Schedulability analysis of global edf

The generalized multiframe task model (GMF) extends the sporadic task model and multiframe task model. Each frame in the GMF model contains an execution time, a relative deadline, and a minimum inter-arrival time. These parameters are fixed after task specification time in the GMF model. However, multimedia and adaptive control systems may be overloaded and no longer stabilized when the task parameters in such systems are not flexible. In order to address this problem, deadlines and periods of frames may change to alleviate temporal overload, e.g., in the parameter adaptation and elastic scheduling model. In this paper, we propose a new model GMF-PA (the GMF model with parameter adaptation). This model allows task parameters to be flexible in arbitrary-deadline systems. A necessary schedulability test based on mixed-integer linear programming is given to check the schedulability under EDF scheduling and optimally assign frame deadlines and periods at the same time. We also prove that the test is a sufficient and necessary schedulability test when frame deadlines and periods must be integers. An approximation algorithm is also deployed to reduce computational running time and indicates a sufficient schedulability test in general. The speed-up factor of our approximation algorithm is $$1+\epsilon $$ where $$\epsilon $$ can be arbitrarily small, with respect to the exact schedulability test of GMF-PA tasks under EDF. We also apply the GMF model to self-suspending tasks. By extending recent work on scheduling self-suspending tasks, we remove the assumption that frame deadlines are equally assigned in self-suspending tasks, and the system is extended from constrained-deadline systems to arbitrary-deadline systems. We have done extensive experiments to show that the schedulability ratio is improved using our techniques in our GMF-PA model.

Although preemptive uniprocessor scheduling algorithms are able to successfully schedule some systems that cannot be scheduled by any non-preemptive scheduling algorithm, the run-time overhead associated with implementing preemptive algorithms is often higher than for non-preemptive algorithms. In choosing between preemptive and non-preemptive scheduling algorithms on uniprocessors, the tradeoff is therefore between enhanced feasibility on the one hand, and increased overheads on the other. Hybrid scheduling schemes are proposed and evaluated here: these schemes permit preemption where necessary for feasibility, but attempt to avoid unnecessary preemptions during run-time. This is done by determining, for each task in the system, the longest amount of time for which the task may execute non-preemptively without compromising the feasibility of the system.

A polynomial-time algorithm is presented for partitioning a collection of sporadic tasks among the processors of an identical multiprocessor platform. Since the partitioning problem is NP-hard in the strong sense, this algorithm is unlikely to be optimal. A quantitative characterization of its worst-case performance is provided in terms of resource augmentation; it is shown that any set of sporadic tasks that can be partitioned among the processors of an m-processor identical multiprocessor platform will be partitioned by this algorithm on an m-processor platform in which each processor is (4 - 2/m) times as fast

This paper presents a new algorithm for fixed-priority scheduling of sporadic task systems on multiprocessors.The algorithm is categorized to such a scheduling class that qualifies a few tasks to migrate across processors, while most tasks are fixed to particular processors. We design the algorithm so that a task is qualified to migrate, only if it cannot be assigned to any individual processors, in such a way that it is never returned to the same processor within the same period, once it is migrated from one processor to another processor. The scheduling policy is then conformed to deadline monotonic. According to the simulation results, the new algorithm significantly outperforms the traditional fixed-priority algorithms in terms of schedulability.

End-to-end flows, which have a set of chainlike subtasks, are widely used in distributed real-time systems. For instance, multimedia and automative applications require that subtasks finish executing on a chain of processors before their end-to-end deadlines. The scheduling of such chained subtasks decides the schedulability of a distributed realtime system. Since the subtask priority assignment problem is NP-hard in general, most heuristics are presented to schedule end-to-end flows in two separate steps. The first step calculates intermediate relative deadlines for frames, and the second step makes scheduling decisions under EDF scheduling. Because the quality of the priority assignment of subtasks will directly affect the schedulability of the distributed systems, the two separate steps may cause pessimism in schedulability analysis. To reduce potential pessimism, we combine the two steps in our novel dGMF-PA (distributed generalized multiframe tasks with parameter adaption) model. We present an algorithm based on mixed-integer linear programming for optimally selecting frame relative deadlines in the dGMF-PA model. An approximation algorithm is also proposed to reduce computational running time. Our approximation algorithm has a tunable speed-up factor of 1 + ϵ where ϵ can be arbitrarily small, with respect to the exact schedulability test of dGMF-PA tasks under EDF scheduling. Extensive experiments have shown that our approximation algorithm (which is a sufficient schedulability test) can schedule at most 44 % more than HOSPA, an existing state-of-the-art algorithm.

The integration of mixed-critical tasks into a platform is an increasingly important trend in the design of real-time systems due to its efficient resource usage. With a growing variety of activation patterns considered in real-time systems, some of them capture arbitrary activation patterns. As a consequence, the existing scheduling approaches in mixed-criticality systems (MCs), which assume the sporadic tasks with implicit deadlines, have sometimes become inapplicable or are ineffective. In this paper, we extend the sporadically activated task model to the arbitrarily activated task model in MCs with the preemptive fixed-task-priority schedule. By using the event arrival curve to model task activations, we present the necessary and sufficient schedulability tests that are based on the well-established results from Real-Time Calculus. We propose to use the busy-window analysis to do the sufficient test because it has been shown to be tighter than the sufficient test of using Real-Time Calculus. According to our experimental results, for sporadic task sets, our proposed test can achieve the same performance as the state-of-the-art schedulability test. However, compared with the previous schedulability analysis of preemptive fixed-task-priority, our approaches can handle more general tasks with blocking, jitter, and arbitrary deadlines.

