CN115865804A - SDN route optimization method based on link flow prediction - Google Patents
SDN route optimization method based on link flow prediction Download PDFInfo
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Abstract
The invention discloses an SDN route optimization method based on link flow prediction, wherein a network link flow prediction model is designed based on an attention mechanism and a multi-graph view diagram neural network, link flow data can be directly processed in an original graph-based network topology, dynamic space-time characteristics are effectively captured, and the accuracy of link flow prediction is improved. According to the invention, the influence caused by the time delay of the controller for acquiring the network state is reduced through the prediction model, so that the routing decision of the controller is more accurate.
Description
Technical Field
The invention relates to the technical field of Software Defined Networking (SDN), in particular to an SDN route optimization method based on link flow prediction.
Background
In recent years, the popularity of social media, high-definition movies, and online games has led to a rapid increase in network traffic and an increasing scale of networks. Under a huge traffic data environment, network devices face an increasing forwarding pressure. In a real network environment, network traffic may peak within a certain period of time, and a valley period may occur. When the generated traffic is excessive and concentrated, it may cause the network to be broken down; in the area with sparse traffic, the network device may not obtain a good utilization rate because it is in an idle state for a long time.
In software defined networks, making routing decisions requires obtaining network link traffic information. However, there is a delay in the process of periodically acquiring the network link traffic information by the controller, including: a. the time delay of a safe channel from the switch to the controller; b. link delay of the forwarding layer; c. the switch processes the delay of the data packet, and the existence of the delay causes the time difference between the network link flow information acquired by the controller and the current information. At this time, the link resources may have changed, so that the issued flow table cannot effectively utilize the network resources, and the network congestion may be aggravated accordingly in the case of high load.
Disclosure of Invention
The invention aims to solve the problem that the existing software defined network has time delay in acquiring network link flow information so as to influence routing decision, and provides an SDN (software defined network) route optimization method based on link flow prediction.
In order to solve the problems, the invention is realized by the following technical scheme:
an SDN route optimization method based on link flow prediction comprises the following steps:
Step 2, constructing a link flow prediction model by an SDN application plane; the link flow prediction model consists of 4 sub-models and a selection full-connection layer; each sub-model consists of an input full-link layer, an attention mechanism module, a convolution module consisting of a graph convolution unit and a time convolution unit, and an output full-link layer; the input end of the submodel is formed by the input end of the input full connection layer, the output end of the input full connection layer is connected with the input end of the attention mechanism module, the output end of the attention mechanism module is connected with the input end of the graph convolution unit, the output end of the graph convolution unit is connected with the input end of the time convolution unit, and the output end of the time convolution unit is connected with the input end of the output full connection layer; the input ends of the 4 sub-models form 4 groups of input ends of the link flow prediction model, the output ends of the 4 sub-models are simultaneously connected with the input end of the selected full connection layer, and the output end of the selected full connection layer forms the output end of the link flow prediction model;
step 3, the SDN application plane utilizes the training data set to carry out off-line training on the link flow prediction model, namely, an adjacent matrix A in the training data set is firstly used AD Short-term traffic sequence with historical time tSending the data into a first group of input ends of a link flow prediction model, and training an adjacency matrix A in a data set AD Long-term flow sequence based on the historical time t->Sending the traffic into a second set of input terminals of the link traffic prediction model, and training a source-destination traffic matrix at the historical time t in the data set to->Short-term flow sequence based on the historical time t->Sending the traffic into a third group of input ends of the link traffic prediction model, and training a source-destination traffic matrix of the historical time t in the data set to be->Long-term flow sequence based on the historical time t->Sending the link flow into a fourth group of input ends of the link flow prediction model, and outputting a predicted value of the link flow at historical time t +1 by an output end of the link flow prediction model>And then the predicted value of the link flow at the historical time t +1 output by the link flow prediction model is used for combining>True value X of link traffic with historical time t +1 in training dataset t+1 The mean square error of the model is used as a loss function, and model parameters are updated through back propagation, so that a trained link flow prediction model is obtained;
step 4, the SDN control plane collects real-time network information and flow data of the SDN data plane and sends the real-time network information and flow data into the SDN application plane; wherein the real-time network information and traffic data comprises an adjacency matrix A AD Source-destination traffic matrix for current time tShort-term flow sequence at the present time t>And a long-term flow sequence at the current time t>
Step 5, the SDN application plane sends real-time network information and flow data into a trained link flow prediction model for prediction, namely an adjacency matrix A AD Short-term traffic sequence with current time tFeeding into a first set of inputs of a trained link traffic prediction model, an adjacency matrix A AD Long-term flow sequence based on the current time t>The source-destination traffic matrix at the current time t' is asserted into a second set of inputs of the trained link traffic prediction model>Short-term flow sequence based on the current time t>A source-destination traffic matrix->Long-term flow sequence based on the current time t>Sending the data to the fourth group of input ends of the trained link flow prediction model, and outputting the data from the output end of the trained link flow prediction modelThe next time t' +1 of the link trafficAnd returning to the SDN control plane;
step 6, the SDN control plane uses the predicted value of the link flow at the next time t' +1And calculating a data packet forwarding path as a link weight of a Dijkstra algorithm, generating a switch flow entry, and sending the switch flow entry to each switch of the SDN data plane to realize the routing optimization of the SDN data plane.
