Recent research in compositional real-time systems has focused on determination of a component's real-time interface parameters. An important objective in interface-parameter determination is minimizing the bandwidth allocated to each component of the system while simultaneously guaranteeing component schedulability. With this goal in mind, in this paper we develop a fully-polynomial-time approximation scheme (FPTAS) for allocating bandwidth for sporadic task systems scheduled by fixed priority (e.g., deadline monotonic, rate monotonic) upon an Explicit-Deadline Periodic (EDP) resource. Our parametric algorithm takes the task system and an accuracy parameter $\epsilon > 0$ as input, and returns a bandwidth which is guaranteed to be at most a factor $(1 + \epsilon)$ times the optimal minimum bandwidth required to successfully schedule the task system. By simulations over synthetically generated task systems, we observe a significant decrease in runtime and a small relative error when comparing our proposed algorithm with the exact algorithm and the sufficient algorithm.