Algorithms for Hierarchical and Semi-Partitioned Parallel Scheduling

We propose a model for scheduling jobs in a parallel machine setting that takes into account the cost of migrations by assuming that the processing time of a job may depend on the specific set of machines among which the job is migrated. For the makespan minimization objective, the model generalizes classical scheduling problems such as unrelated parallel machine scheduling, as well as novel ones such as semi-partitioned and clustered scheduling. In the case of a hierarchical family of machines, we derive a compact integer linear programming formulation of the problem and leverage its fractional relaxation to obtain a polynomial-time 2-approximation algorithm. Extensions that incorporate memory capacity constraints are also discussed

REAL-TIME SCHEDULING ON ASYMMETRIC MULTIPROCESSOR PLATFORMS

Real-time scheduling analysis is crucial for time-critical systems, in which provable timing guarantees are more important than observed raw performance. Techniques for real-time scheduling analysis initially targeted uniprocessor platforms but have since evolved to encompass multiprocessor platforms. However, work directed at multiprocessors has largely focused on symmetric platforms, in which every processor is identical. Today, it is common for a multiprocessor to include heterogeneous processing elements, as this offers advantages with respect to size, weight, and power (SWaP) limitations. As a result, realizing modern real-time systems on asymmetric multiprocessor platforms is an inevitable trend. Unfortunately, principles and mechanisms regarding real-time scheduling on such platforms are relatively lacking. The goal of this dissertation is to enrich such principles and mechanisms, by bridging existing analysis for symmetric multiprocessor platforms to asymmetric ones and by developing new techniques that are unique for asymmetric multiprocessor platforms. The specific contributions are threefold. First, for a platform consisting of processors that differ with respect to processing speeds only, this dissertation shows that the preemptive global earliest-deadline-first (G-EDF) scheduler is optimal for scheduling soft real-time (SRT) task systems. Furthermore, it shows that semi-partitioned scheduling, which is a hybrid of conventional global and partitioned scheduling approaches, can be applied to optimally schedule both hard real-time (HRT) and SRT task systems. Second, on platforms that consist of processors with different functionalities, tasks that belong to different functionalities may process the same source data consecutively and therefore have producer/consumer relationships among them, which are represented by directed acyclic graphs (DAGs). End-to-end response-time bounds for such DAGs are derived in this dissertation under a G-EDF-based scheduling approach, and it is shown that such bounds can be improved by a linear-programming-based deadline-setting technique. Third, processor virtualization can lead a symmetric physical platform to be asymmetric. In fact, for a designated virtual-platform capacity, there exist an infinite number of allocation schemes for virtual processors and a choice must be made. In this dissertation, a particular asymmetric virtual-processor allocation scheme, called minimum-parallelism (MP) form, is shown to dominate all other schemes including symmetric ones.Doctor of Philosoph

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

Scheduling techniques to improve the worst-case execution time of real-time parallel applications on heterogeneous platforms

The key to providing high performance and energy-efficient execution for hard real-time applications is the time predictable and efficient usage of heterogeneous multiprocessors. However, schedulability analysis of parallel applications executed on unrelated heterogeneous multiprocessors is challenging and has not been investigated adequately by earlier works. The unrelated model is suitable to represent many of the multiprocessor platforms available today because a task (i.e., sequential code) may exhibit a different work-case-execution-time (WCET) on each type of processor on an unrelated heterogeneous multiprocessors platform. A parallel application can be realistically modeled as a directed acyclic graph (DAG), where the nodes are sequential tasks and the edges are dependencies among the tasks. This thesis considers a sporadic DAG model which is used broadly to analyze and verify the real-time requirements of parallel applications. A global work-conserving scheduler can efficiently utilize an unrelated platform by executing the tasks of a DAG on different processor types. However, it is challenging to compute an upper bound on the worst-case schedule length of the DAG, called makespan, which is used to verify whether the deadline of a DAG is met or not. There are two main challenges. First, because of the heterogeneity of the processors, the WCET for each task of the DAG depends on which processor the task is executing on during actual runtime. Second, timing anomalies are the main obstacle to compute the makespan even for the simpler case when all the processors are of the same type, i.e., homogeneous multiprocessors. To that end, this thesis addresses the following problem: How we can schedule multiple sporadic DAGs on unrelated multiprocessors such that all the DAGs meet their deadlines. Initially, the thesis focuses on homogeneous multiprocessors that is a special case of unrelated multiprocessors to understand and tackle the main challenge of timing anomalies. A novel timing-anomaly-free scheduler is proposed which can be used to compute the makespan of a DAG just by simulating the execution of the tasks based on this proposed scheduler. A set of representative task-based parallel OpenMP applications from the BOTS benchmark suite are modeled as DAGs to investigate the timing behavior of real-world applications. A simulation framework is developed to evaluate the proposed method. Furthermore, the thesis targets unrelated multiprocessors and proposes a global scheduler to execute the tasks of a single DAG to an unrelated multiprocessors platform. Based on the proposed scheduler, methods to compute the makespan of a single DAG are introduced. A set of representative parallel applications from the BOTS benchmark suite are modeled as DAGs that execute on unrelated multiprocessors. Furthermore, synthetic DAGs are generated to examine additional structures of parallel applications and various platform capabilities. A simulation framework that simulates the execution of the tasks of a DAG on an unrelated multiprocessor platform is introduced to assess the effectiveness of the proposed makespan computations. Finally, based on the makespan computation of a single DAG this thesis presents the design and schedulability analysis of global and federated scheduling of sporadic DAGs that execute on unrelated multiprocessors

