Multi-Access Edge Computing (MEC) is widely recognized as an essential enabler for applications that necessitate minimal latency. However, the dropped task ratio metric has not been studied thoroughly in literature. Neglecting this metric can potentially reduce the system's capability to effectively manage tasks, leading to an increase in the number of eliminated or unprocessed tasks. This paper presents a 5G-MEC task offloading scenario with a focus on minimizing the dropped task ratio, computational latency, and communication latency. We employ Mixed Integer Linear Programming (MILP), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA) to optimize the latency and dropped task ratio. We conduct an analysis on how the quantity of tasks and User Equipment (UE) impacts the ratio of dropped tasks and the latency. The tasks that are generated by UEs are classified into two categories: urgent tasks and non-urgent tasks. The UEs with urgent tasks are prioritized in processing to ensure a zero-dropped task ratio. Our proposed method improves the performance of the baseline methods, First Come First Serve (FCFS) and Shortest Task First (STF), in the context of 5G-MEC task offloading. Under the MILP-based approach, the latency is reduced by approximately 55% compared to GA and 35% compared to PSO. The dropped task ratio under the MILP-based approach is reduced by approximately 70% compared to GA and by 40% compared to PSO.
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