This review covers research on the topic of mixed criticality systems that has been published since Vestal’s 2007 paper. It covers the period up to and including December 2015. The review is organised into the following topics: introduction and motivation, models, single processor analysis (including job-based, hard and soft tasks, fixed priority and EDF scheduling, shared resources and static and synchronous scheduling), multiprocessor analysis, related topics, realistic models, formal treatments, and systems issues. An appendix lists funded projects in the area of mixed criticality.

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Mixed Criticality Systems - A Review

Efficiently scheduling data processing jobs on distributed compute clusters requires complex algorithms. Current systems use simple, generalized heuristics and ignore workload characteristics, since developing and tuning a scheduling policy for each workload is infeasible. In this paper, we show that modern machine learning techniques can generate highly-efficient policies automatically. Decima uses reinforcement learning (RL) and neural networks to learn workload-specific scheduling algorithms without any human instruction beyond a high-level objective, such as minimizing average job completion time. However, off-the-shelf RL techniques cannot handle the complexity and scale of the scheduling problem. To build Decima, we had to develop new representations for jobs' dependency graphs, design scalable RL models, and invent RL training methods for dealing with continuous stochastic job arrivals. Our prototype integration with Spark on a 25-node cluster shows that Decima improves average job completion time by at least 21% over hand-tuned scheduling heuristics, achieving up to 2x improvement during periods of high cluster load.

https://dl.acm.org/doi/pdf/10.1145/3341302.3342080

Learning scheduling algorithms for data processing clusters

Efficiently scheduling data processing jobs on distributed compute clusters requires complex algorithms. Current systems, however, use simple generalized heuristics and ignore workload characteristics, since developing and tuning a scheduling policy for each workload is infeasible. In this paper, we show that modern machine learning techniques can generate highly-efficient policies automatically. Decima uses reinforcement learning (RL) and neural networks to learn workload-specific scheduling algorithms without any human instruction beyond a high-level objective such as minimizing average job completion time. Off-the-shelf RL techniques, however, cannot handle the complexity and scale of the scheduling problem. To build Decima, we had to develop new representations for jobs' dependency graphs, design scalable RL models, and invent RL training methods for dealing with continuous stochastic job arrivals. Our prototype integration with Spark on a 25-node cluster shows that Decima improves the average job completion time over hand-tuned scheduling heuristics by at least 21%, achieving up to 2x improvement during periods of high cluster load.

Learning Scheduling Algorithms for Data Processing Clusters

This survey covers research into mixed criticality systems that has been published since Vestal’s seminal paper in 2007, up until the end of 2016. The survey is organised along the lines of the major research areas within this topic. These include single processor analysis (including fixed priority and Earliest Deadline First (EDF) scheduling, shared resources, and static and synchronous scheduling), multiprocessor analysis, realistic models, and systems issues. The survey also explores the relationship between research into mixed criticality systems and other topics such as hard and soft time constraints, fault tolerant scheduling, hierarchical scheduling, cyber physical systems, probabilistic real-time systems, and industrial safety standards.

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A Survey of Research into Mixed Criticality Systems

This paper considers the scheduling of parallel real-time tasks with implicit deadlines. Each parallel task is characterized as a general directed acyclic graph (DAG). We analyze three different real-time scheduling strategies: two well known algorithms, namely global earliest-deadline-first and global rate-monotonic, and one new algorithm, namely federated scheduling. The federated scheduling algorithm proposed in this paper is a generalization of partitioned scheduling to parallel tasks. In this strategy, each high-utilization task (utilization age; 1) is assigned a set of dedicated cores and the remaining low-utilization tasks share the remaining cores. We prove capacity augmentation bounds for all three schedulers. In particular, we show that if on unit-speed cores, a task set has total utilization of at most m and the critical-path length of each task is smaller than its deadline, then federated scheduling can schedule that task set on m cores of speed 2, G-EDF can schedule it with speed 3 + v5/2 2.618, and G-RM can schedule it with speed 2 + v3 3.732. We also provide lower bounds on the speedup and show that the bounds are tight for federated scheduling and G-EDF when m is sufficiently large.

