Stable and reliable wireless connections during the user equipment's mobility are the critical issue in future mobile communication networks especially during UE's high-speed scenarios over dense heterogeneous networks (HetNets). Thus, setting an accurate value for the handover control parameters (HCPs) (i.e., time-to-trigger (TTT) and handover margin (HOM)) at different speed scenarios is required for system performance. This study proposes six different systems and each one employs different HCP settings using various mobile speed scenarios over a HetNet. Several performance metrics (i.e., received signal reference power (RSRP), handover ping-pong (HOPP), radio link failure (RLF), handover probability (HOP), handover interruption time (HOIT), and handover failure (HOF)) were used as key performance indicators (KPIs) for systems evaluations. Furthermore, 20 users were evaluated in this study using a 40 ms measurement interval. The results show a different impacts of each system on the performance of the deployed HetNet. However, System 1 (lowest TTT & moderate HOM) was the best system in term of RSRP and RLF but on the expense of HOPP. Furthermore, assigning high level of the TTT and HOM (i.e., TTT >1000 ms and HOM >8 dB) leads to 0 HOPP but high RLFs. Moreover, the best system performance in term of HOP, HOIT, and HOF were System 6 (highest TTT & high HOM) with 0.06 %, 3 %, and 0.004 %, respectively. System 4 represents the best trading off system between HOPP and RLF due to the proper configuration of the HCPs. However, the aims of evaluating several systems based on fixed HCPs over several mobile speed scenarios were to see the behaviors of the systems performance when different setting values are applied. Furthermore, this study proposes a HO self-optimization algorithm for auto-tuning the HCPs. Weighted function algorithm along with a trigger timer is used for reducing unnecessary HOs while RLF minimized by setting a trigger timer under a certain conditions when the RSRP of the serving base station (BS) goes below the received signal strength indicators (RSSI). The proposed algorithm shows a significant improvement in term of HOPP, RLF, HOP, and HOF compared to System 4 and FLC algorithm. The RSRP of the proposed algorithm is kept within acceptable range. Thus, accurate setting values for the HCPs are significant to keep the tradeoff between RLF and HOPP at the minimum level.