There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The Grid 2: Blueprint for a New Computing Infrastructure

This survey covers hard real-time scheduling algorithms and schedulability analysis techniques for homogeneous multiprocessor systems. It reviews the key results in this field from its origins in the late 1960s to the latest research published in late 2009. The survey outlines fundamental results about multiprocessor real-time scheduling that hold independent of the scheduling algorithms employed. It provides a taxonomy of the different scheduling methods, and considers the various performance metrics that can be used for comparison purposes. A detailed review is provided covering partitioned, global, and hybrid scheduling algorithms, approaches to resource sharing, and the latest results from empirical investigations. The survey identifies open issues, key research challenges, and likely productive research directions.

/pdf/a-survey-of-hard-real-time-scheduling-for-multiprocessor-313o35g6ho.pdf

A survey of hard real-time scheduling for multiprocessor systems

This paper is based on a conjecture that the more confidence one needs in a task execution time bound (the less tolerant one is of missed deadlines), the larger and more conservative that bound tends to become in practice. We assume different tasks perform functions having different criticalities and requiring different levels of assurance. We assume a task may have a set of alternative worst-case execution times, each assured to a different level of confidence. This paper presents ways to use this information to obtain more precise schedulability analysis and more efficient preemptive fixed priority scheduling. These methods are evaluated using workloads abstracted from production avionics systems.

Preemptive Scheduling of Multi-criticality Systems with Varying Degrees of Execution Time Assurance

In this 25th year anniversary paper for the IEEE Real Time Systems Symposium, we review the key results in real-time scheduling theory and the historical events that led to the establishment of the current real-time computing infrastructure. We conclude this paper by looking at the challenges ahead of us.

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Real Time Scheduling Theory: A Historical Perspective

The scheduling of systems of periodic tasks upon multiprocessor platforms is considered. Utilization-based conditions are derived for determining whether a periodic task system meets all deadlines when scheduled using the earliest deadline first scheduling algorithm (EDF) upon a given multiprocessor platform. A new priority-driven algorithm is proposed for scheduling periodic task systems upon multiprocessor platforms: this algorithm is shown to successfully schedule some task systems for which EDF may fail to meet all deadlines.

Priority-Driven Scheduling of Periodic Task Systems on Multiprocessors

Each processor in a uniform multiprocessor machine is characterized by a speed or computing capacity, with the interpretation that a job executing on a processor with speed s for t time units completes (s/spl times/t) units of execution. The on-line scheduling of hard-real-time systems, in which all jobs must complete by specified deadlines, on uniform multiprocessor machines is considered It is known that online algorithms tend to perform very poorly in scheduling such hard-real-time systems on multiprocessors; resource-augmentation techniques are presented here that permit online algorithms to perform better than may be expected given the inherent limitations. Results derived here are applied to the scheduling of periodic task systems on uniform multiprocessor machines.

http://cobweb.cs.uga.edu/~shelby/pubs/funkGB2001.pdf

On-line scheduling on uniform multiprocessors

Current trends in the embedded systems field tend to collocate multiple functionalities upon a single computing platform, the aim being to reduce both the size and cost of embedded systems. Nevertheless, it is unlikely that all functionalities share the same level of criticality, and certification of the system has to be achieved using varying degrees of rigorousness. Typically, a task tau_i is guaranteed to meet its temporal constraints up to a criticality level that is equal to its own criticality. When those conditions are no longer met, i.e. when another higher priority task tau_j has its execution time that exceeds its Worst Case Execution Time (WCET) w.r.t. the criticality level of tau_i, a common approach is to suspend tau_i. However, in some cases, it may not be necessary to suspend tasks with a lower criticality immediately as they could still be executed without compromising the deadlines of high criticality tasks. As a step towards this aim, we propose a method, denoted Latest Completion Time (LCT), that allows lower criticality tasks to proceed with their execution as long as they do not prevent higher criticality tasks from meeting their deadlines. Furthermore, we show that tasks suspension can only be temporary, and prove that a particular definition of idle times can be used to reset the system's criticality level. Finally, we study the performances of our LCT mechanism w.r.t. the classical mechanism that suspends a task as soon as the system criticality level becomes higher than its own criticality.

Relaxing Mixed-Criticality Scheduling Strictness for Task Sets Scheduled with FP

These last years, we have witnessed a dramatic increase in the number of cores available in computational platforms. Concurrently, a new coding paradigm dividing tasks into smaller execution instances called threads, was developed to take advantage of the inherent parallelism of multiprocessor platforms. However, only few methods were proposed to efficiently schedule hard real-time multi-threaded tasks on multiprocessor. In this paper, we propose techniques optimizing the number of processors needed to schedule such sporadic parallel tasks with constrained deadlines. We first define an optimization problem determining, for each thread, an intermediate (artificial) deadline minimizing the number of processors needed to schedule the whole task set. The scheduling algorithm can then schedule threads as if they were independent sequential sporadic tasks. The second contribution is an efficient and nevertheless optimal algorithm that can be executed online to determine the thread's deadlines. Hence, it can be used in dynamic systems were all tasks and their characteristics are not known a priori. We finally prove that our techniques achieve a resource augmentation bound of 2 when the threads are scheduled with algorithms such as U-EDF, PD^2, LLREF, DP-Wrap, etc.

/pdf/techniques-optimizing-the-number-of-processors-to-schedule-2g7iggh4zn.pdf

Techniques Optimizing the Number of Processors to Schedule Multi-threaded Tasks

https://hal.inria.fr/inria-00192215/document

Joël Goossens

Papers

Priority-Driven Scheduling of Periodic Task Systems on Multiprocessors

On-line scheduling on uniform multiprocessors

Relaxing Mixed-Criticality Scheduling Strictness for Task Sets Scheduled with FP

Techniques Optimizing the Number of Processors to Schedule Multi-threaded Tasks

Integrating job parallelism in real-time scheduling theory