmission cost between the center computing center and the enterprise is:

[0049] In this example, we consider the simplest case, assuming that the data is converted into an equal amount of information after being calculated, that is, α6=α7=1, that is,

[0050] For the upper system manager, under the constraint of a fund budget of 1000 million yuan, the investment in improving the bandwidth B ii , B ik of data transmission in the computing power network is considered. The investment cost functions are:

[0051] Where β1=1 and β2=1. In the model solving process, first, the upper government determines the optimal investment strategy to determine the bandwidth increment ΔB ii , ΔB ik on the ij and jk edges, and then the lower enterprises make path selection and computing power demand decisions based on the policy framework.

[0052] The model is solved using a two-level optimization algorithm based on gradient projection and MSA, and the total cost and data flow distribution under the optimal investment scheme and computing power network equilibrium state are obtained. The total cost of the system after investment is 474.9, and the corresponding investment scheme is shown in the table, and the equilibrium flow, cost and information on each link are shown in Table 4. Table 4 Equilibrium results Table 5 Flow under the equilibrium state of each link

[0053] From the experimental results in Table 4, it can be seen that after solving by gradient projection and MSA alternating iteration algorithm, the computing power network reaches a stable investment-flow balance state under the given budget constraint D = 1000 million yuan. The optimal investment scheme at the government level is concentrated on the key links from enterprises to edge nodes and from edge nodes to central computing nodes. Among them, the investment proportion on the two links of 7 to 10 and 7 to 8 is as high as 23.33% and 19.83% respectively, indicating that in the computing power network structure, the central node 7 as a high-load computing power hub has a significant impact on the overall performance of the system. In contrast, the investment proportion of the enterprise-end links (such as 3 to 5, 3 to 4) is relatively low, only about 3%, showing that the edge layer transmission bottleneck is relatively light.

[0054] From the traffic distribution results, the overall network presents a bottom-up traffic concentration and computing layering feature. The traffic from the enterprise end to the edge node remains balanced (about 400-500 GB), while at the edge node to the central computing node stage, the traffic is significantly concentrated on some backbone links (such as 4 to 6, 5 to 7), indicating that under the condition of concentrated allocation of computing resources, the system naturally forms an equilibrium pattern of "core node intensive computing and edge node distributed collaboration". In addition, the path cost decreases significantly with investment - before investment, the average cost of the main links is about 20.3; after investment, it decreases to about 16, the total operating cost of the system decreases from about 640 to 474.9, with a decrease of 25.8%, verifying the policy investment regulation effect of the model.

Claims

1. A method for making bandwidth investment decisions in computing power networks based on game theory analysis, the method comprising the following technical features: (1) The upper layer takes the government as the decision-making body and establishes a bandwidth investment optimization model under the constraint of total investment budget. The goal is to minimize the total operating cost of the computing power network system. It comprehensively considers the bandwidth investment allocation of key links such as enterprise to edge computing nodes and edge computing nodes to central computing power nodes. This process determines the optimal investment ratio and allocation scheme of each link by setting the correspondence between bandwidth expansion and investment cost, thereby optimizing the bandwidth structure and improving network transmission performance. The upper layer also designs investment budget constraints, bandwidth capacity limits and investment cost non-negative conditions to ensure the feasibility and rationality of investment allocation. In each iteration, the upper layer model dynamically adjusts the investment strategy according to the changes in system operating cost and investment returns, and transmits the updated bandwidth structure and resource distribution information to the lower layer model to drive the computing power balance solution of the lower layer, so as to realize the linkage optimization of government investment decision and enterprise computing power response. (2) The lower layer constructs a computing network containing enterprise nodes, edge computing nodes and central computing nodes. Enterprise data is distributed and processed and computed through edge computing nodes and central computing nodes. The process includes: data transmission from the enterprise to the edge computing node, determining the transmission rate and transmission cost based on bandwidth and signal-to-noise ratio, the edge computing node performing fusion, cleaning and standardization processing on multi-source heterogeneous data, calculating the processing cost based on the processing rate, transmitting the processed data to the central computing node, completing deep computing at the central computing node, calculating the computing cost based on the computing rate, transmitting the generated information products back to the enterprise node through a virtual link, and determining the information conversion amount. (3) Map node costs to edge weights through network transformation to construct an analyzable network cost model; (4) Establish a two-level planning model between government managers and computing power networks: Among them B ij B jk Let ΔB represent the initial bandwidths between ij and jk, respectively. ij ΔB jk Let I represent the bandwidth invested between ij and jk, respectively, and D represent the total investment amount. ij I jk Let represent the bandwidth investment amount on edges ij and jk, respectively; β1 and β2 are coefficients related to investment costs; 'a' is any edge in the computing power network; A is the set of edges in the computing power network; A1, A2, A3, A4, and A5 represent the road segments between the enterprise and edge computing nodes, the road segments on the virtual edges of edge computing nodes, the road segments between edge computing nodes and central computing power nodes, the road segments on the virtual edges of central computing power nodes, and the virtual road segments from central computing power nodes to enterprises, respectively; and c... ij c represents the data transfer cost between ij. j For the data processing cost of edge computing node j, c jk For the data transfer cost between jk, c k The data computation cost for the central computing node k, c ki For the cost of data product transmission between ki, Let r be the data traffic on the p-th path with a starting point r and an ending point s. These are 0-1 variables related to road segments and paths. If road segment a belongs to the p-th path starting from r and ending at s, then... otherwise α represents the parameters related to the algorithm and hardware used by edge computing node j. k q represents the parameters related to the algorithm and hardware used by the central computing node k. rs The total amount of data, starting from r and ending at r; (5) The algorithm of alternating iteration based on outer layer investment optimization and inner layer traffic balance is used to solve the problem until the convergence condition is reached. Finally, the optimal bandwidth investment plan of the government and the balanced allocation of computing network resources, the cost of each link and the final system cost are obtained.

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