Satellite-terrestrial integrated networks (STIN) are envisioned as a promising architecture for ubiquitous network connections to support diversified services. In this paper, we propose a novel resource slicing scheme with cross-cell coordination in STIN to satisfy distinct service delay requirements and efficient resource usage. To address the challenges posed by spatiotemporal dynamics in service demands and satellite mobility, we formulate the resource slicing problem into a long-term optimization problem and propose a distributed resource slicing (DRS) scheme for scalable and flexible resource management across different cells. Specifically, a hybrid data-model co-driven approach is developed, including an asynchronous multi-agent reinforcement learning-based algorithm to determine the optimal satellite set serving each cell and a distributed optimization-based algorithm to make the resource reservation decisions for each slice. Simulation results demonstrate that the proposed scheme outperforms benchmark methods in terms of resource usage and delay performance.
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