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Autonomous vehicles (AVs) must drive across a variety of challenging environments that impose continuously-varying deadlines and runtime-accuracy tradeoffs on their software pipelines. A deadline-driven execution of such AV pipelines requires a new class of systems that enable the computation to maximize accuracy under dynamically-varying deadlines. Designing these systems presents interesting challenges that arise from combining ease-of-development of AV pipelines with deadline specification and enforcement mechanisms. Our work addresses these challenges through D3 (Dynamic Deadline-Driven), a novel execution model that centralizes the deadline management, and allows applications to adjust their computation by modeling missed deadlines as exceptions. Further, we design and implement ERDOS, an open-source realization of D3 for AV pipelines that exposes finegrained execution events to applications, and provides mechanisms to speculatively execute computation and enforce deadlines between an arbitrary set of events. Finally, we address the crucial lack of AV benchmarks through our state-of-the-art open-source AV pipeline, Pylot, that works seamlessly across simulators and real AVs. We evaluate the efficacy of D3 and ERDOS by driving Pylot across challenging driving scenarios spanning 50km, and observe a 68% reduction in collisions as compared to prior execution models.