## 2 System Model and the Optimization Problem  
In a mobile communication network, in order to ensure the communication quality of the mobile terminal UE, instant handover to a base station with better link quality is an effective guarantee for its link quality. Especially with the increase of the communication frequency band, the coverage distance becomes smaller and the density of the base station is also increasing to ensure the coverage quality. The mobility management of UDN is also one of the key requirements for determining the system capacity. Usually handover events can be triggered by the relative signal strength relationship between the serving base station and neighboring base stations. For example, in the A3 event [18], which is the typical event for handover triggering, the following relationship needs to be satisfied to maintain TTT measurement periods:  
\[RSRP_{n}>RSRP_{s}+\text{Hys}, \tag{1}\]  
where Hys is an offset value, \(RSRP_{n}\) is the reference signal receiving strength of a neighboring base station, and \(RSRP_{s}\) is the reference signal receiving strength of the serving base station. In brief, A3 event requires that the signal strength of the neighboring base station exceeds a certain threshold Hys of the serving base station and that it is maintained for a certain period of time TTT. However, in an actual system, there are various phenomena that are not conducive to the stability and efficiency of the communication link, such as handover failure and handover ping-pong, which necessitate strict requirements on the setting of handover parameters. Handover failure refers to the unexpected interruption of the handover process due to various reasons, such as weak link quality or strong interference [11]. The handover failure rate can be calculated as:  
\[p_{f}=\frac{N_{HO\_failure}}{N_{HO}}, \tag{2}\]  
where \(N_{HO\_failure}\) is the number of handover failures and \(N_{HO}\) is the total number of handovers. Usually, more conservative handover parameters such as a larger TTT and a larger Hys could lead to handover failure more easily because conservative parameters tends to miss the best handover timing. However, in UDN, close inter-site distance makes the interference more severe, and unsuitable handover parameters could lead to a higher failure rate. Handover ping-pong is an event where a UE is handed over to a new base station and then is handed over back to the original base station in less than a certain period of time [12]. The handover ping-pong rate can be calculated as:  
\[p_{pp}=\frac{N_{HO\_pingping}}{N_{HO}}, \tag{3}\]  
where \(N_{HO\_pingping}\) is the number of ping-pong handover. This phenomenon indicates that the current UE does not need to handover to the target base station, which can be regarded as a redundant handover and also a burden on the mobile communication system. Ping-pong handover increases signaling overhead for handover, and is not conducive to improving communication efficiency. Under normal circumstances, aggressive handover parameters tend to lead to more ping-pong handover, such as a smaller TTT and a smaller Hys, which could cause easier and more frequent triggering of A3 events [19], increasing the proportion of ping-pong handover in all handover. In UDN, the phenomenon of ping-pong handover are more obvious because the closer the station distance, the more drastic the signal strength change, and once the handover parameters are set unreasonably, the ping-pong rate would also rise sharply [17]. Neither handover failure or handover ping-pong is the expected effective handover.