In the step 1:
adjacency matrix A AD Comprises the following steps:
A AD =[a ij ] k×k
Actual value X of link flow at historical time t +1 t+1 Comprises the following steps:
in the formula, a ij For switches v in SDN data plane i And a switch v j (ii) an adjacent relationship of (a);for a source host h in the SDN data plane at the current time t i To the destination host h j A normalized value of the transmitted traffic; />Switch links e in the historical time t +1SDN data plane respectively 1 ,e 2 ,…,e r The flow transmitted between the exchangers at the two ends; x ■ The actual value of link traffic for time 9632; r is the interception length of the short-term flow sequence, L is the interception length of the long-term flow sequence, n is the sampling frequency of the link flow per hour, and m is the number of sampling points intercepted by the link flow per hour; k is the number of switches in the SDN data plane, l is the number of hosts in the SDN data plane, and r is the number of switch links in the SDN data plane.
In the step 4:
adjacency matrix A AD Comprises the following steps:
A AD =[a ij ] k×k
in the formula, a ij For switches v in SDN data plane i And a switch v j (ii) an adjacent relationship of (a);for a source host h in the SDN data plane at the current time t i To the destination host h j A normalized value of the transmitted traffic; x ■ The actual value of link traffic for time 9632; r is the interception length of the short-term flow sequence, L is the interception length of the long-term flow sequence, n is the sampling frequency of the link flow per hour, and m is the number of sampling points intercepted by the link flow per hour; k is the number of switches in the SDN data plane, l is the number of hosts in the SDN data plane, and r is the number of switch links in the SDN data plane.
Compared with the prior art, the network link flow prediction model is designed based on the attention mechanism and the multi-graph view neural network, the link flow data can be directly processed in the original graph-based network topology, the dynamic space-time characteristics are effectively captured, and the accuracy of link flow prediction is improved. According to the invention, the influence caused by the time delay of the controller for acquiring the network state is reduced through the prediction model, so that the routing decision of the controller is more accurate.
Drawings
Fig. 1 is an architecture diagram of a link traffic prediction model.
Fig. 2 is a schematic diagram of an SDN architecture to which the present invention is applied.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to specific examples.
Modeling a computer network scenario of an SDN data plane. A data plane of the SDN may represent a topological network formed by switches and hosts with a symbol G, defining G = (H, V, E); h represents a set of hosts in a computer network topology, H = (H) 1 ,h 2 ,…,h l ) L is the number of all hosts; v denotes a set of switches in a computer network topology, V = (V) 1 ,v 2 ,…,v k ) K is the number of all switches; if the exchange v i And a switch v j Adjacent exchange v i And v j There is a link connected between them, the link connected is defined as a switch v i And a switch v j Switch link e between ij The set of all edges is denoted as E, E = (E) 1 ,e 2 ,…,e r ) And r is the number of all switch links.
Flow rateDenotes the source host h at time t i To the destination host h j Sending flow is all source hosts h of the computer network of the SDN data plane in time t i To the destination host h j The transmitted traffic constitutes a traffic demand matrixWhere l is the number of all hosts.
