Joint User Association, Resource Allocation, and Beamforming in RIS-Assisted Multi-Server MEC Systems

Multi-access edge computing (MEC) is a promising solution to supporting resource-intensive applications on mobile devices (MDs), which enables computation offloading from MDs to edge servers at their proximities. However, the quality of the communication links and the limited communication and computing resources significantly impact the performance of MEC systems. In this paper, we leverage the emerging reconfigurable intelligent surfaces (RISs) to assist the computation offloading and balance the computing workloads in a multi-server MEC system with limited communication and computing resources. Specifically, when a nearby edge server is overwhelmed by multiple computing tasks, some MDs can be redirected to potentially distant but lighter-loaded edge servers by employing passive beamforming enabled by RISs. Thus, to maximize the task completion rate, we formulate a joint optimization problem for user association, passive beamforming at RISs, receive beamforming at BSs, and computing resource allocation on edge servers. Since the problem is a mixed integer nonlinear programming (MINLP), which is challenging to solve, we first decompose it into two tractable subproblems through the block coordinate descent (BCD) technique and then solve them by the penalty dual decomposition (PDD) method and a swap matching-based algorithm, respectively. Numerical results demonstrate that the task completion rate can be significantly increased by incorporating RISs into multi-server MEC systems. Besides, the proposed algorithms outperform other benchmark schemes in terms of both the task completion rate and the design complexity.