## 3 Initial State of SBSs Based on Relaxed Threshold for LSTM Traffic Prediction
### Initial State Strategy for SBSs Based on LSTM Traffic Prediction  
To initially obtain the state of the SBS in the next period, we use LSTM models to predict the traffic of each SBS in the next period. LSTM is a recurrent neural network (RNN) architecture for making predictions on time-series data, and it is capable of learning long-term dependencies. Compared to traditional RNN models, LSTM models can eliminate the problem of gradient disappearance or gradient explosion. LSTM contains four components: cell states, input gates, output gates, and forgetting gates, which are specially developed to solve the gradient disappearance and gradient explosion problems in traditional RNN networks. Figure 3 shows the internal cell states of an LSTM model cell [22].  
The cell state can be thought of as a long continuous chain through which a number of small interactions with cells are generated. It is a line consisting of \(c_{t-1}\) and \(c_{t}\) in Figure 3. The first step of the LSTM network is to identify the information that needs to be removed or forgotten from the cell. This process can be handled with a sigmoid layer/forgetting gate layer. The forgetting gate layer can be represented as follows  
\[f_{t}=\sigma\Big{(}w_{f}[h_{t-1},x_{t}]+b_{f}\Big{)} \tag{19}\]  
where \(x_{t}\), \(w_{f}\), \(h_{t-1}\), and \(b_{f}\) denote the new input, the weight function, the output of the previous period, and the bias value, respectively. \([h_{t-1},x_{t}]\) denotes the sigmoid function, which represents the stitching of two matrices together. The output value of Equation (19) is either 0 or 1. When the output is 0 it means that the value is dropped completely, and when the output is 1 the value is preserved. In the next step, the data to be included in the cell state will be decided. The sigmoid layer, also known as the input gate layer, determines the value to be recovered. The 'tanh' layer produces a new vector of candidate values that can be combined with the current state.  
\[i_{t}=\sigma(w_{i}[h_{t-1},x_{t}]+b_{i}) \tag{20}\]  
\[\widetilde{c}_{t}=\tanh(w_{c}[h_{t-1},x_{t}]+b_{c}) \tag{21}\]  
where \(i_{t}\) is the input layer and \(\widetilde{c}_{t}\) is a new candidate vector. The new candidate vector value for the next state can be obtained from Equations (20) and (21), i.e.,  
\[c_{t}=f_{t}*c_{t-1}+i_{t}*\widetilde{c}_{t} \tag{22}\]  
The last step is to get the output. A sigmoid layer is executed. This selects which part of the cell state is the output, then inserts the cell state and multiplies the output generated by the cell state and the sigmoid gate through the 'tanh' layer (placing the value between \(-1\) and \(1\)). This is done in order to get the output of the decision part.  
\[o_{t}=\sigma(w_{o}[h_{t-1},x_{t}]+b_{o}) \tag{23}\]  
Figure 3: Internal cell states of LSTM model.  
\[h_{t}=o_{t}*\tanh(c_{t}) \tag{24}\]  
where \(o_{t}\) is the output of the sigmoid layer and \(h_{t}\) is the output of the decision part. This new output will be input to another layer and then the cycle continues. The flow of predicting the traffic load of each SBS for the next period using the LSTM model is shown in Figure 4.