Characterization of task response time in fog enabled networks using queueing theory under different virtualization modes

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.