Makespan computation for GPU threads running on a single streaming multiprocessor

Graphics processors were originally developed for rendering graphics but have recently evolved towards being an architecture for general-purpose computations. They are also expected to become important parts of embedded systems hardware -- not just for graphics. However, this necessitates the development of appropriate timing analysis techniques which would be required because techniques developed for CPU scheduling are not applicable. The reason is that we are not interested in how long it takes for any given GPU thread to complete, but rather how long it takes for all of them to complete. We therefore develop a simple method for finding an upper bound on the makespan of a group of GPU threads executing the same program and competing for the resources of a single streaming multiprocessor (whose architecture is based on NVIDIA Fermi, with some simplifying assunptions). We then build upon this method to formulate the derivation of the exact worst-case makespan (and corresponding schedule) as an optimization problem. Addressing the issue of tractability, we also present a technique for efficiently computing a safe estimate of the worstcase makespan with minimal pessimism, which may be used when finding an exact value would take too long.

Dynamic global scheduling of parallel real-time tasks

High-level parallel languages offer a simple way for application programmers to specify parallelism in a form that easily scales with problem size, leaving the scheduling of the tasks onto processors to be performed at runtime. Therefore, if the underlying system cannot efficiently execute those applications on the available cores, the benefits will be lost. In this paper, we consider how to schedule highly heterogenous parallel applications that require real-time performance guarantees on multicore processors. The paper proposes a novel scheduling approach that combines the global Earliest Deadline First (EDF) scheduler with a priority-aware work-stealing load balancing scheme, which enables parallel realtime tasks to be executed on more than one processor at a given time instant. Experimental results demonstrate the better scalability and lower scheduling overhead of the proposed approach comparatively to an existing real-time deadline-oriented scheduling class for the Linux kernel.

Job phasing aware preemption deferral

Preemptions account for a non-negligible overhead during system execution. There has been substantial amount of research on estimating the delay incurred due to the loss of working sets in the processor state (caches, registers, TLBs) and some on avoiding preemptions, or limiting the preemption cost. We present an algorithm to reduce preemptions by further delaying the start of execution of high priority tasks in fixed priority scheduling. Our approaches take advantage of the floating non-preemptive regions model and exploit the fact that, during the schedule, the relative task phasing will differ from the worst-case scenario in terms of admissible preemption deferral. Furthermore, approximations to reduce the complexity of the proposed approach are presented. Substantial set of experiments demonstrate that the approach and approximations improve over existing work, in particular for the case of high utilisation systems, where savings of up to 22% on the number of preemption are attained.

Implementing slot-based task-splitting multiprocessor scheduling

Consider the problem of scheduling a set of sporadic tasks on a multiprocessor system to meet deadlines using a task-splitting scheduling algorithm. Task-splitting (also called semi-partitioning) scheduling algorithms assign most tasks to just one processor but a few tasks are assigned to two or more processors, and they are dispatched in a way that ensures that a task never executes on two or more processors simultaneously. A particular type of task-splitting algorithms, called slot-based task-splitting dispatching, is of particular interest because of its ability to schedule tasks with high processor utilizations. Unfortunately, no slot-based task-splitting algorithm has been implemented in a real operating system so far. In this paper we discuss and propose some modifications to the slot-based task-splitting algorithm driven by implementation concerns, and we report the first implementation of this family of algorithms in a real operating system running Linux kernel version 2.6.34. We have also conducted an extensive range of experiments on a 4-core multicore desktop PC running task-sets with utilizations of up to 88%. The results show that the behavior of our implementation is in line with the theoretical framework behind it.

Practical aspects of slot-based task- splitting dispatching in its schedulability analysis

Consider the problem of scheduling a set of sporadic tasks on a multiprocessor system to meet deadlines using a tasksplitting scheduling algorithm. Task-splitting (also called semipartitioning) scheduling algorithms assign most tasks to just one processor but a few tasks are assigned to two or more processors, and they are dispatched in a way that ensures that a task never executes on two or more processors simultaneously. A certain type of task-splitting algorithms, called slot-based task-splitting, is of particular interest because of its ability to schedule tasks at high processor utilizations. We present a new schedulability analysis for slot-based task-splitting scheduling algorithms that takes the overhead into account and also a new task assignment algorithm.

Global-EDF scheduling of multimode real- time systems considering mode independent tasks

Embedded real-time systems often have to support the embedding system in very different and changing application scenarios. An aircraft taxiing, taking off and in cruise flight is one example. The different application scenarios are reflected in the software structure with a changing task set and thus different operational modes. At the same time there is a strong push for integrating previously isolated functionalities in single-chip multicore processors. On such multicores the behavior of the system during a mode change, when the systems transitions from one mode to another, is complex but crucial to get right. In the past we have investigated mode change in multiprocessor systems where a mode change requires a complete change of task set. