VNF multi-dimensional resource demand prediction method based on synchronous and asynchronous space-time characteristic fusion

By integrating the asynchronous spatiotemporal characteristics in VNF multi-dimensional resource demand prediction and building a multi-module prediction network model, the problem of ignoring asynchronous features in the existing technology is solved, and the prediction accuracy and the accuracy of resource scheduling are significantly improved.

CN119740095AActive Publication Date: 2025-04-01XIDIAN UNIV
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Patent Information

Application Number
CN202411811742.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-10
Publication Date
2025-04-01
Estimated Expiration
2044-12-10

AI Technical Summary

Technical Problem

When predicting the multi-dimensional resource requirements of virtual network functions (VNF), the prior art ignores the impact of asynchronous between different VNFs, resulting in insufficient prediction accuracy.

Method used

The VNF multi-dimensional resource demand prediction method based on the fusion of homo-asynchronous spatiotemporal characteristics is adopted. By constructing a prediction network model including a cascading enhanced feature extraction module, a delay correlation extraction module, an asynchronous adjacency matrix construction module and an asynchronous spatiotemporal feature fusion module, a synchronous spatial characteristics, asynchronous spatial characteristics and temporal characteristics of VNF are fused.

Benefits of technology

It effectively improves the prediction accuracy of VNF multi-dimensional resource requirements, avoids the defect of ignoring asynchronous features in the prior art, and significantly improves the accuracy of resource scheduling.

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Abstract

The invention provides a VNF multi-dimensional resource demand prediction method based on synchronous and asynchronous time-space characteristic fusion. The implementation steps are as follows: obtaining an auxiliary sample set, a training sample set and a test sample set; constructing a VNF multi-dimensional resource demand prediction network model based on synchronous and asynchronous time-space characteristic fusion, and performing iterative training on the VNF multi-dimensional resource demand prediction network model; and obtaining a VNF multi-dimensional resource demand prediction result. In the process of carrying out iterative training on the prediction network model and obtaining the prediction result, the synchronous-asynchronous spatial-temporal feature fusion module can fuse the synchronous spatial feature, the asynchronous spatial feature and the time feature of the VNF at the same time by replacing the normalized adjacent matrix of the graph with the synchronous-asynchronous adjacent matrix; the defect that asynchronous spatial features between different VNFs are ignored in the prior art is avoided, and the prediction precision of the VNF multi-dimensional resource demand is effectively improved.
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Description

Technical Field

[0001] The present invention belongs to the field of network and communication technology, and relates to a VNF multi-dimensional resource demand prediction method based on the fusion of synchronous and asynchronous spatiotemporal characteristics, which can be applied to predicting the multi-dimensional resource demand of VNF. Background Art

[0002] Network Function Virtualization (NFV) is a network architecture and concept that separates traditional network functions (such as routing, switching, firewalls, load balancing, etc.) from dedicated hardware devices through virtualization technology and deploys them on general-purpose hardware devices. Virtualized Network Functions (VNF) is a specific implementation in the NFV framework, which represents a specific instance of network functions in a virtualized environment. Each VNF implements a specific function of the network, such as firewalls, routers, switches, etc. They no longer rely on dedicated hardware, but run on a virtualized platform. Multiple VNFs are linked together in a specific order to form a service function chain (SFC). Through SFC, data flows through a series of VNFs in a predetermined order in the network, thereby realizing complex network services. The demand for CPU resources, memory resources, and bandwidth resources of running VNFs is highly dynamic. On the one hand, if there is no prediction, there may be over-allocation of resources, resulting in resource waste; on the other hand, if there are insufficient resources, VNFs may not operate normally, affecting the quality of network services. By predicting the CPU resource requirements, memory resource requirements, and bandwidth resource requirements (multi-dimensional resource requirements) of VNFs, resource scheduling can be performed in advance based on future resource requirements to achieve elastic scaling of resources.

[0003] In July 2024, Tang Lun et al. proposed a prediction model (DT-TCN) based on graph convolutional neural network (GCN) and temporal convolutional network (TCN) in a patent application with patent publication number CN119030877A and titled "A method for active migration of virtual network functions assisted by digital twins based on resource prediction". The model extracts spatiotemporal features based on SFC topology to improve the accuracy of VNF resource demand prediction. GCN extracts spatial features based on the graph adjacency matrix, and TCN is used to extract global information of time series. The defect of this method is that when GCN is used to extract spatial features, only the synchronous spatial correlation between different VNFs can be extracted, while the asynchronous influence between different VNFs is ignored. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and propose a VNF multi-dimensional resource demand prediction method based on the fusion of synchronous and asynchronous spatiotemporal characteristics, aiming to improve the accuracy of VNF multi-dimensional resource demand prediction.

[0005] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0006] (1) Obtain auxiliary sample sets, training sample sets, and test sample sets:

[0007] The multi-dimensional resource demand data of T time steps contained in each VNF in N VNFs are normalized, and the multi-dimensional resource demand data of S time steps of each VNF are divided, and then the first U data blocks of length M and their labels after division are used as training sample sets, and the remaining V data blocks are used as test sample sets. P The auxiliary sample set consists of multi-dimensional resource demand data, where N≥1, T=S+T P , T≥10000, S=U+V+M, M≥5;

[0008] (2) Construct a VNF multi-dimensional resource demand prediction network model based on the fusion of synchronous and asynchronous spatiotemporal characteristics:

[0009] Construct a VNF multi-dimensional resource demand prediction network model O including a cascaded enhanced feature extraction module, a delay correlation extraction module, a synchronous and asynchronous adjacency matrix construction module, and a synchronous and asynchronous spatiotemporal feature fusion module;

[0010] (3) Iterative training of the prediction network model:

[0011] The prediction network model O is iteratively trained through the auxiliary sample set and the training sample set to obtain the trained prediction network model O * ;

[0012] (4) Obtain VNF multi-dimensional resource demand prediction results:

[0013] The test sample set is used as the trained prediction network model O * The input is forward propagated to obtain the predicted value of each test sample.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] In the process of iteratively training the prediction network model and obtaining the prediction results, the synchronous and asynchronous spatiotemporal feature fusion module of the present invention replaces the normalized adjacency matrix of the graph with the synchronous and asynchronous adjacency matrix, which can simultaneously fuse the synchronous spatial features, asynchronous spatial features and time features of the VNF, avoiding the defect of the prior art that ignores the asynchronous spatial features between different VNFs, and effectively improving the prediction accuracy of the VNF multi-dimensional resource requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flow chart for realizing the present invention;

[0017] Figure 2 The figure is a comparison chart of simulation results of prediction accuracy between the present invention and the prior art. DETAILED DESCRIPTION

[0018] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0019] Reference Figure 1 , the present invention comprises the following steps:

[0020] Step 1: Get auxiliary sample set, training sample set and test sample set:

[0021] Step 1a) For each of the N VNFs, the multi-dimensional resource demand data X = {X1, X1, …, X2, …, X3, …, X4, …, X5, …, …, X6, …, …, X7, …, …, X8, …, …, X9, …, …, X1 ...2, …, …, X3, …, …, X4, …, …, X8, n ,…,X N}Min-Max normalization is performed, where N=6, T=15000, and the time interval of each time step is 30s. It is a VNF n Multidimensional resource demand data with a total of T time steps, It is a VNF n Multidimensional resource demand data at the tth time step, VNF n The CPU resource requirements, memory requirements, and bandwidth requirements at the tth time step are expressed as Represents VNF n The r-type demand at the t-th time step, r∈{cpu,mem,bdw}, The normalized formula is:

[0022]

[0023] in, yes The normalized result, x r,min 、x r,maxThey are the minimum and maximum values ​​of N×T r types of resource demand data respectively; data normalization is to scale the data proportionally to the same data interval and range to reduce the impact of scale, characteristics, distribution differences on the model, which can effectively improve the convergence speed and fitting effect of the model.

[0024] Step 1b) The normalized multi-dimensional resource demand data of each VNF in S time steps are divided by a sliding window of length M+1 time steps with a time step as the step length, and the first M of the multi-dimensional resource demand data of each N VNF after each division, each containing M+1 time steps, are used as a data block, and the last one is used as the label of the data block. A total of SM divisions are performed to obtain SM data blocks of size N×M and their labels. The first U data blocks of length M after the division and their labels form the training sample set, the remaining V data blocks form the test sample set, and the normalized N×T data blocks that are not divided are used as the test sample set. P The multi-dimensional resource demand data is used to form an auxiliary sample set to extract enhanced features, where S = 13000, T p =2000, M=9; each sample obtained by the above division is the historical resource demand data of 6 VNFs, each containing 9 time steps, and the corresponding label is the multi-dimensional resource demand data of the 6 VNFs in the next time step, that is, the multi-dimensional resource demand data of each VNF in the previous 9 time steps is used to predict the multi-dimensional resource demand data of the VNF in the next time step.

[0025] Step 2: construct a VNF multi-dimensional resource demand prediction network model O including a cascaded enhanced feature extraction module, a delay correlation extraction module, a synchronous and asynchronous adjacency matrix construction module, and a synchronous and asynchronous spatiotemporal feature fusion module:

[0026] Step 2a) Construct an enhanced feature extraction module: Since the multi-dimensional resource requirements of each VNF, namely, the CPU resource requirements, memory resource requirements, and bandwidth resource requirements, are inconsistent over time, it is necessary to extract a time series that can reflect the overall change trend of these three-dimensional features for each VNF, namely, the enhanced feature, which is used to analyze the latency correlation between different VNFs; VNF n The enhanced features can be expressed as in The calculation formula is:

[0027]

[0028] It is a VNF n In the t p With t p -Euclidean distance of multi-dimensional resource demand data at 1 time step, indicating VNF nThe overall change of the three-dimensional resource demand data at this time step relative to the three-dimensional resource demand data at the previous time step; The sign of is determined by the voting mechanism, that is, if there is more than one resource demand data in the three-dimensional resource demand data that increases relative to the previous time step, then is positive, otherwise it is negative.

[0029] Step 2b) constructing a delay correlation extraction module: the delay correlation extraction module includes a cascaded delay correlation calculation submodule and a maximum correlation delay extraction submodule;

[0030] The delay correlation calculation submodule obtains the enhanced feature set EF={EF1, EF2, …EF n ,…,EF N}, calculate each two adjacent VNFs i and VNF j Enhanced features of EF i With EF j,Δt Delay correlation The calculation formula is:

[0031]

[0032] Where DR(·) represents the operation of calculating the Spearman correlation coefficient, and Δt is VNF j Enhanced features of EF j Relative VNF i Enhanced features of EF i Delayed time step; The Spearman correlation coefficient is a statistic that measures the strength of the monotonic relationship between two time series and can also be used for nonlinear analysis; The value of the Spearman correlation coefficient is between -1 and 1. The closer it is to 1, the stronger the correlation between the two series.

[0033] The maximum correlation delay extraction submodule calculates the maximum correlation delay of each pair of adjacent VNFs based on the delay correlation calculation submodule. i and VNF j The delay correlation between them is calculated, and the delay when their delay correlation is the largest is calculated:

[0034]

[0035] Where Δt0 is The value of Δt at the maximum, 1≤i,j≤N, i≠j, max(@) indicates the operation of taking the maximum value;

[0036] Finally, the maximum correlation delay extraction submodule obtains the maximum correlation delay set D = {D i,j |1≤i,j≤N}.

[0037] Step 2c) Constructing a synchronous and asynchronous adjacency matrix construction module: The synchronous and asynchronous adjacency matrix construction module needs to construct the maximum correlation delay set D={D i,j |1≤i,j≤N} to construct the synchronous and asynchronous adjacency matrix M SA , M SA It includes M×M sub-blocks of dimension N×N, and the sub-block A in the rth row and cth column r,c The construction method is:

[0038] When r = c:

[0039] A r,c =A adj

[0040] When r≠c:

[0041]

[0042] Among them, A r,c is the block matrix M SA The sub-block of row r and column c, A adj is the adjacency matrix of the graph representing the service function chain, is the matrix A r,c The element in row a and column b, D a,b ∈D;

[0043] M SA It will be used in the synchronous and asynchronous spatiotemporal feature fusion module to extract synchronous and asynchronous spatiotemporal features.

[0044] Step 2d) constructing a synchronous and asynchronous spatiotemporal feature fusion module: comprising a cascaded synchronous and asynchronous spatial feature fusion graph convolution submodule and a long short-term memory LSTM submodule, wherein the long short-term memory LSTM submodule comprises N parallel LSTM networks;

[0045] The synchronous and asynchronous spatial feature fusion graph convolution submodule is composed of two layers of graph convolutional networks GCN stacked together. The activation function of each GCN layer is ReLU, and the adjacency matrix of each GCN layer is replaced by the synchronous and asynchronous adjacency matrix M SA Instead, the forward propagation formula of the synchronous and asynchronous spatial feature fusion graph convolution submodule is:

[0046] H = ReLU(M SA ReLU(M SA XW1)W2)

[0047] Where ReLU(·) represents the activation function, X=[X t-M+1 ,X t-M+2 ,…,X t ] T is a training sample, where is the multi-dimensional resource demand data of N VNFs at the t-th time step, and is a learnable weight parameter.

[0048] Use M SA The purpose of replacing the adjacency matrix is: when using the adjacency matrix for graph convolution, each VNF can only fuse the features of the adjacent VNFs at that time step, that is, the synchronous spatial features, and cannot consider the asynchronous features of the adjacent VNFs. By replacing the adjacency matrix with the synchronous and asynchronous adjacency matrix, in the process of graph convolution, VNF i Features extracted at time step t for:

[0049]

[0050] in, It is a VNF i The feature at the tth time step, is the total number of VNFs at time step t i The sum of the features of adjacent VNFs, Is with VNF i Adjacent VNFs k At t+D i,k The characteristics of the time step, where D i,k It is a VNF i With VNF k The maximum correlation delay between them is W∈{W1,W2}; then yes Hidden features after aggregating synchronous spatial features and asynchronous spatial features.

[0051] The LSTM submodule consists of N parallel LSTM networks. Each LSTM network consists of two stacked LSTM layers and a fully connected layer. The number of LSTM neurons in each layer is set to N, and the number of neurons in the fully connected network is set to 1. The N LSTM networks receive the hidden features of N VNFs respectively. n The hidden features of There are M time steps in total.

[0052] Step 3: Iteratively train the prediction network model:

[0053] Step 3a) Initialize the number of iterations to k, the maximum number of iterations to K, K = 100, and the prediction network model O of the kth iteration k The weight is W k , and let k = 1;

[0054] Step 3b) The enhanced feature extraction module extracts the enhanced features EF of each VNF based on the auxiliary sample set.n , then the enhanced features of N VNFs constitute the enhanced feature set EF = {EF1, EF2, …EF n ,…,EF N}, The delay correlation extraction module extracts the delay correlation of EF; the synchronous and asynchronous adjacency matrix construction module constructs a synchronous and asynchronous adjacency matrix M with a dimension of MN×MN through the extracted maximum correlation delay set D. SA , where EF n It is a VNF n The enhanced features of It is the tth p Enhanced features of time steps;

[0055] Step 3c) Synchronous and asynchronous spatiotemporal feature fusion module with M SA As the adjacency matrix, we perform graph convolution on the training samples and obtain the hidden features H = [H1, H2, ..., H n ,…,H N ] T , the N LSTM networks connected in parallel in the LSTM submodule extract H1, H2, …, H n ,…,H N The time characteristics of each training sample are obtained by pred ,in It is a VNF n Hidden features of

[0056] Step 3d) Use the mean square error loss function and pass the true label Y of each training sample true and the predicted value Y pred Calculate the loss value Loss of the prediction network model, and then use Loss to k Update to get the prediction network model O of this iteration k ; The calculation formula of the loss value Loss, and the calculation of W k The update formulas for updating are:

[0057]

[0058] m k =β1m k-1 +(1-β1)g k

[0059]

[0060]

[0061] in Represents VNF n The predicted value and actual value of multi-dimensional resource demand data, α=0.01 represents the learning rate, g k is the loss function for the parameter W k Find the gradient after partial derivative, m k and v k are the first-order moment estimate and the second-order moment estimate of the gradient in momentum form, and is the bias-corrected first-order moment estimate and the bias-corrected second-order moment estimate, β1=0.9 and β2=0.999 are the decay rates, ε=10 -8 is a constant.

[0062] Step 3e) Determine k = K, if so, obtain the trained prediction network model O * , otherwise, let k = k + 1, O k =O, and execute step 3c).

[0063] Step 4: Obtain VNF multi-dimensional resource demand prediction results: Use the test sample set as the trained prediction network model * The input is forward propagated to obtain the predicted value of each test sample.

[0064] The technical effect of the present invention is further described below in conjunction with simulation experiments:

[0065] 1. Simulation experiment conditions:

[0066] The simulation experiment software platform of the present invention is: the experimental computer operating system is Window10 (64-bit), the memory is 32GB, the processor configuration is: Intel(R) Core(TM) i7-10870H CPU@2.20GHz2.21GHz, implemented in Python language, version is Python3.8, the experimental operating environment is JetBrains PyCharm Community Edition2020.2, and the deep learning framework is Pytorch2.1.0.

[0067] 2. Simulation content and results analysis:

[0068] The prediction accuracy of the present invention and an existing digital twin-assisted virtual network function active migration method based on resource prediction are compared and simulated, and the results are as follows: Figure 2 As shown:

[0069] Reference Figure 2 (a), (b), and (c) are three indicators of prediction accuracy: mean square error MSE, mean absolute error MAE, and determination coefficient R2-SCORE. The horizontal axis is the resource demand type, and the vertical axis is the values ​​of MSE, MAE, and R2-SCORE, respectively.

[0070] The calculation formulas for MSE, MAE and R2-SCORE are:

[0071]

[0072]

[0073] Among them, x t Represents the true value of the sampling point at sampling time t, represents the predicted value of the sampling point at sampling time t, Represents the mean of all sampling points contained in the training sample.

[0074] from Figure 2 It can be seen that the values ​​of MSE and MAE of the present invention are closer to 0, and R2-SCORE is closer to 1, indicating that the prediction accuracy of the present invention is significantly higher than that of the prior art.

Claims

1. A VNF multi-dimensional resource demand prediction method based on the fusion of synchronous and asynchronous spatiotemporal characteristics, characterized in that: The steps include: (1) Obtain auxiliary sample sets, training sample sets, and test sample sets: The multi-dimensional resource demand data of T time steps contained in each VNF in N VNFs are normalized, and the multi-dimensional resource demand data of S time steps of each VNF are divided, and then the first U data blocks of length M and their labels after division are used as training sample sets, and the remaining V data blocks are used as test sample sets. P The auxiliary sample set consists of multi-dimensional resource demand data, where N≥1, T=S+T P , T≥10000, S=U+V+M, M≥5; (2) Construct a VNF multi-dimensional resource demand prediction network model based on the fusion of synchronous and asynchronous spatiotemporal characteristics: Construct a VNF multi-dimensional resource demand prediction network model O including a cascaded enhanced feature extraction module, a delay correlation extraction module, a synchronous and asynchronous adjacency matrix construction module, and a synchronous and asynchronous spatiotemporal feature fusion module; (3) Iterative training of the prediction network model: The prediction network model O is iteratively trained through the auxiliary sample set and the training sample set to obtain the trained prediction network model O * ; (4) Obtain VNF multi-dimensional resource demand prediction results: The test sample set is used as the trained prediction network model O * The input is forward propagated to obtain the predicted value of each test sample.

2. The method according to claim 1, characterized in that The multi-dimensional resource demand data of each VNF in the N VNFs described in step (1) is normalized for the T time steps, where VNF n Multidimensional resource demand data at the tth time step Including VNF n CPU resource demand data Memory requirements data and bandwidth requirements data right The normalization formula is: in, yes The normalized result is It is a VNF n The resource demand data of type r at the tth time step, X r,min , X r,max They are respectively the minimum and maximum values ​​of r-type resource demand data among N×T multi-dimensional resource demand data.

3. The method according to claim 1, characterized in that The normalized multi-dimensional resource demand data of each VNF in S time steps described in step (1) is divided as follows: Through a sliding window with a length of M+1 time steps, the normalized multi-dimensional resource demand data of S time steps of each VNF is divided with a time step as the step size, and the first M data blocks of the multi-dimensional resource demand data of M+1 time steps of each N VNF after each division are used as the label of the data block, and a total of SM divisions are performed to obtain SM data blocks of size N×M and their labels.

