## 3 The LBOP-ARIMA Model  
For the downlink communication mechanism, when the network traffic information is collected, the link bandwidth occupancy rate (LBOP) at time \(t\) can be calculated according to Equation (3). To develop the proper downlink communication routing strategy, the bandwidth occupancy rate at time \(t+T\) needs to be determined. Here, the LBOP-ARIMA model is developed to predict the occupancy rate at time \(t+T\). The general auto-regressive integrated moving average model ARIMA model is characterized by the terms: \(p\), \(d\), \(q\), where \(p\) is the order of the AR (auto-regressive) term, \(q\) is the order of the MA (moving average) term, and \(d\) is the number of differencing required to make the time series stationary. When the second-order difference sequence is used, the ARIMA (\(p\), \(d\), \(q\)) is described as following, in which parameter d is 2:  
\[y_{t}=\varepsilon_{t}+\sum_{i=1}^{p}a_{i}y_{t-i}+\sum_{i=1}^{q}\beta_{i}y_{t- i}+c \tag{4}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Port** & & **Expalation** & **Parameters of** & **Sign** & **Explanation** \\
**Parameter** & & & **Flow Entries** & **\%** & **\%** \\ \hline \(p_{a,q}^{1}(t)\) & rx\_packets & number of packets received & \(f_{a}^{1}(t)\) & length & capacity of switch flow entries \\ \(p_{a,q}^{2}(t)\) & tx\_packets & number of packets forwarded & \(f_{a}^{2}(t)\) & priority & matching order of flow entries \\ \(p_{a,q}^{3}(t)\) & rx\_bytes & bytes received & \(f_{a}^{3}(t)\) & packet\_count & number of packets forwarded \\ \(p_{a,q}^{4}(t)\) & tx\_bytes & bytes forwarded & \(f_{a}^{4}(t)\) & byte\_count & bytes forwarded \\ \(p_{a,q}^{5}(t)\) & rx\_dropped & number of packets dropped & \(f_{a}^{5}(t)\) & duration\_sec & duration of data flow \\ \(p_{a,q}^{6}(t)\) & tx\_dropped & number of packets dropped & \(f_{a}^{6}(t)\) & duration\_nsec & extra time of data flow to live \\  & & while forwarding & & & relative time to remove \\ \(p_{a,q}^{7}(t)\) & tx\_errors & number of packets with errors & \(f_{a}^{2}(t)\) & idle\_timeout & flow entries \\  & & while forwarding & & & absolute time to remove \\ \(p_{a,q}^{8}(t)\) & rx\_frame\_err & when receiving & \(f_{a}^{8}(t)\) & hard\_timeout & flow entries \\ \(p_{a,q}^{9}(t)\) & rx\_over\_err & number of packets overflowed & & & \\  & & when receiving & – & – & – \\ \hline \hline \end{tabular}
\end{table}
Table 2: The port parameter of the SDN switch and status parameters of the flow entries in the LoRaWAN.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(\mu_{j}(t)\) & \(\mu_{j}(t)\)**Level** & **link Congestion Status** & \(s_{j}(t)\) \\ \hline
0–0.6 & 1 & no congestion & 1 \\
0.6–0.7 & 2 & normal load & 2 \\
0.7–0.8 & 3 & possible congestion & 3 \\
0.8–0.9 & 4 & general congestion & 4 \\ >0.9 & 5 & severe congestion & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The congestion level of the link bandwidth occupancy rate.  
where \(y_{t}\) is defined as the time series value at time \(t\), \(\varepsilon_{t}\) represents the random error at time \(t\), \(y_{t-i}\) is the observation value of the time series at time \(t-i\), and \(a_{i}\), \(\beta_{i}\), and \(c\) are the regression parameters. The basic steps of establishing the ARIMA model are shown in Figure 4. Data acquisition and pre-processing is carried out in the first step. Secondly, time difference is used to check the smoothness of the time series data. Then, the \(p\), and \(q\) terms are determined, and the model predictions are verified using the preset validation data set. The modeling process shown in Figure 4 is able to provide accurate predictions for data demonstrating periodicity and regularity. When there is data volatility involved, the process in Figure 4 may not be effective enough in providing accurate results and therefore must be improved.