Energy-Constrained DAG Scheduling on Edge and Cloud Servers with Overlapped Communication and Computation

Mobile edge computing (MEC) has been widely applied to numerous areas and aspects of human life and modern society. Many such applications can be represented as directed acyclic graphs (DAG). Device-edge-cloud fusion provides a new kind of heterogeneous, distributed, and collaborative computing environment to support various MEC applications. DAG scheduling is a procedure employed to effectively and efficiently manage and monitor the execution of tasks that have precedence constraints on each other. In this paper, we investigate the NP-hard problems of DAG scheduling and energy-constrained DAG scheduling on mobile devices, edge servers, and cloud servers by designing and evaluating new heuristic algorithms. Our contributions to DAG scheduling can be summarized as follows. First, our heuristic algorithms guarantee that all task dependencies are correctly followed by keeping track of the number of remaining predecessors that are still not completed. Second, our heuristic algorithms ensure that all wireless transmissions between a mobile device and edge/cloud servers are performed one after another. Third, our heuristic algorithms allow an edge/cloud server to start the execution of a task as soon as the transmission of the task is finished. Fourth, we derive a lower bound for the optimal makespan such that the solutions of our heuristic algorithms can be compared with optimal solutions. Our contributions to energy-constrained DAG scheduling can be summarized as follows. First, our heuristic algorithms ensure that the overall computation energy consumption and communication energy consumption does not exceed the given energy constraint. Second, our algorithms adopt an iterative and progressive procedure to determine appropriate computation speed and wireless communication speeds while generating a DAG schedule and satisfying the energy constraint. Third, we derive a lower bound for the optimal makespan and evaluate the performance of our heuristic algorithms in such a way that their heuristic solutions are compared with optimal solutions. To the author’s knowledge, this is the first paper that considers DAG scheduling and energy-constrained DAG scheduling on edge and cloud servers with sequential wireless communications and overlapped communication and computation to minimize makespan.