Generalized tardiness bounds for global multiprocessor scheduling

We consider the issue of deadline tardiness under global multiprocessor scheduling algorithms. We present a general tardiness-bound derivation that is applicable to a wide variety of such algorithms (including some whose tardiness behavior has not been analyzed before). Our derivation is very general: job priorities may change rather arbitrarily at runtime, capacity restrictions may exist on certain processors, and, under certain conditions, non-preemptive regions are allowed. Our results show that, with the exception of static-priority algorithms, most global algorithms considered previously have bounded tardiness. In addition, our results provide a simple means for checking whether tardiness is bounded under newly-developed algorithms

GEDF Tardiness: Open Problems Involving Uniform Multiprocessors and Affinity Masks Resolved

Prior work has shown that the global earliest-deadline-first (GEDF) scheduler is soft real-time (SRT)-optimal for sporadic task systems in a variety of contexts, meaning that bounded deadline tardiness can be guaranteed under it for any task system that does not cause platform overutilization. However, one particularly compelling context has remained elusive: multiprocessor platforms in which tasks have affinity masks that determine the processors where they may execute. Actual GEDF implementations, such as the SCHED_DEADLINE class in Linux, have dealt with this unresolved question by foregoing SRT guarantees once affinity masks are set. This unresolved question, as it pertains to SCHED_DEADLINE, was included by Peter Zijlstra in a list of important open problems affecting Linux in his keynote talk at ECRTS 2017. In this paper, this question is resolved along with another open problem that at first blush seems unrelated but actually is. Specifically, both problems are closed by establishing two results. First, a proof strategy used previously to establish GEDF tardiness bounds that are exponential in size on heterogeneous uniform multiprocessors is generalized to show that polynomial bounds exist on a wider class of platforms. Second, both uniform multiprocessors and identical multiprocessors with affinities are shown to be within this class. These results yield the first polynomial GEDF tardiness bounds for the uniform case and the first such bounds of any kind for the identical-with-affinities case

Federated Scheduling for Stochastic Parallel Real-time Tasks

Federated scheduling is a strategy to schedule parallel real-time tasks: It allocates a dedicated cluster of cores to high-utilization task (utilization \u3e1); It uses a multiprocessor scheduling algorithm to schedule and execute all low-utilization tasks sequentially, on a shared cluster of the remaining cores. Prior work has shown that federated scheduling has the best known capacity augmentation bound of 2 for parallel tasks with implicit deadlines. In this paper, we explore the soft real-time performance of federated scheduling and address the average-case workloads instead of the worst-case values. In particular, we consider stochastic tasks -- tasks for which execution time and critical-path length are random variables. In this case, we use bounded expected tardiness as the schedulability criterion. We define a stochastic capacity augmentation bound and prove that federated scheduling algorithms guarantee the same bound of 2 for stochastic tasks. We present three federated mapping algorithms for core allocation. All of them guarantee bounded expected tardiness and provide the same capacity augmentation bound; In practice, however, we expect them to provide different performances, both in terms of the task sets they can schedule and the actual tardiness they guarantee. Therefore, we performed numerical evaluations using randomly generated task sets to understand the practical differences between the three algorithms

Tight Tardiness Bounds for Pseudo-Harmonic Tasks Under Global-EDF-Like Schedulers

The global earliest-deadline-first (GEDF) scheduler and its variants are soft-real-time (SRT) optimal for periodic/sporadic tasks, meaning they provide bounded tardiness so long as the underlying platform is not over-utilized. Although their SRT-optimality has long been known, tight tardiness bounds for these schedulers have remained elusive. In this paper, a tardiness bound, that does not depend on the processor or task count, is derived for pseudo-harmonic periodic tasks, which are commonly used in practice, under global-EDF-like (GEL) schedulers. This class of schedulers includes both GEDF and first-in-first-out (FIFO). This bound is shown to be generally tight via an example. Furthermore, it is shown that exact tardiness bounds for GEL-scheduled pseudo-harmonic periodic tasks can be computed in pseudo-polynomial time

10071 Abstracts Collection -- Scheduling

From 14.02. to 19.02.2010, the Dagstuhl Seminar 10071 ``Scheduling \u27\u27 was held in Schloss Dagstuhl-Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Experimental Analysis of the Tardiness of Parallel Tasks in Soft Real-time Systems

