Much research has focused on task offloading in fog-enabled IoT networks. However, there is an important offloading issue that has hardly been addressed—the impact of different virtualization modes on task response (TR) time. In the present article, we bridge this gap, introducing three virtualization modes, and characterizing the TR time under each. In each mode the virtual machines (VM) at the fog are customized differently, leveraging VM elasticity. In the perfect virtualization mode, the VM is customized to match exactly the computational load of the incoming task. This ensures that each task, regardless of which VM it goes to, will have the same service time. In the semiperfect virtualization mode, a less stringent, thus more practical, alternative, the VM is customized to match roughly the computational load of the incoming task. This results in a uniformly distributed task service time. Finally, in the baseline virtualization mode, the VM is customized to just be fast, with no regard to the computational load of the incoming task. This mode, which just re-scales the processing time of the task, is the default in existing research, and is re-introduced here for only comparison purposes. We characterize the TR time for the three modes leveraging M/G/1 and M/G/m queueing models, with the queueing stability condition identified for each mode. The obtained analytical results are successfully validated by discrete event Monte Carlo simulation. The numerical results show that the first mode results in the shortest TR time, followed by the second mode, then the third mode. That is, if virtualization is managed adequately, significant improvement in TR time can be gained.

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.