Analysis and implementation of the multiprocessor bandwidth inheritance protocol

The Multiprocessor Bandwidth Inheritance (M-BWI) protocol is an extension of the Bandwidth Inheritance (BWI) protocol for symmetric multiprocessor systems. Similar to Priority Inheritance, M-BWI lets a task that has locked a resource execute in the resource reservations of the blocked tasks, thus reducing their blocking time. The protocol is particularly suitable for open systems where different kinds of tasks dynamically arrive and leave, because it guarantees temporal isolation among independent subsets of tasks without requiring any information on their temporal parameters. Additionally, if the temporal parameters of the interacting tasks are known, it is possible to compute an upper bound to the interference suffered by a task due to other interacting tasks. Thus, it is possible to provide timing guarantees for a subset of interacting hard real-time tasks. Finally, the M-BWI protocol is neutral to the underlying scheduling policy: it can be implemented in global, clustered and semi-partitioned scheduling. After introducing the M-BWI protocol, in this paper we formally prove its isolation properties, and propose an algorithm to compute an upper bound to the interference suffered by a task. Then, we describe our implementation of the protocol for the LITMUS RT real-time testbed, and measure its overhead. Finally, we compare M-BWI against FMLP and OMLP, two other protocols for resource sharing in multiprocessor systems

CPU Energy-Aware Parallel Real-Time Scheduling

Both energy-efficiency and real-time performance are critical requirements in many embedded systems applications such as self-driving car, robotic system, disaster response, and security/safety control. These systems entail a myriad of real-time tasks, where each task itself is a parallel task that can utilize multiple computing units at the same time. Driven by the increasing demand for parallel tasks, multi-core embedded processors are inevitably evolving to many-core. Existing work on real-time parallel tasks mostly focused on real-time scheduling without addressing energy consumption. In this paper, we address hard real-time scheduling of parallel tasks while minimizing their CPU energy consumption on multicore embedded systems. Each task is represented as a directed acyclic graph (DAG) with nodes indicating different threads of execution and edges indicating their dependencies. Our technique is to determine the execution speeds of the nodes of the DAGs to minimize the overall energy consumption while meeting all task deadlines. It incorporates a frequency optimization engine and the dynamic voltage and frequency scaling (DVFS) scheme into the classical real-time scheduling policies (both federated and global) and makes them energy-aware. The contributions of this paper thus include the first energy-aware online federated scheduling and also the first energy-aware global scheduling of DAGs. Evaluation using synthetic workload through simulation shows that our energy-aware real-time scheduling policies can achieve up to 68% energy-saving compared to classical (energy-unaware) policies. We have also performed a proof of concept system evaluation using physical hardware demonstrating the energy efficiency through our proposed approach

Energy-efficient thermal-aware multiprocessor scheduling for real-time tasks using TCPNs

We present an energy-effcient thermal-aware real-time global scheduler for a set of hard real-time (HRT) tasks running on a multiprocessor system. This global scheduler fulfills the thermal and temporal constraints by handling two independent variables, the task allocation time and the selection of clock frequency. To achieve its goal, the proposed scheduler is split into two stages. An off-line stage, based on a deadline partitioning scheme, computes the cycles that the HRT tasks must run per deadline interval at the minimum clock frequency to save energy while honoring the temporal and thermal constraints, and computes the maximum frequency at which the system can run below the maximum temperature. Then, an on-line, event-driven stage performs global task allocation applying a Fixed-Priority Zero-Laxity policy, reducing the overhead of quantum-based or interval-based global schedulers. The on-line stage embodies an adaptive scheduler that accepts or rejects soft RT aperiodic tasks throttling CPU frequency to the upper lowest available one to minimize power consumption while meeting time and thermal constraints. This approach leverages the best of two worlds: the off-line stage computes an ideal discrete HRT multiprocessor schedule, while the on-line stage manage soft real-time aperiodic tasks with minimum power consumption and maximum CPU utilization