https://www.cse.wustl.edu/%7Elu/papers/ecrts14.pdf

Analysis of Federated and Global Scheduling for Parallel Real-Time Tasks

Multi-core processors offer a significant performance increase over single-core processors. They have the potential to enable computation-intensive real-time applications with stringent timing constraints that cannot be met on traditional single-core processors. However, most results in traditional multiprocessor real-time scheduling are limited to sequential programming models and ignore intra-task parallelism. In this paper, we address the problem of scheduling periodic parallel tasks with implicit deadlines on multi-core processors. We first consider a synchronous task model where each task consists of segments, each segment having an arbitrary number of parallel threads that synchronize at the end of the segment. We propose a new task decomposition method that decomposes each parallel task into a set of sequential tasks. We prove that our task decomposition achieves a resource augmentation bound of 4 and 5 when the decomposed tasks are scheduled using global EDF and partitioned deadline monotonic scheduling, respectively. Finally, we extend our analysis to a directed acyclic graph (DAG) task model where each node in the DAG has a unit execution requirement. We show how these tasks can be converted into synchronous tasks such that the same decomposition can be applied and the same augmentation bounds hold. Simulations based on synthetic workload demonstrate that the derived resource augmentation bounds are safe and sufficient.

Multi-core real-time scheduling for generalized parallel task models

Recently, multi-core processors have become mainstream in processor design. To take full advantage of multi-core processing, computation-intensive real-time systems must exploit intra-task parallelism. In this paper, we address the problem of real-time scheduling for a general model of deterministic parallel tasks, where each task is represented as a directed acyclic graph (DAG) with nodes having arbitrary execution requirements. We prove processor-speed augmentation bounds for both preemptive and non-preemptive real-time scheduling for general DAG tasks on multi-core processors. We first decompose each DAG into sequential tasks with their own release times and deadlines. Then we prove that these decomposed tasks can be scheduled using preemptive global EDF with a resource augmentation bound of 4. This bound is as good as the best known bound for more restrictive models, and is the first for a general DAG model. We also prove that the decomposition has a resource augmentation bound of 4 plus a constant non-preemption overhead for non-preemptive global EDF scheduling. To our knowledge, this is the first resource augmentation bound for non-preemptive scheduling of parallel tasks. Finally, we evaluate our analytical results through simulations that demonstrate that the derived resource augmentation bounds are safe in practice.

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Parallel Real-Time Scheduling of DAGs

As multicore processors become ever more prevalent, it is important for real-time programs to take advantage of intra-task parallelism in order to support computation-intensive applications with tight deadlines. We prove that a Global Earliest Deadline First (GEDF) scheduling policy provides a capacity augmentation bound of 4-2/m and a resource augmentation bound of 2-1/m for parallel tasks in the general directed a cyclic graph model. For the proposed capacity augmentation bound of 4-2/m for implicit deadline tasks under GEDF, we prove that if a task set has a total utilization of at most m/(4-2/m) and each task's critical path length is no more than 1/(4-2/m) of its deadline, it can be scheduled on a machine with m processors under GEDF. Our capacity augmentation bound therefore can be used as a straightforward schedulability test. For the standard resource augmentation bound of 2-1/m for arbitrary deadline tasks under GEDF, we prove that if an ideal optimal scheduler can schedule a task set on m unit-speed processors, then GEDF can schedule the same task set on m processors of speed 2-1/m. However, this bound does not lead to a schedulabilty test since the ideal optimal scheduler is only hypothetical and is not known. Simulations confirm that the GEDF is not only safe under the capacity augmentation bound for various randomly generated task sets, but also performs surprisingly well and usually outperforms an existing scheduling technique that involves task decomposition.

Outstanding Paper Award: Analysis of Global EDF for Parallel Tasks

The multi-core revolution presents both opportunities and challenges for real-time systems. Parallel computing can yield significant speedup for individual tasks (enabling shorter deadlines, or more computation within the same deadline), but unless managed carefully may add complexity and overhead that could potentially wreck real-time performance. There is little experience to date with the design and implementation of realtime systems that allow parallel tasks, yet the state of the art cannot progress without the construction of such systems. In this work we describe the design and implementation of a scheduler and runtime dispatcher for a new concurrency platform, RT-OpenMP, whose goal is the execution of real-time workloads with intra-task parallelism.

https://www.cse.wustl.edu/~kunal/resources/Papers/rtsched.pdf

Jing Li

Papers

Multi-core real-time scheduling for generalized parallel task models

Analysis of Federated and Global Scheduling for Parallel Real-Time Tasks

Parallel Real-Time Scheduling of DAGs

Outstanding Paper Award: Analysis of Global EDF for Parallel Tasks

A real-time scheduling service for parallel tasks