k2U: A General Framework from k-Point Effective Schedulability Analysis to Utilization-Based Tests

To deal with a large variety of workloads in different application domains in real-time embedded systems, a number of expressive task models have been developed. For each individual task model, researchers tend to develop different types of techniques for deriving schedulability tests with different computation complexity and performance. In this paper, we present a general schedulability analysis framework, namely the k2U framework, that can be potentially applied to analyze a large set of real-time task models under any fixed-priority scheduling algorithm, on both uniprocessor and multiprocessor scheduling. The key to k2U is a k-point effective schedulability test, which can be viewed as a "blackbox" interface. For any task model, if a corresponding k-point effective schedulability test can be constructed, then a sufficient utilization-based test can be automatically derived. We show the generality of k2U by applying it to different task models, which results in new and improved tests compared to the state-of-the-art. Analogously, a similar concept by testing only k points with a different formulation has been studied by us in another framework, called k2Q, which provides quadratic bounds or utilization bounds based on a different formulation of schedulability test. With the quadratic and hyperbolic forms, k2Q and k2U frameworks can be used to provide many quantitive features to be measured, 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 a "blackbox" interface for schedulability tests and response-time analysis

Quasinormal Modes and Hidden Conformal Symmetry of Warped dS3_3 Black Hole

In this paper, we analytically calculate the quasinormal modes of scalar, vector, tensor, and spinor perturbations of the warped dS$_3$ black hole. There are two horizons for the warped dS$_3$ black hole, namely, the black hole horizon $r_b$ and the cosmological horizon $r_c$. In the calculation, we impose the ingoing boundary condition at the black hole horizon and the outgoing boundary condition at the cosmological horizon. We also investigate the hidden conformal symmetry of the warped dS$_3$ black hole in the region between the black hole horizon and the cosmological horizon $r_b<r<r_c$. We use the hidden conformal symmetry to construct the quasinormal modes in an algebraic way and find that the results agree with the analytically ones. It turns out that the frequencies of the quasinormal modes could be identified with the poles in the thermal boundary-boundary correlators.Comment: 26 pages, references added, published versio