# An Uncertainty-Driven Proactive Self-Healing Model for
###### Abstract
In [8], the authors propose a low-complexity, greedy, heuristic algorithm to cope with the task offloading problem in a multi-cell Mobile-Edge Computing network. In [9], the authors formulate the offloading of tasks using binary variables to determine the best task offloading choices for mobile users. A model for simultaneous resource allocation and offloading decision optimization is suggested for mobile edge computing. Another task offloading technique for mobile edge computing systems is described in [10]. The authors take a real-world scenario into consideration while optimizing the software runtime environment with task offloading. A reinforcement-learning algorithm is proposed in [11] to deal with the resource management issue in edge servers and choose the best offloading strategy for reducing system costs, such as energy usage and delay. In [12, 13, 14], the authors adopt the principles of Optimal Stopping Theory (OST) to deal with the challenge of determining when to offload data to edge servers for computing analytics tasks. At the same time, the authors take into account the overall delay caused by each server. Furthermore, in [15], the authors extend the aforementioned works, assuring the Quality of Service (QoS) and reducing the anticipated execution time for tasks. The QoS is also taken into consideration in [16]. The authors introduce a heuristic algorithm to handle the offloading decision, and assign priority to nodes that control the order in which they will perform the task offloading. Finally, in [17], a deep-reinforcement-learning algorithm is adopted for dealing with the same problem. The purpose is to perform task offloading in Vehicular Fog Computing, taking into account the priorities of tasks. In contrast to the aforementioned approaches, the novelty of our paper is that the proposed model has the ability to keep enough space in the local queue to host high-priority tasks and tasks that exhibit a high demand avoiding offloading decisions for these tasks. This way, we ensure that requestors will receive the final response in the minimum possible time. At the same time, when a node is detected as potentially overloaded, low priority tasks are offloaded to peer nodes. Our ultimate goal is to minimize the times that the queue is full with obvious negative effects in the performance of the node as it is necessary in such cases to offload all the incoming tasks no matter their priority. We propose the adoption of a statistical method that reveals the trend and the probability of overloading based on the rates of incoming tasks and the rate of execution. The probability of overloading is combined with the trend of the rate of execution adopting a Fuzzy Logic system in order to handle the uncertainty in decision making. The proposed model works in a self-healing way since without external intervention, the node achieves high performance in real time, as it manages to handle the overloading situations in such a way so as to execute locally a high percentage of high-priority and high-demand tasks, providing results in the shortest possible time. More specifically, this overload avoidance provides continuous service to the aforementioned tasks, keeping latency low and QoS high. The following list reports on the contributions of our work:  
* We propose a self-healing model for maximizing the number of high-priority tasks served by an edge node. We pursue keeping free space in the local queue to host those tasks in support of real-time applications;
* We ensure the smooth operation of edge nodes under heavy traffic, avoiding overloading scenarios;
* We achieve the efficient management of the incoming load by taking the appropriate decisions for the offloading actions, taking into consideration the priority of tasks combined with their demand;
* We report on an extensive evaluation process of the proposed model, revealing its pros and cons. The rest of the paper is organized as follows. Section 2 outlines our problem and provides the main notations adopted in our model.