Laxity dynamics and LLF schedulability analysis on multiprocessor platforms

LLF (Least Laxity First) scheduling, which assigns a higher priority to a task with a smaller laxity, has been known as an optimal preemptive scheduling algorithm on a single processor platform. However, little work has been made to illuminate its characteristics upon multiprocessor platforms. In this paper, we identify the dynamics of laxity from the system’s viewpoint and translate the dynamics into LLF multiprocessor schedulability analysis. More specifically, we first characterize laxity properties under LLF scheduling, focusing on laxity dynamics associated with a deadline miss. These laxity dynamics describe a lower bound, which leads to the deadline miss, on the number of tasks of certain laxity values at certain time instants. This lower bound is significant because it represents invariants for highly dynamic system parameters (laxity values). Since the laxity of a task is dependent of the amount of interference of higher-priority tasks, we can then derive a set of conditions to check whether a given task system can go into the laxity dynamics towards a deadline miss. This way, to the author’s best knowledge, we propose the first LLF multiprocessor schedulability test based on its own laxity properties. We also develop an improved schedulability test that exploits slack values. We mathematically prove that the proposed LLF tests dominate the state-of-the-art EDZL tests. We also present simulation results to evaluate schedulability performance of both the original and improved LLF tests in a quantitative manner.

A conjecture about provably good task assignment on heterogeneous multiprocessor platforms but with a stronger adversary

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a heterogeneous multiprocessor platform. We use an algorithm proposed in [1] (we refer to it as LP-EE) from state-of-the-art for assigning tasks to heterogeneous multiprocessor platform and (re-)prove its performance guarantee but for a stronger adversary.We conjecture that if a task set can be scheduled to meet deadlines on a heterogeneous multiprocessor platform by an optimal task assignment scheme that allows task migrations then LP-EE meets deadlines as well with no migrations if given processors twice as fast. We illustrate this with an example.

Provably good task assignment on heterogeneous multiprocessor platforms for a restricted case but with a stronger adversary

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a heterogeneous multiprocessor platform. We consider a restricted case where the maximum utilization of any task on any processor in the system is no greater than one. We use an algorithm proposed in [1] (we refer to it as LP-EE) from state-of-the-art for assigning tasks to heterogeneous multiprocessor platform and (re-)prove its performance guarantee for this restricted case but for a stronger adversary. We show that if a task set can be scheduled to meet deadlines on a heterogeneous multiprocessor platform by an optimal task assignment scheme that allows task migrations then LP-EE meets deadlines as well with no migrations if given processors twice as fast.

Partitioned scheduling of multimode systems on multiprocessor platforms: when to do the mode transition?

Systems composed of distinct operational modes are a common necessity for embedded applications with strict timing requirements. With the emergence of multi-core platforms protocols to handle these systems are required in order to provide this basic functionality.In this work a description on the problems of creating an effective mode-transition protocol are presented and it is proven that in some cases previous single-core protocols can not be extended to handle the mode-transition in multi-core.

Two protocols without periodicity for the global and preemptive scheduling problem of multi-mode real-time systems upon multiprocessor Platforms

We consider the problem of scheduling a multi-mode real-time system upon identical multiprocessor platforms. Since it is a multi-mode system, the system can change from one mode to another such that the current task set is replaced with a new task set. Ensuring that deadlines are met requires not only that a schedulability test is performed on tasks in each mode but also that (i) a protocol for transitioning from one mode to another is specified and (ii) a schedulability test for each transition is performed. We propose two protocols which ensure that all the expected requirements are met during every transition between every pair of operating modes of the system. Moreover, we prove the correctness of our proposed algorithms by extending the theory about the makespan determination problem.

LLF schedulability analysis on multiprocessor platforms

LLF (Least Laxity First) scheduling, which assigns a higher priority to a task with smaller laxity, has been known as an optimal preemptive scheduling algorithm on a single processor platform. However, its characteristics upon multiprocessor platforms have been little studied until now. Orthogonally, it has remained open how to efficiently schedule general task systems, including constrained deadline task systems, upon multiprocessors. Recent studies have introduced zero laxity (ZL) policy, which assigns a higher priority to a task with zero laxity, as a promising scheduling approach for such systems (e.g., EDZL). Towards understanding the importance of laxity in multiprocessor scheduling, this paper investigates the characteristics of ZL policy and presents the first ZL schedulability test for any work-conserving scheduling algorithm that employs this policy. It then investigates the characteristics of LLF scheduling, which also employs the ZL policy, and derives the first LLF-specific schedulability test on multiprocessors. It is shown that the proposed LLF test dominates the ZL test as well as the state-of-art EDZL test.

