Generalizing Response-Time Analysis

Abstract

In real-time theory, basically two approaches for the computation of response-times exist. One of them is the busy window method, the other is the real-time calculus, an extension of the network calculus. While both can be used to compute the bounds of response-times, they have different properties that make them suitable for different system architectures. The busy window approach on the one hand is able to obtain tight bounds for scheduling policies like round-robin. It is also capable of considering offsets, therefore delivering better results in the relevant cases. Hierarchical scheduling on the other hand can be better accounted for by the real-time calculus, where this is an inherent feature of the underlying concept. The approach we present in this paper takes the theory of hierarchy from the realtime calculus and uses it to generalize the response-time analysis. This is implemented as an extension of the busy window method, which enables it to analyze scheduling hierarchies of an arbitrary depth.

Probabilistic response‐time analysis for real‐time systems in body area sensor networks

“…; /, and let ‰ t denote the maximal subset of ‰ such that under any scenario 2 ‰ t , t is the minimal positive integer such that the cumulative request equals to t at time t . According to Lemma 4.1, the response time of task i under any scenario 2 ‰ t is t , and the probability that t is a response time of task i is the sum of the probability associated with each scenario 2 ‰ t based on equality (15), which is equal to the probability that t is the minimal positive integer such that the cumulative request for the task i and …. ; / (i.e., for the scenario set ‰) is t at time t .…”

“…Bini et al [14] studied the technique possessing continuity, efficient computability, and approximability for response-time bound analysis in fixed-priority scheduling with arbitrary deadlines. Pollex et al [15] presented a hierarchical response-time analysis based on real-time calculus. Nguyen et al [16] proposed an exact processor demand analysis method and defined a parametric polynomial time algorithm for the analysis of the approximate feasibility and the response-time upper bound.…”

General and efficient Response Time Analysis for EDF scheduling

“…It turns out that the RTA problem of EDF is more difficult than that of fixedpriority scheduling. Although RTA for fixed-priority scheduling has been extended to general workload and resource models represented by request bound functions (arrival curves) and supply bound functions (service curves) [10], no such work has been done for EDF to our best knowledge.…”