In this paper we introduce a robust earliest deadline scheduling algorithm for dealing with hard aperiodic tasks under overloads in a dynamic real-time environment. The algorithm synergistically combines many features including dynamic guarantees, graceful degradation in overloads, deadline tolerance, resource reclaiming, and dynamic re-guarantees. A necessary and sufficient schedulability test is presented, and an efficient 0(n) guarantee algorithm is proposed. The new algorithm is evaluated via simulation and compared to several baseline algorithms. The experimental results show excellent performance of the new algorithm in normal and overload conditions.

We address the problem of schedulability analysis for a set of sporadic real-time tasks scheduled by the Global Earliest Deadline First (G-EDF) policy on a multiprocessor platform. State-of-the-art tests for schedulability analysis of multiprocessor global scheduling are often incomparable. That is, a task set that is judged not schedulable by a test may be verified to be schedulable by another test, and vice versa. In this paper, we first develop a new schedulability test that integrates the limited carry-in technique and Response Time Analysis (RTA) procedure for Global EDF schedulability analysis. Then, we provide an over-approximate variant of this test with better run-time efficiency. Later, we extend these two tests to self-suspending tasks. All schedulability tests proposed in the paper have provable dominance over their state-of-the-art counterparts. Finally, we conduct extensive comparisons among different schedulability tests. Our new tests show significant improvements for schedulability analysis of Global EDF.

An efficient approach for the multiprocessor non-preemptive strictly periodic task scheduling problem

On Non-preemptive Scheduling of Recurring Tasks Using Inserted Idle Times

Heterogeneous multiprocessor architectures allow embedded real-time systems to better match computing resources to each application's needs and dynamic workload requirements, thereby providing many opportunities for improved performance with reduced power consumption. Unfortunately, guaranteeing real-time requirements on heterogeneous multiprocessors remains a critical problem due to the lack of appropriate scheduling algorithms and analysis methods. In this paper, we consider EDZL (Earliest Deadline First until Zero-Laxity) for performance asymmetric multiprocessor scheduling. EDZL has been shown to outperform other scheduling policies such as global EDF on identical multiprocessors. We show that EDZL is still effective on performance asymmetric multi-processors, and present an efficient EDZL schedulability test. Experimental results show that EDZL scheduling is able to schedule up to 20% more task sets than global EDF and that our new EDZL schedulability test can accept up to 30% more schedulable task sets than a presently exiting one.

A schedulability test is defined to be sustainable if any task system deemed schedulable by the test remains so if it behaves better than mandated by its system specifications. We provide a formal definition of sustainability, and subject the concept to systematic analysis in the context of the uniprocessor scheduling of periodic and sporadic task systems. We argue that it is in general good engineering practice to use sustainable tests if possible, and classify common uniprocessor schedulability tests according to whether they are sustainable or not.

Schedulability analysis techniques that are well understood within the real-time scheduling community are applied to the analysis of recurrent real-time workloads that are modeled using the synchronous data-flow graph (SDFG) model. An enhancement to the standard SDFG model is proposed, that permits the specification of a real-time latency constraint between a specified input and a specified output of an SDFG. A technique is derived for transforming such an enhanced SDFG to a collection of traditional 3-parameter sporadic tasks, thereby allowing for the analysis of systems of SDFG tasks using the methods and algorithms that have previously been developed within the real-time scheduling community for the analysis of systems of such sporadic tasks. The applicability of this approach is illustrated by applying prior results from real-time scheduling theory to construct an exact preemptive uniprocessor schedulability test for collections of recurrent processes that are each represented using the enhanced SDFG model.

Real-time systems usually consist of a set of periodic and sporadic tasks. Periodic tasks can be divided into two classes: synchronous and asynchronous. The first type does not define the task first release, contrary to the second. Hence, synchronous periodic tasks are assumed to be released at the worst instant: the critical instant. The schedulability test is reduced to check a single execution of the task under analysis. The integration of sporadic tasks is also straightforward: they are treated as a periodic task with maximum arrival frequency. On the other hand, asynchronous periodic tasks require a test for each release in the hyper period and the integration of sporadic tasks is not trivial: the worst release instant is unknown a priori. However, they do not assume that the tasks are released at the worst instant.This paper presents a new schedulability analysis method based on the Response Time Analysis (RTA) to determine the worst response time of both asynchronous periodic and sporadic tasks, scheduled by a fixed-priority preemptive algorithm with general deadlines. It also presents another method that enables the introduction of a user configurable degree of pessimism, reducing the hyper period dependency.

The generalized multiframe task model (GMF) extends the sporadic task model and multiframe task model. Each frame in the GMF model contains an execution time, a relative deadline, and a minimum inter-arrival time. These parameters are fixed after task specification time in the GMF model. However, multimedia and adaptive control systems may be overloaded and no longer stabilized when the task parameters in such systems are not flexible. In order to address this problem, deadlines and periods may change to alleviate temporal overload, for example in the parameter adaption and elastic scheduling model. In this paper, we propose a new model GMF-PA (the GMF model with parameter adaption). This model allows task parameters to be flexible in arbitrary-deadline systems. A necessary schedulability test based on mixed-integer linear programming (MILP) is given to check the schedulability under EDF scheduling and optimally assign deadlines and periods at the same time. We also prove that the test is a sufficient and necessary schedulability test when task parameters must be integers. An approximation algorithm is also deployed to reduce computational running time. The speed-up factor of our approximation algorithm is 1+a#x0395; where a#x0395; can be arbitrarily small, with respect to the exact schedulability test of GMF-PA tasks under EDF. We also apply the GMF model to self-suspending tasks. By extending recent work on scheduling self-suspending tasks, we remove the assumption that deadlines are equally assigned in self-suspending tasks, and the system is extended from constrained-deadline systems to arbitrary-deadline systems. We have done exhaustive experiments to show that the schedulability ratio is improved using our techniques in our GMF-PA model.