Methodologies for implement video decoders over multiprocessor platforms

The latest video coding standards developed, like HEVC (High Efficiency Video Coding, approved in January 2013), require for their implementation the use of devices able to support a high computational load. Considering that currently it is not enough the usage of one unique Digital Signal Processor (DSP), multicore devices have appeared recently in the market. However, due to its novelty, the working methodology that allows produce solutions for these configurations is in a very initial state, since currently the most part of the work needs to be performed manually. In consequence, the objective set consists on finding methodologies that ease this process. The study has been focused on extend a methodology, under development, for the generation of solutions for PCs and embedded systems. During this study, the standards RVC (Reconfigurable Video Coding) and HEVC have been employed, as well as DSPs of the Texas Instruments company. In its development, it has been tried to address all the factors that influence both the development and deployment of these new implementations of video decoders, ranging from tools up to aspects of the partitioning of algorithms, without this can cause a drop in application performance. The results of this study are the description of the employed methodology, the characterization of the software migration process and performance measurements for the HEVC standard in an RVC-based implementation. RESUMEN Los estándares de codificación de vídeo desarrollados más recientemente, como HEVC (High Efficiency Video Coding, aprobado en enero de 2013), requieren para su implementación el uso de dispositivos capaces de soportar una elevada carga computacional. Teniendo en cuenta que actualmente no es suficiente con utilizar un único Procesador Digital de Señal (DSP), han aparecido recientemente dispositivos multinúcleo en el mercado. Sin embargo, debido a su novedad, la metodología de trabajo que permite elaborar soluciones para tales configuraciones se encuentra en un estado muy inicial, ya que actualmente la mayor parte del trabajo debe realizarse manualmente. En consecuencia, el objetivo marcado consiste en encontrar metodologías que faciliten este proceso. El estudio se ha centrado en extender una metodología, en desarrollo, para la generación de soluciones para PC y sistemas empotrados. Durante dicho estudio se han empleado los estándares RVC (Reconfigurable Video Coding) y HEVC, así como DSPs de la compañía Texas Instruments. En su desarrollo se ha tratado de atender a todos los factores que influyen tanto en el desarrollo como en la puesta en marcha de estas nuevas implementaciones de descodificadores de vídeo; abarcando desde las herramientas a utilizar hasta aspectos del particionado de los algoritmos, sin que por ello se produzca una reducción en el rendimiento de las aplicaciones. Los resultados de este estudio son una descripción de la metodología empleada, la caracterización del proceso de migración de software, y medidas de rendimiento para el estándar HEVC en una implementación basada en RVC.

The generalized multiprocessor periodic resource interface model for hierarchical multiprocessor scheduling

Composition is a practice of key importance in software engineering. When real-time applications are composed it is necessary that their timing properties (such as meeting the deadlines) are guaranteed. The composition is performed by establishing an interface between the application and the physical platform. Such an interface does typically contain information about the amount of computing capacity needed by the application. In multiprocessor platforms, the interface should also present information about the degree of parallelism. Recently there have been quite a few interface proposals. However, they are either too complex to be handled or too pessimistic.In this paper we propose the Generalized Multiprocessor Periodic Resource model (GMPR) that is strictly superior to the MPR model without requiring a too detailed description. We describe a method to generate the interface from the application specification. All these methods have been implemented in Matlab routines that are publicly available.

Optimal virtual cluster-based multiprocessor scheduling

Scheduling of constrained deadline sporadic task systems on multiprocessor platforms is an area which has received much attention in the recent past. It is widely believed that finding an optimal scheduler is hard, and therefore most studies have focused on developing algorithms with good processor utilization bounds. These algorithms can be broadly classified into two categories: partitioned scheduling in which tasks are statically assigned to individual processors, and global scheduling in which each task is allowed to execute on any processor in the platform. In this paper we consider a third, more general, approach called cluster-based scheduling. In this approach each task is statically assigned to a processor cluster, tasks in each cluster are globally scheduled among themselves, and clusters in turn are scheduled on the multiprocessor platform. We develop techniques to support such cluster-based scheduling algorithms, and also consider properties that minimize total processor utilization of individual clusters. In the last part of this paper, we develop new virtual cluster-based scheduling algorithms. For implicit deadline sporadic task systems, we develop an optimal scheduling algorithm that is neither Pfair nor ERfair. We also show that the processor utilization bound of us-edf{m/(2m−1)} can be improved by using virtual clustering. Since neither partitioned nor global strategies dominate over the other, cluster-based scheduling is a natural direction for research towards achieving improved processor utilization bounds.

