LADO: Lyapunov-ADMM Optimization for Task Scheduling and Resource Allocation in Edge Computing

With the rapid growth of IoT devices and the increasing demand for low-latency applications, edge computing has become a key paradigm. Scheduling tasks between resource-constrained edge devices and cloud servers to optimize performance (e.g., cost, delay) while ensuring service quality (e.g., queue stability, energy consumption) is a challenging problem. This paper addresses dynamic task scheduling and resource allocation in an edge computing system with multiple edge devices and a cloud server. The goal is to minimize the long-term average system cost (e.g., weighted sum of task completion delay) while ensuring that task queues are stable, and meeting energy consumption constraints. We apply Lyapunov optimization to transform the long-term optimization problem into deterministic subproblems per time slot, introducing actual and virtual queues for energy constraints. Then a distributed Alternating Direction Method of Multipliers(ADMM) algorithm is designed to optimize local decisions at each device and coordinate with the cloud server with minimal information exchange. We use bayesian methods to handle system uncertainty, improving adaptability via online learning. Theoretical analysis shows that this algorithm guarantees task and virtual queue stability and ensures long-term energy constraints, with the system cost converging to a near-optimal value at a rate of O(1/V) by adjusting parameter V in Lyapunov optimization, achieving a balance between performance and backlog.