[Paper Review] Energy-efficient Resource Allocation for Mobile Edge Computing Aided by Multiple Relays

Xiang Li, Rongfei Fan+3 more|arXiv (Cornell University)|Apr 8, 2020

IoT and Edge/Fog Computing23 references4 citations

TL;DR

This paper proposes energy-efficient resource allocation in mobile edge computing (MEC) systems using multiple relay nodes to minimize total energy consumption. It formulates and solves non-convex optimization problems for decode-and-forward (DF-TDMA, DF-FDMA) and amplify-and-forward (AF) relaying modes, achieving optimal or convergent solutions via convex relaxation, monotonic optimization, and successive convex approximation, with numerical results confirming significant energy savings across all modes.

ABSTRACT

In this paper, we study a mobile edge computing (MEC) system with the mobile device aided by multiple relay nodes for offloading data to an edge server. Specifically, the modes of decode-and-forward (DF) with time-division-multiple-access (TDMA) and frequency-division-multiple-access (FDMA), and the mode of amplify-and-forward (AF) are investigated, which are denoted as DF-TDMA, DF-FDMA, and AF, respectively. Our target is to minimize the total energy consumption of the mobile device and multiple relay nodes through optimizing the allocation of computation and communication resources. Optimization problems under the three considered modes are formulated and shown to be non-convex. For DF-TDMA mode, we transform the original non-convex problem to be a convex one and further develop a low computation complexity yet optimal solution. In DF-FDMA mode, with some transformation on the original problem, we prove the mathematical equivalence between the transformed problem in DF-FDMA mode and the problem under DF-TDMA mode. In AF mode, the associated optimization problem is decomposed into two levels, in which monotonic optimization is utilized in upper level and successive convex approximation (SCA) is adopted to find the convergent solution in the lower level. Numerical results prove the effectiveness of our proposed methods under various working modes.

Motivation & Objective

• To minimize total energy consumption in mobile edge computing (MEC) systems with multiple relay nodes.
• To address the non-convex nature of resource allocation problems in MEC with relay-assisted offloading.
• To develop low-complexity, optimal, or convergent solutions for three relaying modes: DF-TDMA, DF-FDMA, and AF.
• To evaluate the performance gains of the proposed schemes under various channel and system conditions.

Proposed method

• Transforms the non-convex DF-TDMA problem into a convex one using variable substitution and applies convex optimization for an optimal solution.
• Proves mathematical equivalence between the DF-FDMA and DF-TDMA problems through variable transformation, enabling reuse of the DF-TDMA solution method.
• Decomposes the AF mode problem into two levels: uses monotonic optimization in the upper level and successive convex approximation (SCA) in the lower level to achieve convergence.
• Employs first-order convex approximation of logarithmic terms in SCA to iteratively refine the solution while maintaining feasibility.
• Uses a surrogate function based on the first-order Taylor expansion to lower-bound the original objective, ensuring monotonic descent in the SCA process.
• Validates convergence of the SCA method by proving that the surrogate problem’s objective at each iteration is a lower bound of the original problem.

Experimental results

Research questions

• RQ1 How can energy consumption be minimized in an MEC system with multiple relay nodes under different relaying protocols?
• RQ2 Can the non-convex optimization problems in DF-TDMA and DF-FDMA modes be transformed into convex forms for optimal solution?
• RQ3 What is the most effective approach to solve the non-convex AF mode resource allocation problem?
• RQ4 How do the proposed schemes compare in terms of energy efficiency and computational complexity across different relaying modes?

Key findings

• The DF-TDMA problem is transformed into a convex problem, enabling a low-complexity optimal solution.
• The DF-FDMA problem is mathematically equivalent to the DF-TDMA problem, allowing reuse of the same solution method.
• The AF mode solution converges via successive convex approximation (SCA), with convergence proven using Cauchy’s theorem and surrogate function analysis.
• Numerical results demonstrate significant energy reduction across all three relaying modes—DF-TDMA, DF-FDMA, and AF—under various channel and system conditions.
• The SCA-based method for AF mode ensures monotonic decrease in the objective function, with the sequence of solutions converging to a stationary point.
• The proposed schemes outperform baseline methods in energy efficiency, particularly in poor channel conditions or high data offloading demands.