Joint Optimal Allocation of Radio and Computational Resources Aiming at Minimizing Global Average Task Offloading Age for Long-Term Multi-Cell MEC Systems

This paper investigates the joint optimal allocation of radio and computational resources aiming to minimize global average task offloading age (TOA) over all time slots and mobile devices (MDs) for long-term multi-cell MEC systems with continuous arrival of MDs. TOA represents the total number of offloading time slots, including both transmission and computation. The joint resource allocation problem cannot be solved online because its objective function is long-term average of TOA over all time slots. We transform the long-term resource allocation problem into an online one by the Lyapunov method, then an iterative algorithm is proposed to solve the online problem. The idea of this algorithm is computing iteratively the two sub-problems which optimize sub-channel allocation and offloading power and computational resources joint allocation based on an initial resource allocation scheme. The alternating direction method of multipliers (ADMM) method is employed to solve the first sub-problem. For the second sub-problem, a closed-form expression of optimal power is deduced by solving a convex optimization problem using the Lagrange multiplier method, then the sub-problem is simplified into a linear programming (LP) problem about computational resource allocation. The improved iterative greedy (IIG) algorithm is applied to solve the LP problem. Simulation results demonstrate that the proposed algorithm approaches the performance of the optimal branch-and-bound (BnB) algorithm in the MEC systems with one-time arrival of MDs, and outperforms two benchmark schemes such as first in first out (FIFO) and Chang’s algorithm.