Multiprocessor real-time scheduling considering concurrency and urgency

It has been widely studied how to schedule real-time tasks on multiprocessor platforms. Several studies find optimal scheduling policies for implicit deadline task systems, but it is hard to understand how each policy utilizes the two important aspects of scheduling real-time tasks on multiprocessors:inter-job concurrency and job urgency. In this paper, we introduce a new scheduling policy that considers these two properties. We prove that the policy is optimal for the special case when the execution time of all tasks are equally one and deadlines are implicit, and observe that the policy is a new concept in that it is not an instance of Pfair or ERfair. It remains open to find a schedulability condition for general task systems under our scheduling policy.

Compositional multiprocessor scheduling: the GMPR interface

Composition is a practice of key importance in software engineering. When real-time applications are composed, it is necessary that their timing properties (such as meeting the deadlines) are guaranteed. The composition is performed by establishing an interface between the application and the physical platform. Such an interface typically contains information about the amount of computing capacity needed by the application. For multiprocessor platforms, the interface should also present information about the degree of parallelism. Several interface proposals have recently been put forward in various research works. However, those interfaces are either too complex to be handled or too pessimistic. In this paper we propose the generalized multiprocessor periodic resource model (GMPR) that is strictly superior to the MPR model without requiring a too detailed description. We then derive a method to compute the interface from the application specification. This method has been implemented in Matlab routines that are publicly available.

A synchronous transition protocol with periodicity for global scheduling of multimode real-time systems on multiprocessors

We consider the global scheduling problem of multimode real-time systems upon identical multiprocessor platforms. During the execution of a multimode system, the system can change from one mode to another such that the current task set is replaced with a new task set. Thereby, ensuring that deadlines are met requires not only that a schedulability test is performed on tasks in each mode but also that (i) a protocol for transitioning from one mode to another is specified and (ii) a schedulability test for each transition is performed. In this paper, we extend the synchronous transition protocol SM-MSO in order to take into account mode-independent tasks [1], i.e., tasks of which the execution pattern must not be jeopardized by the mode changes.

Scheduling arbitrary-deadline sporadic task systems on multiprocessors

A new algorithm is proposed for scheduling preemptible arbitrary-deadline sporadic task systems upon multiprocessor platforms, with interprocessor migration permitted. This algorithm is based on a task-splitting approach - while most tasks are entirely assigned to specific processors, a few tasks (fewer than the number of processors) may be split across two processors. This algorithm can be used for two distinct purposes: for actually scheduling specific sporadic task systems, and for feasibility analysis. Simulation- based evaluation indicates that this algorithm offers a significant improvement on the ability to schedule arbitrary- deadline sporadic task systems as compared to the contemporary state-of-art. With regard to feasibility analysis, the new algorithm is proved to offer superior performance guarantees in comparison to prior feasibility tests.

Considerations on the Least Upper Bound for Mixed-Criticality Real-Time Systems

5th Brazilian Symposium on Computing Systems Engineering, SBESC 2015 (SBESC 2015). 3 to 6, Nov, 2015. Foz do Iguaçu, Brasil.

Provably good scheduling of sporadic tasks with resource sharing on a two-type heterogeneous multiprocessor platform

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a two-type heterogeneous multiprocessor platform where a task may request at most one of |R| shared resources. There are m1 processors of type-1 and m2 processors of type-2. Tasks may migrate only when requesting or releasing resources. We present a new algorithm, FF-3C-vpr, which offers a guarantee that if a task set is schedulable to meet deadlines by an optimal task assignment scheme that only allows tasks to migrate when requesting or releasing a resource, then FF-3Cvpr also meets deadlines if given processors 4+6*ceil(|R|/min(m1,m2)) times as fast. As far as we know, it is the first result for resource sharing on heterogeneous platforms with provable performance.