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In this paper, we investigate on-demand data services for high-speed trains via a cellular/infostation integrated network. Service requests and acknowledgements are sent through the cellular network to a content server, while data delivery is achieved via trackside infostations. The optimal resource allocation problem is formulated by taking account of the intermittent network connectivity and multi-service demands. In order to achieve efficient resource allocation with low computational complexity, the original problem is transformed into a single-machine preemptive scheduling problem based on a time-capacity mapping. As the service demands are not known a priori, an online resource allocation algorithm based on Smith ratio and exponential capacity is proposed. The performance bound of the online algorithm is characterized based on the theory of sequencing and scheduling. If the link from the backbone network to an infostation is a bottleneck, a service pre-downloading algorithm is also proposed to facilitate the resource allocation. The performance of the proposed algorithms is evaluated based on a real high-speed train schedule. Compared with the existing approaches, our proposed algorithms can significantly improve the quality of on-demand data service provisioning over the trip of a train.