Parallel scheduling of multiple tasks in heterogeneous fog networks

Fog computing has been promoted to support delay-sensitive applications in future Internet of Things (IoT) and wireless networks. For a general heterogeneous fog network consisting of many dispersive Fog Nodes (FNs) with diverse resources and capabilities, some of them have delay-sensitive tasks to process, i.e., Task Nodes (TNs), while some have spare resources to help their neighboring TNs to process tasks, i.e., Helper Nodes (HNs). How to effectively map multiple tasks or TNs into multiple HNs to minimize every task's service delay in a distributed manner is a fundamental challenge, which is key to reap the full benefits of fog computing. The problem becomes more challenging when tasks can be divided into multiple subtasks to further reduce the service delay via distributed computing. To tackle this challenge, in this paper, a generalized nash equilibrium (NE) game called Parallel Scheduling of Multiple Tasks (PSMT) is formulated and studied. The structure properties of the problem are deduced and thus the existence of NE is proven by the fixed point theorem. Further, the corresponding distributed task scheduling algorithm/mechanism is developed via Gauss-Seidel-type method. Simulation results show that the proposed PSMT algorithm can converge in a fast way and offer much better performance in system average delay and number of beneficial TNs, comparing to the Paired Offloading of Multiple Tasks (POMT) solution to the counterpart problem not supporting distributed computing.