Matrix of demand for flowCarrying out Min-Max data normalization processing to obtain a source-destination matrixWherein->To source host h at time t i To the destination host h j Normalized value of traffic sent to each other:
in the formula (I), the compound is shown in the specification,to source host h at time t i To the destination host h j The transmitted flow is->As a traffic demand matrix D t Is selected, and a minimum flow of>As a traffic demand matrix D t Of the flow rate.
(2) Defining an adjacency matrix A AD
Adjacency matrix A AD =[a ij ] k×k Wherein a is ij Representing a switch v i And a switch v j The adjacent relation of (2). When the switch v i And a switch v j When adjacent to each other, a ij =1; when the switch v i And a switch v j When they are not adjacent, a ij =0。
(3) Defining link traffic X over time t t
Switch link e during time t ij Flow rate ofEqual to switch v during time t i And exchange v j The traffic sent to each other, namely:
in the formula (I), the compound is shown in the specification,for the exchange v within time t i To the exchange v j The transmitted flow is->For switching v within time t j To the exchange v i The traffic sent.
Link traffic X consisting of traffic of all switch links in a computer network of SDN data plane within time t t Comprises the following steps:
in the formula (I), the compound is shown in the specification,respectively representing the switch link e during time t 1 ,e 2 ,…,e r The flow rate of (c).
Consider that link traffic of a computer network has both short-term and long-term temporal dependencies. In order to capture the periodic characteristics of the data long-term flow sequence and the short-term flow sequence, the invention sets two sequence sampling modes of long term and short term. Assuming that the sampling frequency is n times per hour, the interception length of the short-term flow sequence is R, and the interception length of the long-term flow sequence is L.
The short-term flow sequence is a continuous sequence, R link flows are continuously intercepted, and the short-term flow sequence of time tComprises the following steps:
the long-term flow sequence is a discrete sequence, and m sampling points are intercepted every hour, wherein m<n, the long-term flow sequence intercepts the data of the previous L/m hours, and then the long-term flow sequence of the time tComprises the following steps:
an SDN route optimization method based on link flow prediction specifically comprises the following steps:
A traffic monitoring module of the SDN control plane obtains historical network information and traffic data, including an adjacency matrix A AD Source-destination traffic matrix for historical time tShort-term traffic sequence in history time t>Long-term flow sequence ^ at historical time t>And the actual value X of the link traffic at the historical time t + 1 t+1 。
And 2, constructing a link flow prediction model by the SDN application plane.
The architecture of the link traffic prediction model is shown in fig. 1. The link flow prediction model is based on the multiple map view angles of the adjacency graph and the OD graph, and is constructed by adopting two modes of a short-term flow sequence and a long-term flow sequence. The model has two structurally identical components from two perspectives of a neighborhood network map (neighborhood matrix) and an OD map (OD matrix), each component containing two submodels to capture features of short-term and long-term traffic sequence characteristics. Each sub-model consists of an input full link layer, an attention mechanism module, a convolution module and an output full link layer. The convolution module comprises a graph convolution unit and a time convolution unit, wherein the graph convolution unit is a two-layer GCN (graph convolution neural network), and the time convolution unit is a one-layer CNN (convolution neural network). The input end of the submodel is formed by the input end of the input full-connection layer, the output end of the input full-connection layer is connected with the input end of the attention mechanism module, the output end of the attention mechanism module is connected with the input end of the graph convolution unit, the output end of the graph convolution unit is connected with the input end of the time convolution unit, and the output end of the time convolution unit is connected with the input end of the output full-connection layer. The input ends of the 4 sub-models form 4 groups of input ends of the link flow prediction model, the output ends of the 4 sub-models are simultaneously connected with the input end of the selected full connection layer, and the output end of the selected full connection layer forms the output end of the link flow prediction model.
And 3, performing offline training on the link flow prediction model by the SDN application plane by using the training data set to obtain the trained link flow prediction model.
When off-line training is carried out, the adjacent matrix a in the training data set is firstly trained AD Short-term traffic sequence with historical time tFeeding into a first set of inputs of a link flow prediction model, training an adjacency matrix A in a data set AD Long-term traffic sequence in relation to a historical time t>Sending the traffic into a second set of input terminals of the link traffic prediction model, and training a source-destination traffic matrix at the historical time t in the data set to->Short-term flow sequence based on the historical time t->Sending the traffic into a third group of input ends of the link traffic prediction model, and training a source-destination traffic matrix of the historical time t in the data set to be->Long-term flow sequence based on the historical time t->Sending the link flow into a fourth group of input ends of the link flow prediction model, and outputting a predicted value of the link flow at historical time t +1 by an output end of the link flow prediction model>And then the predicted value of the link flow at the historical time t +1 output by the link flow prediction model is used for combining>True value X of link traffic with historical time t +1 in training dataset t+1 The mean square error of the model is used as a loss function, model parameters are updated through back propagation, and when the loss function is converged or reaches a preset training frequency, a trained link flow prediction model is obtained.
