The workload dynamicity of internet of things devices represents a substantial challenge for edge computing environments as it often has limited resources. It requires an efficient elasticity framework that aware of its operational environment in order to adapt in accordance to workload fluctuation which contributes towards efficient resource utilisation, high acceptance rate, and avoids quality of service violation. The edge computing elasticity can be provided through a self-adaptive system that is capable of taking the proper elasticity decisions. This self-adaptive system can be designed using a proactive-, reactive-, or hybrid-adaptation. However, the performance of these adaptation approaches may vary according to the domain, application, and workload. Therefore, this paper designs an edge computing self-adaptive system that can support proactive-, reactive-, and hybridadaptation. It also conducts simulation-based investigations on the performance of the adaptation approaches in an edge computing environment under different workloads and application scenarios. The experimental results reveal that the hybrid adaptation performs at least 10% better than other approaches whereas the performance of both proactive and reactive adaptations is application scenarios dependent.