# Energy-Efficient BWP Configuration for Multi-Slice Users
## 6 Performance Evaluation  
We used Python for simulations to compare both approaches against each other and against the legacy scheme where all users are configured with a single BWP for both services with a band \(B_{legacy}\). CPLEX solver was used to solve the ILP problem in the centralized approach. Simulations were run several times (\(\approx\)100 times) with a different number of users each time, and the same results were observed regardless of the number of users. Therefore, we start by putting the focus on the scenario with \(N_{users}=20\). Afterwards, we display results for \(N_{users}=30\). The simulation parameters from the system model are shown in Table 1.  
As for the results, we display the energy efficiency and total throughput Cumulative Distribution Functions (CDFs) for all users and the users' overall sojourn time in the network CDF for all users. The energy efficiency of UE \(u\) selecting the strategy \(MN\) is computed as follows:  
\[EE_{u,MN}=\frac{Thr_{u,eb}+Thr_{u,uc}}{P_{BWP1}+P_{BWP2}} \tag{12}\]  
where \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline \(R\) & Coverage area & 300 m \\ \(V_{URLLC}\) & URLLC volume of data & 2–15 Mbits \\ \(V_{eMBB}\) & eMBB volume of data & 5–50 Mbits \\ \(SwDlu\) & User’s BWP switching delay & 1 ms [5] \\ \(B_{total}\) & Operator band & 100 MHz \\ \(B_{eMBB}\) & eMBB BWP band & 40 MHz \\ \(B_{URLLC}\) & URLLC BWP band & 20 MHz \\ \(B_{mixed}\) & Mixed BWP band & 30 MHz \\ \(B_{legacy}\) & Legacy BWP band & 60 MHz \\ \(P_{BWP1}\) & Power consumption for scanning BWP 1 (eMBB) & 1000 mW \\ \(P_{BWP2}\) & Power consumption for scanning BWP 2 (URLLC) & 500 mW \\ \(P_{BWP3}\) & Power consumption for scanning BWP 3 (mixed) & 750 mW \\ \(P_{legacy}\) & Power consumption for scanning legacy BWP & 1500 mW \\ \(\alpha_{u,eMBB}\) & Normalizing factor for cost function & 1 \\ \(\alpha_{u,URLLC}\) & Normalizing factor for cost function & 2 \\ \(\beta_{u}\) & Normalizing factor for cost function & 0.001–0.099 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. * \(EE_{u,MN}\) is the energy efficiency of UE \(u\) selecting the \(MN\) strategy. * \(P_{\textit{WWP}}\) is the UE power consumption for scanning BWP \(bwp\). When UE \(u\) selects the \(SN\) strategy, its energy efficiency is \(EE_{u,SN}=\frac{T\hat{\textit{Thr}}_{u}}{P_{\textit{WWP}}}\). As for the overall sojourn time of UE \(u\), it is \(ST_{u,c}=\sum_{s\in\{c\mathbf{b},uc\}}DST_{u,s,c}+\theta_{c}\cdot SwDl_{u}\). As for the overall sojourn time of UE \(u\), it is calculated as follows:  
\[ST_{u,MN}=\sum_{s\in\{c\mathbf{b},uc\}}\frac{V_{u,s}}{T\hat{\textit{Thr}}_{u,s}}+ SwDl_{u} \tag{13}\]  
\[ST_{u,SN}=\frac{\sum_{s\in\{c\mathbf{b},uc\}}V_{u,s}}{T\hat{\textit{Thr}}_{u}} \tag{14}\]  
Figure 2 displays the number of users associated with each strategy using the exhaustive search algorithm for 20 users. Results show that a higher number of users prefer the single-numerology scheme, as it is more adapted to these users from an energy-efficiency perspective, since users scan a single and narrower BWP without BWP switching. Additionally, the single-numerology strategy is mainly selected for users with a low battery level on average, whereas the multi-numerology scheme is chosen for users with a high battery level on average. This is due to the fact that users with a low battery level require more energy savings, which explains why they favor the single-numerology scheme. Figure 3 represents the users' energy-efficiency CDF for the centralized, distributed and legacy schemes for 20 users. It can be concluded that both proposed solutions--centralized and distributed--realize a higher energy efficiency than the legacy scheme thanks to the astute cost function that helped strike a nice balance between energy efficiency and QoS. Moreover, the centralized scheme performs slightly better than the distributed scheme. Figure 4 represents the users' total throughput CDF for the centralized, distributed and legacy schemes for 20 users.