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We describe a new framework for resource allocation that unifies the well-known proportional share and reservation policies. By exploiting the duality between these policies, we provide a level of integration for scheduling batch, interactive, and real time applications not achieved before. To each client we associate a weight that represents the rate at which the client has to pay for the resource, and a share that represents the fraction of the resource that the client should receive. These two parameters are interdependent. A fixed rate corresponds to a proportional share allocation, while a fixed share corresponds to a reservation. Furthermore, once one parameter is fixed the other one results automatically: if a client asks for a fixed share then the competition for the resource determines the rate at which it has to pay, while if the rate is fixed, the competition determines the service time the client should receive. To implement this framework we have developed a new proportional share algorithm, called Earliest Eligible Virtual Deadline First, that achieves optimal accuracy, i.e., the difference between the service time that a client should receive in an ideal system, and the service time it has actually received in the real system is bounded by the size of a time quantum. This tight bound makes it possible to provide support for highly predictable, real-time services. As a proof of concept we have implemented a prototype of a CPU scheduler under the FreeBSD operating system. The experimental results show that our scheduler achieves the goal of providing integrated support for batch and real-time applications. Moreover, the accuracy of our implementation was within 10% of the theoretical bounds.