Multi-access Edge Computing (MEC) is an enabling technology to leverage new network applications, such as virtual/augmented reality, by providing faster task processing at the network edge. This is done by deploying servers closer to the end users to run the network applications. These applications are often intensive in terms of task processing, memory usage, and communication; thus mobile devices may take a long time or even not be able to run them efficiently. By transferring (offloading) the execution of these applications to the servers at the network edge, it is possible to achieve a lower completion time (makespan) and meet application requirements. However, offloading multiple entire applications to the edge server can overwhelm its hardware and communication channel, as well as underutilize the mobile devices' hardware. In this paper, network applications are modeled as Directed Acyclic Graphs (DAGs) and partitioned into tasks, and only part of these tasks are offloaded to the edge server. This is the DAG application partitioning and offloading problem, which is known to be NP-hard. To approximate its solution, this paper proposes the FlexDO algorithm. FlexDO combines a greedy phase with a permutation phase to find a set of offloading decisions, and then chooses the one that achieves the shortest makespan. FlexDO is compared with a proposal from the literature and two baseline decisions, considering realistic DAG applications extracted from the Alibaba Cluster Trace Program. Results show that FlexDO is consistently only 3.9% to 8.9% above the optimal makespan in all test scenarios, which include different levels of CPU availability, a multi-user case, and different communication channel transmission rates. FlexDO outperforms both baseline solutions by a wide margin, and is three times closer to the optimal makespan than its competitor.
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