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Advances in hardware capacity, especially I/O devices such as cameras and displays, are driving the development of applications like high-definition video conferencing that have tight timing and CPU requirements. Unfortunately, current operating systems do not adequately provide the timing response needed by these applications. In this paper, we present a hierarchical scheduling model that aims to provide these applications with tight timing response, while at the same time preserve the strengths of current schedulers, namely fairness and efficiency. Our approach, called cooperative polling, consists of an application-level event scheduler and a kernel thread scheduler that cooperate to dispatch time-constrained application events accurately and with minimal kernel preemption, while still ensuring rigorously that all applications share resources fairly. Fairness is enforced in a flexible manner, allowing sharing according to a mixture of both traditional resource-centric metrics and new application-centric metrics, the latter being critical to support graceful application-level adaptation in overload. Unlike traditional real-time systems, our model does not require specification or estimation of resource requirements, simplifying its usage dramatically. Our evaluation, using an adaptive video application and a graphics server, shows that our system has event dispatch accuracies that are one to two orders of magnitude smaller than are achieved by existing schedulers. At the same time, our scheduler still maintains fairness and has low overhead.