An <sc>fptas</sc> for Response Time Analysis of Fixed Priority Real-Time Tasks with Resource Augmentation

Abstract

Response time analysis is required both for on-line admission of applications in dynamic systems and as an integral part of design tools for complex distributed real-time systems. We consider sporadic tasks with fixed-priorities and arbitrary deadlines to be executed upon a uniprocessor platform. Pseudo-polynomial time algorithms are known for computing exact worst-case response times for this task model. Nevertheless, the problem is known NP-hard and there cannot exist a constant approximation algorithm for response time computation, unless P=NP. We propose a fully polynomial time approximation scheme (FPTAS) for computing response time upper bounds under resource augmentation. The resource augmentation is defined as the processor speedup factor bounded by (1 + 1/k), where k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">def</sup> [1 = ε]-1 for any constant ε ∈ (0;1), the FPTAS accuracy parameter. This algorithm is best possible in the sense that resource augmentation is indeed necessary for an efficient response time calculation.