SearcharxivSearch

arXiv · 1505.02155

Evaluate and Compare Two Utilization-Based Schedulability-Test Frameworks for Real-Time Systems

Abstract

This report summarizes two general frameworks, namely k2Q and k2U, that have been recently developed by us. The purpose of this report is to provide detailed evaluations and comparisons of these two frameworks. These two frameworks share some similar characteristics, but they are useful for different application cases. These two frameworks together provide comprehensive means for the users to automatically convert the pseudo polynomial-time tests (or even exponential-time tests) into polynomial-time tests with closed mathematical forms. With the quadratic and hyperbolic forms, k2Q and k2U frameworks can be used to provide many quantitive features to be measured and evaluated, like the total utilization bounds, speed-up factors, etc., not only for uniprocessor scheduling but also for multiprocessor scheduling. These frameworks can be viewed as "blackbox" interfaces for providing polynomial-time schedulability tests and response time analysis for real-time applications. We have already presented their advantages for being applied in some models in the previous papers. However, it was not possible to present a more comprehensive comparison between these two frameworks. We hope this report can help the readers and users clearly understand the difference of these two frameworks, their unique characteristics, and their advantages. We demonstrate their differences and properties by using the traditional sporadic realtime task models in uniprocessor scheduling and multiprocessor global scheduling.

Explore related subjects

Keep this discovery

BibTeXRIS

Jian-Jia Chen, Wen-Hung Huang, Cong Liu. 2015-05-08. Evaluate and Compare Two Utilization-Based Schedulability-Test Frameworks for Real-Time Systems. https://arxiv.org/abs/1505.02155

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS