Green Large-Scale Fog Computing Resource Allocation Using Joint Benders Decomposition, Dinkelbach Algorithm, ADMM, and Branch-and-Bound

With the increasing demands for large-scale computing in Internet of Things network, fog computing emerges as a potential solution. However, the time and energy costs are the bottlenecks for developing fog computing. In this paper, we investigate the green fog computing by maximizing the network utility function considering energy efficiency with the constraints of power and interference. The proposed problem is a large-scale mixed integer nonlinear programming. To deal with such kind of problems, we design an algorithm framework to solve the problem in a distributed and parallel manner. The outer loop of the problem is based on the Benders decomposition to divide the integer variables and continuous variables into the master problems and subproblems, respectively. In the subproblem, we use the Dinkelbach algorithm to transform the fractional programming into an equivalent solvable form. In the inner loop, the large-scale problem with only continuous variables is handled by the alternating direction method of multipliers algorithm. For the master problem, we propose a centralized branch-and-bound algorithm to deal with the complexity. We also discuss the properties and performances of our algorithm. Finally, the simulation results indicate that our proposed algorithm is energy-efficient and time-saving.