Optimal Task Offloading and Resource Allocation for Fog Computing

Thai T. Vu, Diep N. Nguyen, Dinh Thai Hoang, Eryk Dutkiewicz

We propose a novel multi-tier fog and cloud computing architecture that enables edge nodes to cooperate in sharing computing and radio resources so as to minimize the total energy consumption of mobile users subject to their delay requirements. We first formulate the joint task offloading and resource allocation optimization problem as a mixed integer non-linear programming (MINLP). Due to the combination of binary (offloading decisions) and real variables (resource allocations), the problem is an NP-hard and computationally intractable. To circumvent, we relax the binary decision variables to transform the MINLP to a relaxed optimization problem with real variables. After proving that the relaxed problem is a convex one, we propose three solutions namely ROP, IBBA, and FFBD. In ROP, the solution of the relaxing problem is converted to the integer one and used as the final solution. In IBBA, the branch-and-bound method is combined with different offloading priority policies yielding two variants IBBA-LFC and IBBA-LCF. Note that the branch and bound method like IBBA may require exponential complexity in the worst case. As such, we develop a distributed approach, namely feasibility-finding Benders decomposition (FFBD), that decomposes the original problem into a master problem for the offloading decision and subproblems for resource allocation. These (simpler) subproblems can be solved in parallel at fog nodes, thus help reduce both the complexity and the computational time. FFBD has two different versions (FFBD-S and FFBD-F) is a distributed algorithm based on Benders decomposition. The numerical results show that IBBA-LFC/LCF and FFBD-S/F gain the optimal solution minimizing the total energy consumption and meet all delay requirements for mobile users. The FFBD-F with the fast solution detection method also has the least computation time of four algorithms IBBA-LFC/LCF and FFBD-S/F.

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