Collaborative edge computing addresses the resource constraints of individual edge nodes by enabling resource sharing and task co-processing across multiple nodes. To fully leverage the advantages of collaborative edge computing, joint optimization of service deployment and task scheduling is necessary. Existing optimization methods insufficiently address the collaboration across spatial and temporal dimensions, which hinders their adaptability to the spatiotemporally varying nature of user demands and system states. This paper focuses on optimizing the expected task processing delay in edge networks. We propose a two-timescale online optimization framework to jointly determine: i) service deployment decisions at each large timescale; and ii) task scheduling decisions at each small timescale. Specifically, the convex optimization technique is used to solve the task scheduling problem, while a multi-agent deep reinforcement learning technique is employed for the service deployment problem. These two methods are combined for spatiotemporal co-optimization through a two-timescale alternating optimization approach. Compared to the baseline algorithms, the proposed scheme achieves better delay performance, while also exhibiting low running time and favorable convergence behavior.
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