# An Adaptive Control Scheme for Data-Driven Traffic Migration Engineering on 5G Network
## 3 SDN-Driven Traffic Migration Engineering (TME) Model
### Traffic Prediction Model  
The network traffic prediction is very important for traffic migration. As the initial traffic monitoring value is very important for traffic prediction, each OVS has the responsibility for traffic monitoring in this paper. Assume the initial traffic monitoring value in link \((u,v)\in E\) is \(T_{0}\), and the traffic in virtual link \((u,v)\in E\) at time \(t\) is related to instants \(\{1,2,\ldots,t-1\}\). Therefore, we construct the traffic prediction model in link \((u,v)\in E\) at time \(t\), which is shown below  
\[ \begin{array}{rcl}\tau^{t}_{u,v}&=&T_{0}+\omega_{1}\times X^{1}_{u,v}\times \tau^{1}_{u,v}+\omega_{2}\times X^{2}_{u,v}\times\tau^{2}_{u,v}\\ &&+\cdots+\omega_{t-1}\times X^{t-1}_{u,v}\times\tau^{t-1}_{u,v},\end{array}  \tag{1}\]  
where \(\omega_{1},\omega_{2},\ldots,\omega_{t-1}\) are the adaptive control coefficients of the network traffic, satisfying \(\omega_{1}+\omega_{2}+\cdots+\omega_{t-1}=1\) and \(0<\omega_{1},\omega_{2},\ldots,\omega_{t-1}<1\). The values of \(\omega_{1},\omega_{2},\ldots,\omega_{t-1}\) can be achieved by actual simulated traffic. In this paper, we fix \(\omega_{1}\) and provide a degradation traffic coefficient \(d\) such that \(\omega_{t}=d\times\omega_{t-1}\), which is similar to the pheromone degradation mode in the ant colony algorithm. For convenience, we introduce two vectors  
\[W^{t-1}_{u,v}= \begin{bmatrix}\omega_{1}X^{1}_{u,v}\\ \omega_{2}X^{2}_{u,v}\\ \vdots\\ \omega_{t-1}X^{t-1}_{u,v}\end{bmatrix} , \tag{2}\]  
and  
\[T^{t-1}_{u,v}=\Big{[}\tau^{1}_{u,v},\tau^{2}_{u,v},\ldots,\tau^{t-1}_{u,v} \Big{]}. \tag{3}\]  
Therefore, Equation (1) is rewritten as  
\[\tau^{t}_{u,v}=T_{0}+T^{t-1}_{u,v}W^{t-1}_{u,v}. \tag{4}\]  
The traffic prediction model (4) needs to be modified due to the signal noise. Here, we use a traffic modification coefficient \(\rho\) (\(0<\rho<1\)) to improve the traffic prediction model (4). A two-step-modification traffic optimization model is elaborated on in this section. First, we modify the data traffic in link \((u,v)\in E\) at time \(t\), which is related to original  
Figure 2: Traffic migration in virtual network slice layer. predicted traffic \(\tau^{t}_{u,v}\) and the maximum allowed traffic (peak rate) \(R^{t}_{u,v}\). Then, the accuracy of traffic prediction is improved based on the above-predicted traffic at instants \(t\) and \(t-1\). The specific two-step traffic modification model is described as below. **Step 1. ** Denote the first modified value of the predicted traffic in link \((u,v)\in E\) as  
\[\overline{\tau^{T}_{u,v}}=\tau^{t}_{u,v}+\rho\times(R^{t}_{u,v}-\tau^{t}_{u,v}). \tag{5}\]  
According to [PERSON]'s second theorem, peak rate \(R^{t}_{u,v}\) is related to bandwidth \(B_{u,v}\), signal transmitting power \(P^{t}_{u,v}\) and channel noise power \(\delta\) as follows  
\[R^{t}_{u,v}=B_{u,v}\times\log_{2}\left(1+\frac{P^{t}_{u,v}}{B_{u,v}\times \delta}\right). \tag{6}\]  
In real network traffic, we always use signal-to-noise ratio \(SNR^{t}_{u,v}\) instead of \(\frac{P^{t}_{u,v}}{B_{u,v}\times\delta}\). Therefore, Formula (6) can be transformed into  
\[R^{t}_{u,v}=B_{u,v}\times\log_{2}(1+SNR^{t}_{u,v}). \tag{7}\]  
Substituting (7) into (6),the traffic prediction model (5) is changed to  
\[ \begin{split}\overline{\tau^{T}_{u,v}}&=\tau^{t}_{ u,v}+\rho\times(B_{u,v}\times\log_{2}(1+SNR^{t}_{u,v})-\tau^{t}_{u,v})\\ &=(1-\rho)\times\tau^{t}_{u,v}+\rho\times B_{u,v}\times\log_{2}( 1+SNR^{t}_{u,v}).\end{split}  \tag{8}\]  
**Step 2. ** Denote the second modified value of the predicted traffic as \(\overset{\sim}{\widetilde{t}^{t}_{u,v}}\), which is updated by \(\tau^{\overline{t}-1}_{u,v}\) and \(\tau^{\overline{t}}_{u,v}\) in virtual link \((u,v)\in E\) as follows  
\[\widetilde{\tau^{\omega}_{u,v}}=\rho\times\ \overline{\tau^{t-1}_{u,v}}\,+ \,\overline{\tau^{t}_{u,v}}. \tag{9}\]  
By substituting (8) into (9), the final traffic prediction model is changed to  
\[