# A Placement Method of the 5G Edge Nodes Based on the Hotspot Distribution of Mobile Users
## 3 Our Proposed Method  
At present, we mainly use density-based clustering algorithms to analyze the user distribution in a certain target area. However, the density-based clustering algorithm does not consider the timestamp of each location, so the clustering result may not be a real hotspot. For example, the users who quickly pass an area without stopping (such as the subway station entrances) can also be treated as the clustering objects in this algorithm.  
In order to obtain more accurate user hotspots, it is necessary to take into account the timestamp contained in the user's location. Therefore, we must further analyze the time characteristics of the clustering results so as to eliminate the redundant locations obtained by the users in the non-stay state.  
Based on the above ideas, we propose a three-stage method to extract the user distribution features in the deployed area. Firstly, the density-based clustering algorithm (such as DBSCAN) is used to obtain the cluster area. Then, the user characteristics (such as the number of users) and the time characteristics (such as the duration time) of all cluster areas are computed based on the sliding time window. Finally, the hotspot areas are extracted to support the placement of the 5G base station based on the user characteristics and the time characteristics of cluster areas.  
To better understand our method, the following are some definitions of terms.  
**Definition 1**.: _Set of candidate locations for base station deployment._  
It refers to a set of candidate placement locations for deploying base stations.  
\[S\ \{P_{1}(x_{1},y_{1}),P_{2}(x_{2},y_{2}),\cdots,\ P_{i}(x_{i},y_{i}),\cdots,\ P_{n}(x_{n},y_{n})\}.\]  
where \(P_{i}(x_{i},y_{i})\) is the latitude and longitude of the \(i\)th candidate's location. \(|S|\) is the size of the set \(S\), that is, the number of candidate locations.  
**Definition 2**.: _User trajectory._  
It refers to the set of a series of locations when the user moves in the geographical spaces according to the time sequence. A location is usually composed of latitude, longitude, altitude, and timestamp. We defined the trajectory \(Tr_{i}\) of the \(i\)th user as \(Tr_{i}=\left\{\left(P_{1}^{i},T_{1}^{i}\right),\left(P_{2}^{i},T_{2}^{i}\right),\cdots,\left(P_{j^{\prime}}^{i},T_{j}^{i}\right),\cdots,\left(P_{n}^{i},T_{n} ^{i}\right)\right\}\). Here, \(P_{j}^{i}\) represents the location of the \(i\)th user at \(T_{j}\), and \(|T|\) represents the location number of the trajectory.  
Based on the above definition, we further use \(D=\left\{Tr_{1},Tr_{2},\ldots,T_{|D|}\right\}\) to record all user trajectories. Where \(|D|\) represents the number of user trajectories in the trajectory set. \(P_{j}^{i}\) refers to the \(i\)th locations in \(Tr_{i}\), and \(T_{j}^{i}\) is the timestamp of the \(j\)th location in \(Tr_{i}\).  
**Definition 3**.: _User cluster areas._  
It refers to the clustered area where the user locations are concentrated within a small distance, that is, the area with a large density of locations. We use \(C=\left\{C_{1},C_{2},\ldots,C_{k},\ldots C_{|C|}\right\}\) to record all user cluster areas. Where \(|C|\) represents the number of user cluster areas.  
Each location in cluster areas is identified using three parameters: the coordinate of this location, the timestamp of this location, and the user number corresponding to this location. For example, the \(j\)th location of the \(i\)th cluster area is represented by (\(C_{ij}^{loca}\), \(C_{ij}^{time}\), \(C_{ij}^{user}\)).  
**Definition 4**.: _User hotspot areas._  
It refers to the group cluster areas that meet certain conditions (such as duration time and user number). For example, supermarket, hospital, and stadium, etc. Different hotspotareas usually correspond to different user interest scenarios, so the hotspot area is also called the interest area.  
Obviously, for improving the high performance/price at deploying the 5G edge nodes, we first should choice the hotspot areas, especially hotspot areas with long duration time to place 5G base stations.