Low-Earth Orbit (LEO) satellite networks are a key enabler for the 6G Non-Terrestrial Network (NTN) architecture. However, supporting time-sensitive services in LEO networks is challenging due to highly dynamic topologies and the difficulty of maintaining precise global time synchronization. Existing Time-Sensitive Networking (TSN) mechanisms largely rely on static topologies and strict synchronization, which makes them ill-suited to dynamic LEO environments. To address this issue, we propose CRT, a deterministic transmission framework tailored for LEO networks. CRT regulates per-hop residence time using local clocks, thereby compensating for link-delay variations without requiring strict global synchronization. To handle asynchronous collisions, CRT adopts a collision-tolerant scheduling strategy that maximizes the number of schedulable flows while bounding collision-induced jitter. We formalize the corresponding scheduling problem and show that it is NP-hard. We further develop CRT-Fast, an efficient heuristic algorithm. It combines iterative layering with path continuity to control collision intensity and improve path stability under topology changes. Simulations on Iridium and Starlink constellations show that the proposed method achieves lower delay jitter and high schedulability under heavy traffic loads.

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