# A Placement Method of the 5G Edge Nodes Based on the Hotspot Distribution of Mobile Users
## 3 Our Proposed Method
### The Location Selection Algorithm of 5G Edge Nodes Based on Hotspots and Benefit Constraint  
In practical applications, the primary factor that Telcos consider in building 5G base stations is investment and return. Since the 5G base stations adopt the edge computing technology, its main function is not only to provide traditional voice communication, but also to provide data storage and computing services. Since the placement of the 5G base stations (or edge nodes) involves a variety of factors (such as personnel density, geographical conditions, economic constraints, etc. ), this placement work is considered to be complex system engineering. Based on the above analysis, we propose the following placement target of 5G base stations:  
1. Maximize the high load utilization rate of the base station in the target area. 2. Maximize the bandwidth reduction rate of the core network in the target area. **Definition 5**. : _High load utilization rate of base stations._  
It refers to the proportion of the time that the base station is in a high load state in one day. We can describe this definition using the ratio of the time in hotspots to the service time in one day. That is, \(U(i)=CF_{i}^{T}/T\). Here, \(CF_{i}^{T}\) is the hotspot duration time of the \(i\)th base station, and \(T\) is the total service time of the \(i\)th base station in a day. In order to convert the high load utilization rate of the base station to a value between 0 and 1, the high load utilization rate of each base station needs to be normalized. Here, we assume that all base stations have the same service time \(T\) in a day. The normalized \(U(i)\) in the \(i\)th base station is represented as follows:  
\[U^{\prime}(i)=\frac{U(i)}{U(1)+U(2)+\cdots+U(M)}=\frac{CF_{i}^{T}}{\sum_{i=1}^ {M}CF_{i}^{T}}=\frac{CF_{i}^{T}}{U_{all}} \tag{1}\]  
Here, \(M\) is the number of base stations, and \(U_{all}=\sum_{i=1}^{M}CF_{i}^{T}\). **Definition 6**. : _Bandwidth reduction rate of the core network._ \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Time Slices** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \(P_{t}\) & 5 & 6 & 7 & 2 & 5 & 6 & 8 & 7 & 2 & 7 \\ \(S_{t_{t}}\) & 1 & 2 & 3 & 0 & 1 & 2 & 3 & 4 & 0 & 1 \\ \(CF_{i}^{T}\) & 0 & 0 & 30 & 30 & 30 & 30 & 60 & 70 & 70 \\ \(CF_{i}^{U}\) & 5 & 11 & 18 & 20 & 25 & 31 & 39 & 46 & 48 & 55 \\ \hline \end{tabular}
\end{table} 
Table 1: The feature extraction processes for one cluster area. It refers to the ratio of the data generated by all users in new base station to the data generated by all users in all candidate base station in a day. The reason of this define is that the data traffic generated in this hotspot area with new base station will be processed at the edge server, and without occupying the bandwidth of the core network. We use \(B(i)\) to represent the bandwidth reduction rate of the core network after the base station \(i\) is placed. That is,  
\[B(i)=\frac{d_{i}*CF_{i}^{U}}{\sum_{i=1}^{M}\left(d_{i}*CF_{i}^{U}\right)}=\frac {CF_{i}^{U}}{B_{all}} \tag{2}\]  
Here, we assume that the data traffic of \(C_{i}\) is \(d_{i}\) in a day, \(M\) is the number of candidate base stations, \(B_{all}=\sum_{i=1}^{M}\left(d_{i}*CF_{i}^{U}\right)\). According to the above description, if we need to deploy \(N\) base stations after extracting \(M(N\leq M)\) hotspots in one target area, the base station placement problem can now be described as a mathematical problem: select \(N\) locations from \(M\) candidate hotspots to deploy base stations to maximize the base station high load utilization rate and core network bandwidth reduction rate of the communication system in the entire target area. That is, the problem can be formalized as the 0-1 linear programming problem. Firstly, we define a decision variable \(S_{i}\) to indicate whether a base station needs to be placed in the candidate hotspot area \(i\). When \(S_{i}=1\), a base station is placed in the candidate hotspot area \(i\).