Mobile Edge Computing application domains such as vehicular networks, unmanned aerial vehicles, data analytics tasks at the edge and augmented reality have recently emerged. Under such domains, while mobile nodes are moving and have certain tasks to be offloaded to Edge Servers, choosing an appropriate time and an ideally suited server to guarantee the quality of service can be challenging. We tackle the offloading decision making problem by adopting the principles of Optimal Stopping Theory to

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... minimize the execution delay in a sequential decision manner. A performance evaluation is provided by using real data sets compared with the optimal solution. The results show that our approach significantly minimizes the execution delay for task execution and the results are very close to the optimal solution. Index Terms-Mobile edge computing, tasks offloading, optimal stopping theory, sequential decision making. To deal with the disadvantages of MCC, the Mobile Edge Computing (MEC) paradigm has emerged. The rationale architecture of this concept is to offer cloud services closer to mobile devices by placing many data-centres at the edge of the network. The network edge refers to different places e.g., mobile network at the Base Station (BS), or indoor places such Wi-Fi and 3G/4G access points [17] . Motivation & Challenge: An essential use case of MEC is the computing task/data offloading. Computation offloading is the task of sending a computation task and data to a remote server for delegating this computation [1] . As the new emerging applications require intensive computation processes, computation offloading provides a solution to overcome the limitation of the mobile device. Examples of applications that can benefit from computing offloading are mobile AR [6], gaming, Internet of Things (IoT) applications, data analytics tasks at the edge [15] , VN [25] and Unmanned Aerial Vehicles (UAV) [28] . A study showed the benefit of using offloading for the Percipio AR application on a real MEC testbed [7] . The study showed that the computation offloading reduces latency up to 88% and energy consumption of mobile devices up to 93%. Computation offloading faces several challenges, the most significant ones being: (i) the decision of when to offload tasks/data to a MEC server and (ii) mobility patterns/behaviour of the users in such MEC environments. The decision making of tasks/data offloading is of high importance as it is expected to directly affect the Quality of Service (QoS) of the user application including the inherent latency due to the offloading process. Therefore, different parameters have to be considered when to decide to offload tasks and/or data including: the current MEC server load and the transmission / communication status between the mobile node and the MEC server. The decision can be spatial or temporal as stated in [10] . The spatial decision refers to realising the computing tasks locally at the mobile device, in the cloud, or at the edge server [11] . The temporal decision refers to a situation where it is advisable to optimally delay the tasks/data offloading due to the current expected cost in terms of the transmission delay and the processing delay at the MEC server, e.g., from the user prospective, the Wi-Fi connectivity is low, or from the network operator perspective, the server is fully loaded, thus, expecting high latency for delivering the outcome of the delegated computation tasks to the user.