Recent years have witnessed the process of computing gradually move to the edge network, where it is close to the physical data source, to serve applications that require large computations with very little latency. However, the terminal wireless devices’ limited computing and energy resources pose obstacles to the practical implementation of these applications. Mobile Edge Computing (MEC) based non-orthogonal multiple access (NOMA) technology is solving this problem well thanks to its ability to serve many users with high data rates and spectrum utilization efficiency. This study investigates the performance and optimization of MEC surveillance systems using NOMA. Specifically, two camera units (CUs) perform the monitoring task to be accomplished by the MEC access point (AP) through Rayleigh fading wireless links. We then proposed the four-phase protocol for this system. Accordingly, we derive the closed-form exact expressions of the successful computation probability (SCP), and study the impact of the network parameters on the system performance. Furthermore, we propose and compare three meta-heuristic-based algorithms, namely MSCP-GA, MSCP-PSO, and MSCP-HGAPSO, to find the optimal parameters set to help the proposed system achieve the maximum SCP. The results show that the proposed algorithms can significantly improve the system's performance by 40% higher than when the optimal algorithm is not used. Insights on the pros and cons of different algorithms are also discussed in this study. Finally, we use the Monte-Carlo simulation to verify the correctness of this study.