Characterizing optimal task latency in mobile edge computing both mathematically and metaheuristically

Abstract

Abstract A large body of research has recently focused on minimizing task latency in mobile edge computing (MEC). Researchers in the field have typically posed the minimization exercise as a non-convex optimization problem and solved it either mathematically or metaheuristically, overlooking the fact that neither provides the optimal solution. Specifically, the mathematical paradigm provides a lower bound on the optimal solution, and the metaheuristic paradigm provides an upper bound. The present work is the first, to the best of our knowledge, to explore this fact and quantify the gap between the two bounds, where the optimal solution actually lies. To this end, we craft a baseline MEC model and formulate a non-convex optimization problem with the objective to minimize task latency. We then define three partitioning vectors, one for the workloads and two for the MEC resources. By searching for the optimal values of these three partitioners, the solution lower bound is obtained mathematically using Lagrange multipliers, and the solution upper bound is obtained metaheuristically twice using two algorithms, genetic and bee colony. The experimental results show that the gap between the two bounds can be as small as $$2\%$$ and as large as $$14\%$$ , depending on the model parameters, reasserting the fact that settling with only one solution paradigm can be dreadfully misleading.