International audienceA parallel application is defined as the application that can be executed on multiple processors simultaneously. In software, parallelism is a useful programming technique to take advantage of the hard-ware advancement in processors manufacturing nowadays. In real-time systems, where tasks have to respect certain timing constraints during execution, a single task has a shorter response time when executed in parallel than the sequential execution. However, the same cannot be trivially applied to a set of parallel tasks (taskset) sharing the same processing platform, and there is a negative intuition regarding parallelism in real-time systems. In this work, we are interested in analyzing this statement and providing an experimental analysis regarding the effect of parallelism soft on real-time systems. By performing an extensive simulation of the scheduling process of parallel taskset on multiprocessor systems using a known scheduling algorithm called the global Earliest-Deadline First (gEDF), we aim at providing an indication about the effects (positive or negative) of parallelism in real-time scheduling

Compositional Analysis Techniques For Multiprocessor Soft Real-Time Scheduling

The design of systems in which timing constraints must be met (real-time systems) is being affected by three trends in hardware and software development. First, in the past few years, multiprocessor and multicore platforms have become standard in desktop and server systems and continue to expand in the domain of embedded systems. Second, real-time concepts are being applied in the design of general-purpose operating systems (like Linux) and attempts are being made to tailor these systems to support tasks with timing constraints. Third, in many embedded systems, it is now more economical to use a single multiprocessor instead of several uniprocessor elements; this motivates the need to share the increasing processing capacity of multiprocessor platforms among several applications supplied by different vendors and each having different timing constraints in a manner that ensures that these constraints were met. These trends suggest the need for mechanisms that enable real-time tasks to be bundled into multiple components and integrated in larger settings. There is a substantial body of prior work on the multiprocessor schedulability analysis of real-time systems modeled as periodic and sporadic task systems. Unfortunately, these standard task models can be pessimistic if long chains of dependent tasks are being analyzed. In work that introduces less pessimistic and more sophisticated workload models, only partitioned scheduling is assumed so that each task is statically assigned to some processor. This results in pessimism in the amount of needed processing resources. In this dissertation, we extend prior work on multiprocessor soft real-time scheduling and construct new analysis tools that can be used to design component-based soft real-time systems. These tools allow multiprocessor real-time systems to be designed and analyzed for which standard workload and platform models are inapplicable and for which state-of-the-art uniprocessor and multiprocessor analysis techniques give results that are too pessimistic

Parallel Real-Time Scheduling for Latency-Critical Applications

In order to provide safety guarantees or quality of service guarantees, many of today\u27s systems consist of latency-critical applications, e.g. applications with timing constraints. The problem of scheduling multiple latency-critical jobs on a multiprocessor or multicore machine has been extensively studied for sequential (non-parallizable) jobs and different system models and different objectives have been considered. However, the computational requirement of a single job is still limited by the capacity of a single core. To provide increasingly complex functionalities of applications and to complete their higher computational demands within the same or even more stringent timing constraints, we must exploit the internal parallelism of jobs, where individual jobs are parallel programs and can potentially utilize more than one core in parallel. However, there is little work considering scheduling multiple parallel jobs that are latency-critical. This dissertation focuses on developing new scheduling strategies, analysis tools, and practical platform design techniques to enable efficient and scalable parallel real-time scheduling for latency-critical applications on multicore systems. In particular, the research is focused on two types of systems: (1) static real-time systems for tasks with deadlines where the temporal properties of the tasks that need to execute is known a priori and the goal is to guarantee the temporal correctness of the tasks prior to their executions; and (2) online systems for latency-critical jobs where multiple jobs arrive over time and the goal to optimize for a performance objective of jobs during the execution. For static real-time systems for parallel tasks, several scheduling strategies, including global earliest deadline first, global rate monotonic and a novel federated scheduling, are proposed, analyzed and implemented. These scheduling strategies have the best known theoretical performance for parallel real-time tasks under any global strategy, any fixed priority scheduling and any scheduling strategy, respectively. In addition, federated scheduling is generalized to systems with multiple criticality levels and systems with stochastic tasks. Both numerical and empirical experiments show that federated scheduling and its variations have good schedulability performance and are efficient in practice. For online systems with multiple latency-critical jobs, different online scheduling strategies are proposed and analyzed for different objectives, including maximizing the number of jobs meeting a target latency, maximizing the profit of jobs, minimizing the maximum latency and minimizing the average latency. For example, a simple First-In-First-Out scheduler is proven to be scalable for minimizing the maximum latency. Based on this theoretical intuition, a more practical work-stealing scheduler is developed, analyzed and implemented. Empirical evaluations indicate that, on both real world and synthetic workloads, this work-stealing implementation performs almost as well as an optimal scheduler