4. The method according to claim 1, characterized in that: The VNF multi-dimensional resource demand prediction network model based on the fusion of synchronous and asynchronous spatiotemporal characteristics described in step (2), wherein: A delay correlation extraction module, comprising a cascaded delay correlation calculation submodule and a maximum correlation delay extraction submodule; The synchronous and asynchronous spatiotemporal feature fusion module includes a cascaded synchronous and asynchronous spatial feature fusion graph convolution submodule and a long short-term memory LSTM submodule, and the long short-term memory LSTM submodule includes N parallel LSTM networks.

5. The method according to claim 1, characterized in that The iterative training of the prediction network model O described in step (3) is implemented as follows: (5a) The number of initial iterations is k, the maximum number of iterations is K, K ≥ 50, and the prediction network model O of the kth iteration k The weight is W k , and let k = 1; (5b) The enhanced feature extraction module extracts the enhanced features EF of each VNF based on the auxiliary sample set n , then the enhanced features of N VNFs constitute the enhanced feature set EF = {EF1, EF2, …EF n ,…,EF N }, The delay correlation extraction module extracts the delay correlation of EF; the synchronous and asynchronous adjacency matrix construction module constructs a synchronous and asynchronous adjacency matrix M with a dimension of MN×MN through the extracted maximum correlation delay set D. SA , where EF n It is a VNF n The enhanced features of It is the tth p Enhanced features of time steps; (5c) The synchronous and asynchronous spatiotemporal feature fusion module is based on M SA As the adjacency matrix, we perform graph convolution on the training samples and obtain the hidden features H = [H1, H2, ..., H n ,…,H N ] T , the N LSTM networks connected in parallel in the LSTM submodule extract H1, H2, …, H n ,…,H N The time characteristics of each training sample are obtained by pred ,in It is a VNF n Hidden features of (5d) uses the mean square error loss function and passes the true label Y of each training sample true and the predicted value Y pred Calculate the loss value Loss of the prediction network model, and then use Loss to k Update to get the prediction network model O of this iteration k ; (5e) Determine k = K. If so, obtain the trained prediction network model O * , otherwise, let k = k + 1, O k =O, and execute step (5c).

6. The method according to claim 5, characterized in that The tth p Enhanced features of time steps The calculation formula is: Among them, |·| represents the absolute value operation.

7. The method according to claim 5, characterized in that The delay correlation extraction module described in step (5b) extracts the delay correlation of EF, and the implementation steps are as follows: The delay correlation calculation submodule calculates the delay correlation between each two adjacent VNFs in the enhanced feature set EF. i and VNF j Enhanced features of EF i With EF j,Δt Delay correlation The maximum correlation delay extraction submodule is based on Calculating Delay Correlation The maximum delay D i,j , we get the maximum correlation delay set D = {D i,j |1≤i,j≤N}, where D i,j The calculation formulas are: Where DR(·) represents the operation of calculating the Spearman correlation coefficient, and Δt is VNF j Enhanced features of EF j Relative VNF i Enhanced features of EF i The delayed time step, Δt0, is The value of Δt at the maximum, 1≤i,j≤N, i≠j, max(·) represents the operation of taking the maximum value.

8. The method according to claim 5, characterized in that The synchronous and asynchronous adjacency matrix M described in step (5b) SA , including M×M sub-blocks of dimension N×N, sub-block A in row r and column c r,c The construction method is: When r = c: A r,c =A adj When r≠c: Among them, A adj is the adjacency matrix of the graph representing the service function chain, is the matrix A r,c The element in row a and column b, D a,b ∈D.

9. The method according to claim 5, characterized in that The hidden feature H described in step (5c) is calculated as: H=ReLU(M SA ReLU(M SA XW1)W2) Among them, ReLU() represents the activation function, X represents the training sample, and W1 and W2 are learnable weight parameters.

10. The method according to claim 5, characterized in that The calculation formula of the loss value Loss of the prediction network model in step (5d) and the calculation formula of W k The update formulas for updating are: m k =β1m k-1 +(1-β1)g k in Represents VNF n The predicted value and actual value of multi-dimensional resource demand data, α represents the learning rate, g k is the loss function for the parameter W k Find the gradient after partial derivative, m k and v k are the first-order moment estimate and the second-order moment estimate of the gradient in momentum form, and is the bias-corrected first-order moment estimate and the bias-corrected second-order moment estimate, β1 and β2 are the decay rates, and ε is a constant.

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