Abstract: Server-based resource reservation protocols (e.g., periodic and bandwidth-sharing servers) have the advantage of providing temporal isolation between subsystems co-executing upon a shared processing platform. However, for many of these protocols, temporal isolation is often obtained at the price of over-provisioned reservations. Other more fine-grained approaches such as real-time calculus (RTC) permit a precise characterization of the resources required by a subsystem via demand-curve interfaces. An important, unsolved challenge for subsystems specified by demand-curve interfaces is the development of admission control algorithms. Admission control is required to ensure that the demand-curve specified by the interface is never violated. In this paper, we take an initial step towards addressing this challenge by designing an admission controller for a simple, ``single-step'' demand curve. Our approach utilizes and extends techniques originally proposed for admission control in the settings of aperiodic jobs upon dedicated uniprocessors and bandwidth-sharing servers. In future work, we hope to use these techniques as the basis for constructing admission controllers for complex, arbitrary demand-curve interfaces.