The rapid development of autonomous driving poses new research challenges for on-vehicle computing system. The execution time of autonomous driving tasks heavily depends on the driving environment. As the scene becomes complex, task execution time increases significantly, leading to end-to-end deadline misses and potential accidents. Hence, a framework that can effectively schedule tasks according to the driving environment in order to guarantee end-to-end deadlines is critical for autonomous driving. In this article, we propose AutoRS, an environment-dependent real-time scheduling framework for end-to-end autonomous driving. AutoRS consists of two nested control loops. The inner control loop schedules tasks based on the driving environment to help them meet end-to-end deadlines while prioritizing the responsiveness and throughput of control commands. The outer control loop tunes task rates based on schedulability to efficiently utilize system resources with an RL-based design. We conduct extensive experiments on both simulation and hardware testbeds using representative autonomous driving applications. The results demonstrate that AutoRS effectively improves the driving performance by 7.95\%-56.9\%7.95%-56.9% in different driving environments. AutoRS can significantly enhance the safety and reliability of autonomous driving systems by providing timely control commands in complex and dynamic driving environments while guaranteeing task deadlines.