## 4 SBS Energy Efficiency Management Decisions  
### Problem Formulation  
In Section 3, we used the traffic prediction method to obtain a preliminary set of SBS states by setting traffic thresholds and comparing the SBS with the thresholds based on the magnitude of the predicted traffic. Since these state sets are closely related to the threshold settings and there is no scientific mathematical model to strictly control setting the thresholds, this will lead to thresholds set being based on experience which are not universal in different scenarios; therefore, the SBS switching states obtained simply by traffic prediction and threshold settings do not maximize the performance of the network system. In addition, the focus on network performance indicators varies among operators when setting network service strategies, with some focusing on user experience and requiring lower network latency, while others are more sensitive to network energy consumption. All of this has an impact on the switching state of the SBS, so we have constructed a performance function optimization objective for the network:  
\[ \begin{array}{ll}\underset{\mathbf{\rho}^{t},\mathbf{b}^{t}}{\text{min}}&Q\Big{(} \mathbf{\rho}^{t},\mathbf{b}^{t}\Big{)}=D^{t}\big{(}\mathbf{\rho}^{t}\big{)}+\alpha\sum \limits_{i\in B_{s}}\Big{(}P_{i}^{t}+P_{i,h}^{t}\Big{)}\\ \text{s.t.}&b_{t}^{t}=\{-1,0,1\},\quad\forall i\in B\\ &\mathbf{\rho}^{t}\in\mathbf{\Omega}^{t}\big{(}B_{on}^{t}\Big{)}\end{array}  \tag{25}\]  
where \(\alpha\) is a weighting factor that represents the operator's trade-off strategy between latency and energy consumption. Figure 4: Training and testing flow chart of the LSTM network prediction model. Assuming accurate results for traffic prediction based on the LSTM model, a preliminary SBS switching strategy is determined based on the threshold value. For when the SBS state is determined, we have constructed the user associated optimal SBS load optimization objective:  
\[ \begin{array}{ll}\underset{\rho^{t}}{\text{min}}&U\big{(}B_{on}^{t}\big{)}=D^{ t}\big{(}\mathbf{\rho}^{t}\big{)}+\alpha\sum\limits_{i\in B_{on}^{t}}(1-q_{i})\rho_{i}^{t} \mathcal{P}_{i}\\ \text{s.t.}&\mathbf{\rho}^{t}\in\mathbf{\Omega}^{t}\big{(}B_{on}^{t}\big{)}\end{array}  \tag{26}\]  
The fixed energy consumption component of the SBS is ignored in (26) because after determining the set of turned-on SBSs, the fixed energy consumption of the SBS is a constant value, independent of the user association policy. Since the average wake-up delay in \(D^{t}\big{(}\rho^{t}\big{)}\) is related to the state of the SBS in the previous moment, it is a segmentation function, which complicates the problem analysis. Therefore, in order to eliminate the effect of wake-up delay on user association, we propose a SBS state asynchronous switching mechanism. The mechanism can be described as follows: the MBS makes a SBS switching policy in the region of this period at the 0 th second of period \(t\), i.e., it determines \(B_{on}^{t}\), \(B_{stand}^{t}\), and \(B_{sleep}^{t}\), and broadcasts these decisions to all SBSs. Assuming that the process of broadcasting has no time delay, i.e., the SBSs receive the broadcast information at 0 s, after receiving the decision information, the SBSs select different operation modes by combining their current states. For example, if SBS \(i\) is in \(B_{on}^{t}\), if its current state is Sleep, then SBS \(i\) starts to enter the wake-up state immediately after receiving the broadcast signal. If its current state is Standby, it starts to enter the wake-up state at 9.9 s after receiving the broadcast signal.