Scheduling independent tasks on multiple cloud-assisted edge servers with energy constraint

In this paper, we study task scheduling with or without energy constraint in mobile edge computing with multiple cloud-assisted edge servers as combinatorial optimization problems within the framework of classical scheduling theory. The first problem is to schedule a list of independent tasks on a mobile device and several heterogeneous edge servers and cloud servers, such that the makespan is minimized. The second problem is to schedule a list of independent tasks and to determine the computation and communication speeds of a mobile device, such that the makespan is minimized and the energy consumption of the mobile device does not exceed certain energy budget. The paper makes the following tangible contributions. We design heuristic task scheduling algorithms for both problems by considering the heterogeneity of computation and communication speeds. We derive a lower bound for the optimal schedule and prove an asymptotic performance bound for our heuristic algorithms. We experimentally evaluate the performance of our heuristic algorithms and show that their performance is very close to that of an optimal algorithm. Our analysis employs three key techniques, namely, the method of communication unification (i.e., all tasks have the same communication to computation ratio), the concept of effective speed of an edge server or a cloud server (i.e., the perceived speed of a server by ignoring the details and differences of communication speed and computation speed, wireless communication time and wired communication time, a regular edge server and a cloud-assisted edge server, execution time and waiting time), and the construction of virtual tasks (i.e., imaginary tasks which do not exist). Such unique techniques make it possible to derive a lower bound for the optimal solution, to derive an upper bound for the heuristic solution, to prove an asymptotic performance bound, and to find the best edge server order. To the best of the author's knowledge, this is the first paper in the literature which optimizes the makespan of task scheduling with or without energy constraint in mobile edge computing with multiple cloud-assisted edge servers.