Approximate Bandwidth Allocation for Compositional Real-Time Systems

Allocation of bandwidth among components is a fundamental problem in compositional real-time systems. State-of-the-art algorithms for bandwidth allocation use either exponential-time or pseudo-polynomial-time techniques for exact allocation, or linear-time, utilization-based techniques which may over-provision bandwidth. In this paper, we develop a fully-polynomial-time approximation scheme (FPTAS) for allocating bandwidth for sporadic task systems scheduled by earliest-deadline first (EDF) upon an Explicit-Deadline Periodic (EDP) resource. Our algorithm takes, as parameters, the task system and an accuracy parameter $\epsilon ≫ 0$, and returns a bandwidth which is guaranteed to be at most a factor $(1 + \epsilon)$ more than the optimal minimum bandwidth required to successfully schedule the task system. Furthermore, the algorithm has time complexity that is polynomial in the number of tasks and $1/\epsilon$. Via simulations over randomly-generated task systems, we have observed a several orders of magnitude decrease in runtime and a small relative error when comparing our proposed algorithm with the exact algorithm, even for medium-sized values of $\epsilon$ (e.g., $\epsilon \approx .3$).