Mobile Edge Computing (MEC) has emerged as a new computing paradigm to provide computing resources and storing applications closer to the end-users at the operator network boundary. One of the main challenges of MEC is task offloading, i.e., the transfer of computational tasks to a remote processor or external platforms such as a grid of servers or the Cloud. Task offloading mainly faces when and where is best to offload tasks to mitigate a smart device's energy consumption and workload. This paper tackles this challenge by adopting the principles of Optimal Stopping Theory (OST) with three time-optimised sequential decision-making models. A performance evaluation is provided with upon real data-sets on which our proposed models are applied and compared to the theoretical optimal model. Our results show how close our models can be to the theoretical optimal one based on probabilistic and scaling factors. Moreover, in our performance evaluation section, we conclude that one of the applied sequential models can be extremely close to the optimal one making it suitable in single-user and competitive user scenarios.
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