S3.1, splicing the long-term flow sequence or the short-term flow sequence and the adjacent matrix or the OD matrix in the input full-connection layer, and outputting X F 。
The input fully-connected layer of the first submodel will be adjacent to matrix A AD Short-term traffic sequence with historical time tSplicing to obtain X F1 . The input fully-connected layer of the second submodel will be adjacent to matrix A AD Long-term flow sequence based on the historical time t->Splicing to obtain X F2 . The input fully-connected layer of the third submodel will history the source-destination traffic matrix of time tShort-term flow sequence based on the historical time t->Splicing to obtain X F3 . The input fully-connected layer of the fourth submodel combines the source-destination traffic matrix { -at historical time t>Long-term flow sequence based on the historical time t->Splicing to obtain X F4 。
S3.2, in the attention mechanism module, X is firstly carried out F Obtaining link slice data X by link and time-sliced data e And time slice data X t (ii) a Then link the slice data X e The input space attention mechanism unit calculates the characteristic correlation among all links to obtain S A While slicing time-sliced data X t Inputting a time attention mechanism module, calculating the correlation of the characteristics of each time slice to obtain T A (ii) a Then X is put F And S A And T A Performing an exclusive nor operation and outputting
In the formula (I), the compound is shown in the specification,the learning parameter matrixes are all learnable parameter matrixes and are used for learning the weight value of each link of the computer network under each time slice; s A Is the output of the spatial attention mechanism unit, representing the spatial dimension weights of the network topology; t is A Is the output of the time attention mechanism unit, representing the time dimension weight of the network topology.
Since the switch in a computer network is not correlated at different time slices, the traffic of the links at different time slices is also dynamically changed. The invention uses an attention mechanism to dynamically capture the key characteristic that the relevance of the downlink traffic of the switch and the current time link traffic is large at different times.
S3.3, attention paying mechanism module outputSending the image volume unit to capture the space characteristic to obtain->I.e. is>Or
Whether the spectrum domain convolution or the space domain convolution is adopted, the convolution unit of the graph in the GCN is the adjacent switch characteristic of the fusion computing switch. The invention selects a two-layer GCN network structure as a graph convolution unit, and the graph convolution unit selects a ReLU as an activation function. The graph convolution unit comprises a space-time capture module based on the adjacency graph and a space-time capture module based on the OD graph.
in the formula, theta AD And Θ OD Representing the convolution kernels on the adjacency matrix and the OD matrix respectively,and &>Representing the graph convolution operations on the adjacency matrix and the OD matrix, respectively.
S3.3, outputting the graph convolution unitSending the time convolution unit to capture the time characteristic to obtain->
The invention selects CNN as time convolution unit, and the time convolution unit selects ReLU as activation function.
In the formula (I), the compound is shown in the specification,is the output of the time convolution unit>And phi is a convolution kernel and phi is a convolution operation, which are output of the graph convolution unit.
S3.4, convolving the output of the unit with timeThe vector dimension of the input and output full connection layer is converted to obtain a vector of r dimension->Where r is the number of all switch links.
Output full connection layer output of the first sub-modelThe output of the second submodel is fully connected to the layer output->The output of the third submodel is fully connected to the layer output->Output fully connected-layer output +for a fourth sub-model>
S3.5, selecting a full connection layer to output results of 4 submodelsFusing to obtain the predicted value of the link flow>
In the formula, f represents a fusion operation.
S3.6, using the link flow prediction value of the historical time tAnd true value X t+1 The mean square error of the link flow prediction model is used as a Loss function Loss, model parameters are updated through back propagation, and the link flow prediction model is obtained through multiple training.
And 4, the SDN control plane collects real-time network information and flow data of the SDN data plane and sends the SDN data and flow data into the SDN application plane.
