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

Towards Efficient Explainability of Schedulability Properties in Real-Time Systems

The notion of efficient explainability was recently introduced in the context of hard-real-time scheduling: a claim that a real-time system is schedulable (i.e., that it will always meet all deadlines during run-time) is defined to be efficiently explainable if there is a proof of such schedulability that can be verified by a polynomial-time algorithm. We further explore this notion by (i) classifying a variety of common schedulability analysis problems according to whether they are efficiently explainable or not; and (ii) developing strategies for dealing with those determined to not be efficiently schedulable, primarily by identifying practically meaningful sub-problems that are efficiently explainable

Schedulability, Response Time Analysis and New Models of P-FRP Systems

Functional Reactive Programming (FRP) is a declarative approach for modeling and building reactive systems. FRP has been shown to be an expressive formalism for building applications of computer graphics, computer vision, robotics, etc. Priority-based FRP (P-FRP) is a formalism that allows preemption of executing programs and guarantees real-time response. Since functional programs cannot maintain state and mutable data, changes made by programs that are preempted have to be rolled back. Hence in P-FRP, a higher priority task can preempt the execution of a lower priority task, but the preempted lower priority task will have to restart after the higher priority task has completed execution. This execution paradigm is called Abort-and-Restart (AR). Current real-time research is focused on preemptive of non-preemptive models of execution and several state-of-the-art methods have been developed to analyze the real-time guarantees of these models. Unfortunately, due to its transactional nature where preempted tasks are aborted and have to restart, the execution semantics of P-FRP does not fit into the standard definitions of preemptive or non-preemptive execution, and the research on the standard preemptive and non-preemptive may not applicable for the P-FRP AR model. Out of many research areas that P-FRP may demands, we focus on task scheduling which includes task and system modeling, priority assignment, schedulability analysis, response time analysis, improved P-FRP AR models, algorithms and corresponding software. In this work, we review existing results on P-FRP task scheduling and then present our research contributions: (1) a tighter feasibility test interval regarding the task release offsets as well as a linked list based algorithm and implementation for scheduling simulation; (2) P-FRP with software transactional memory-lazy conflict detection (STM-LCD); (3) a non-work-conserving scheduling model called Deferred Start; (4) a multi-mode P-FRP task model; (5) SimSo-PFRP, the P-FRP extension of SimSo - a SimPy-based, highly extensible and user friendly task generator and task scheduling simulator.Computer Science, Department o

The multiprocessor real-time scheduling of general task systems

The recent emergence of multicore and related technologies in many commercial systems has increased the prevalence of multiprocessor architectures. Contemporaneously, real-time applications have become more complex and sophisticated in their behavior and interaction. Inevitably, these complex real-time applications will be deployed upon these multiprocessor platforms and require temporal analysis techniques to verify their correctness. However, most prior research in multiprocessor real-time scheduling has addressed the temporal analysis only of Liu and Layland task systems. The goal of this dissertation is to extend real-time scheduling theory for multiprocessor systems by developing temporal analysis techniques for more general task models such as the sporadic task model, the generalized multiframe task model, and the recurring real-time task model. The thesis of this dissertation is: Optimal online multiprocessor real-time scheduling algorithms for sporadic and more general task systems are impossible; however, efficient, online scheduling algorithms and associated feasibility and schedulability tests, with provably bounded deviation from any optimal test, exist. To support our thesis, this dissertation develops feasibility and schedulability tests for various multiprocessor scheduling paradigms. We consider three classes of multiprocessor scheduling based on whether a real-time job may migrate between processors: full-migration, restricted-migration, and partitioned. For all general task systems, we obtain feasibility tests for arbitrary real-time instances under the full-and restricted-migration paradigms. Despite the existence of tests for feasibility, we show that optimal online scheduling of sporadic and more general systems is impossible. Therefore, we focus on scheduling algorithms that have constant-factor approximation ratios in terms of an analysis technique known as resource augmentation. We develop schedulability tests for scheduling algorithms, earliest-deadline-first (edf) and deadline-monotonic (dm), under full-migration and partitioned scheduling paradigms. Feasibility and schedulability tests presented in this dissertation use the workload metrics of demand-based load and maximum job density and have provably bounded deviation from optimal in terms of resource augmentation. We show the demand-based load and maximum job density metrics may be exactly computed in pseudo-polynomial time for general task systems and approximated in polynomial time for sporadic task systems

Analysis of Real-Time Capabilities of Dynamic Scheduled System

This PhD-thesis explores different real-time scheduling approaches to effectively utilize industrial real-time applications on multicore or manycore platforms. The proposed scheduling policy is named the Time-Triggered Constant Phase scheduler for handling periodic tasks, which determines time windows for each computation and communication in advance by using the dependent task model

EDF-schedulability of synchronous periodic task systems is coNP-hard

In the synchronous periodic task model, a set \tau_1,...,\tau_n of tasks is given, each releasing jobs of running time c_i with relative deadline d_i, at each integer multiple of the period p_i. It is a classical result that Earliest Deadline First (EDF) is an optimal preemptive uni-processor scheduling policy. For constrained deadlines, i.e. d_i = 0: \sum_{i=1}^n (floor(Q-d_i)/p_i) + 1) * c_i <= Q. Though an enormous amount of literature deals with this topic, the complexity status of this test has remained unknown. We prove that testing EDF-schedulability of such a task system is (weakly) coNP-hard. This solves Problem 2 from the survey "Open Problems in Real-time Scheduling" by Baruah & Pruhs. The hardness result is achieved by applying recent results on inapproximability of Diophantine approximation

Efficient Allocation And Enforcement Of Interfaces In Compositional Real-Time Systems

Compositional real-time research has become one of the emerging trends in embedded and real-time systems due to the increasing scale and complexity of such systems. In this design paradigm, a large system is decomposed into smaller and simpler components, each of which abstracts their temporal requirements via interfaces. Such systems are mostly implemented by resource partitions to ensure that the components receive resources according to their interfaces. Potential implementations of a resource partition are via server-based interfaces or demand-based interfaces. In this context, our thesis in this dissertation is as follows: Currently, server-based interfaces ensure strong temporal isolation among components at the cost of resource over-provisioning whereas demand-based interfaces precisely model the resource demand of a component without the guarantee of temporal isolation. For both these models, efficient and effective resource allocation as well as strict temporal isolation among components can be achieved. Specifically, we can obtain efficient and near-optimal bandwidth allocation schemes and admission controllers for periodic resource model and arbitrary demand-based interface respectively. Furthermore, efficient slack reclamation technique can be obtained to allocate unused processing resources at runtime while still enforcing the given interface. To support our thesis, we address efficient resource allocation among components with server-based interfaces by providing fully-polynomial-time approximation schemes (FPTAS) for allocating processing resource to components scheduled by earliest-deadline-first (EDF) or fixed-priority (FP) scheduling algorithm. For enforcing temporal isolation of demand-based interfaces, we provide a parametric approximate admission control algorithm, which has polynomial-time complexity in terms of number of active jobs in the system and the approximation parameter. Finally, to address efficient reclamation of unused processing resources, we give a novel technique to optimally and efficiently determine maximum allowable runtime slack for a component with arbitrary interface, considering active jobs in the system and guaranteeing system schedulability even for worst-case future job arrival scenarios. We expect that these techniques can ultimately be used to minimize the size, weight, and power requirements of real-time and embedded systems by reducing the processing resource requirements of such systems