The flow monitoring module of the SDN control plane acquires real-time network information and flow data, including an adjacency matrix A AD Source-destination traffic matrix for current time tShort-term traffic sequence in conjunction with the current time t>And a long-term flow sequence at the current time t>
Step 5, SDN application plane enables real-time network information and flow quantityThe link flow is sent to a trained link flow prediction model for prediction to obtain the predicted value of the link flow at the next time t' +1And returns to the SDN control plane.
When prediction is performed, the adjacency matrix A is formed AD Short-term traffic sequence with current time tFeeding into a first set of inputs of a trained link traffic prediction model, an adjacency matrix A AD Long-term flow sequence based on the current time t>The source-destination traffic matrix at the current time t' is asserted into a second set of inputs of the trained link traffic prediction model>Short-term flow sequence based on the current time t>A source-destination traffic matrix->Long-term traffic sequence in relation to the current time t>The link flow is sent to a fourth group of input ends of the trained link flow prediction model, and a predicted value of the link flow at the next time t' +1 output by an output end of the trained link flow prediction model>
Step 6, the SDN control plane uses the link at the next time t' +1Flow predictionAnd calculating a data packet forwarding path as a link weight of Dijkstra (Dijkstra) algorithm, generating a switch flow entry, and sending the switch flow entry to each switch of the SDN data plane to realize the routing optimization of the SDN data plane.
Dijkstra (Dijkstra) is a typical shortest path algorithm that extends layer by layer from a starting point to an outer layer until extending to an end point, resulting in one or more shortest paths from one node to other nodes. The invention obtains a plurality of shortest paths between the hosts through a Dijkstra algorithm, sums the flow of the link passed by each path, and then selects the path with the minimum flow as a data packet forwarding path.
An SDN network architecture to which the present invention is applicable is shown in fig. 2, and includes a data plane, a control plane, and an application plane.
The data plane consists of SDN switches and hosts connected under the switches.
The control plane is composed of SDN controllers. The control plane is a network component that forwards control to the data plane downward and transfers data to the application plane upward. The SDN controller is divided into a flow monitoring module and a flow table generating module according to functions. The flow monitoring module periodically acquires network link flow data. And the flow table generating module uses the link flow generated by the link flow prediction model as Dijkstra algorithm link weight, calculates a data packet forwarding path, generates a switch flow table entry and sends the switch flow table entry to each switch of the data plane.
The application plane can customize different applications therein according to the requirements of different scenes. The application plane is composed of a data storage area, a model training module and a link flow prediction model. The data storage area stores network link traffic data as a training data set of a link traffic prediction model. And the model training module is used for training a link flow prediction model according to historical network link information as training data to obtain a trained model which is used as a model of the link flow prediction algorithm. And the link flow prediction model receives the input link flow sequence and outputs the predicted link flow at the next moment.
It should be noted that, although the above-mentioned embodiments of the present invention are illustrative, the present invention is not limited thereto, and thus the present invention is not limited to the above-mentioned embodiments. Other embodiments, which can be made by those skilled in the art in light of the teachings of the present invention, are considered to be within the scope of the present invention without departing from its principles.
Claims (3)
1. An SDN route optimization method based on link flow prediction is characterized by comprising the following steps:
the method comprises the following steps that 1, an SDN control plane collects historical network information and flow data of an SDN data plane to construct a training data set, and the training data set is stored in a data storage area of an SDN application plane; wherein the historical network information and traffic data comprises an adjacency matrix A AD Source-destination traffic matrix for historical time tShort-term flow sequence->Long-term flow sequence ^ at historical time t>And the actual value X of the link traffic at the historical time t +1 t+1 ;
Step 2, constructing a link flow prediction model by an SDN application plane; the link flow prediction model consists of 4 sub-models and a selection full-connection layer; each submodel consists of an input full connection layer, an attention mechanism module, a convolution module consisting of a graph convolution unit and a time convolution unit, and an output full connection layer; the input end of the submodel is formed by the input end of the input full connection layer, the output end of the input full connection layer is connected with the input end of the attention mechanism module, the output end of the attention mechanism module is connected with the input end of the graph convolution unit, the output end of the graph convolution unit is connected with the input end of the time convolution unit, and the output end of the time convolution unit is connected with the input end of the output full connection layer; the input ends of the 4 sub-models form 4 groups of input ends of the link flow prediction model, the output ends of the 4 sub-models are simultaneously connected with the input end of the selected full connection layer, and the output end of the selected full connection layer forms the output end of the link flow prediction model;
step 3, off-line training is carried out on the link flow prediction model by the SDN application plane through the training data set, namely, the adjacent matrix A in the training data set is firstly carried out AD Short-term traffic sequence with historical time tFeeding into a first set of inputs of a link flow prediction model, training an adjacency matrix A in a data set AD Long-term traffic sequence in relation to a historical time t>Sending the traffic into a second set of input terminals of the link traffic prediction model, and training a source-destination traffic matrix at the historical time t in the data set to->Short-term flow sequence based on the historical time t->Sending the traffic into a third group of input ends of the link traffic prediction model, and training a source-destination traffic matrix of the historical time t in the data set to be->Long-term flow sequence based on the historical time t->Sending the data to a fourth group of input ends of the link flow prediction model, and outputting the data at an output end of the link flow prediction modelPrediction value of link traffic at historical time t + 1->Reusing history output by link flow prediction model the prediction value of the link traffic at time t + 1->True value X of link traffic with historical time t +1 in the training dataset t+1 The mean square error of the model is used as a loss function, and model parameters are updated through back propagation, so that a trained link flow prediction model is obtained;
step 4, the SDN control plane collects real-time network information and flow data of the SDN data plane and sends the real-time network information and flow data into the SDN application plane; wherein the real-time network information and traffic data comprises an adjacency matrix A AD Source-destination traffic matrix for current time tShort-term flow sequence at the present time t>And a long-term flow sequence at the current time t>
Step 5, the SDN application plane sends real-time network information and flow data into a trained link flow prediction model for prediction, namely an adjacency matrix A AD Short-term traffic sequence with current time tFeeding into a first set of inputs of a trained link traffic prediction model, an adjacency matrix A AD Long-term flow sequence based on the current time t>A source-destination traffic matrix->Short-term traffic sequence in conjunction with the current time t>The source-destination traffic matrix at the current time t' is asserted into a third set of inputs of the trained link traffic prediction model>Long-term flow sequence based on the current time t>The link flow is sent to a fourth group of input ends of the trained link flow prediction model, and a predicted value of the link flow at the next time t' +1 output by an output end of the trained link flow prediction model>And returning to the SDN control plane;
step 6, the SDN control plane uses the predicted value of the link flow at the next time t' +1And calculating a data packet forwarding path as a link weight of a Dijkstra algorithm, generating a switch flow entry, and sending the switch flow entry to each switch of the SDN data plane to realize the routing optimization of the SDN data plane.
2. The SDN route optimization method based on link flow prediction as claimed in claim 1, wherein in step 1,
adjacency matrix A AD Comprises the following steps:
A AD =[a ij ] k×k
true value X of link traffic at historical time t +1 t+1 Comprises the following steps:
in the formula, a ij For switches v in SDN data plane i And a switch v j (ii) an adjacent relationship of (a);for a source host h in the SDN data plane at the current time t i To the destination host h j A normalized value of the transmitted traffic; />Switch links e in the historical time t +1SDN data plane respectively 1 ,e 2 ,…,e r The flow transmitted between the exchangers at the two ends; x ■ The actual value of link traffic for time 9632; r is the interception length of the short-term flow sequence, L is the interception length of the long-term flow sequence, n is the sampling frequency of the link flow per hour, and m is the number of sampling points intercepted by the link flow per hour; k is the number of switches in the SDN data plane, l is the number of hosts in the SDN data plane, and r is the number of switch links in the SDN data plane.
3. The SDN route optimization method based on link flow prediction as claimed in claim 1, wherein in step 4,
adjacency matrix A AD Comprises the following steps:
A AD =[a ij ] k×k
In the formula, a ij For switches v in SDN data plane i And a switch v j (ii) an adjacent relationship of (a);as the source host h in the SDN data plane at the current time t i To the destination host h j A normalized value of the transmitted traffic; x ■ The actual value of link traffic for time 9632; r is the interception length of the short-term flow sequence, L is the interception length of the long-term flow sequence, n is the sampling frequency of the link flow per hour, and m is the number of sampling points intercepted by the link flow per hour; k is the number of switches in the SDN data plane, l is the number of hosts in the SDN data plane, and r is the number of switch links in the SDN data plane. />
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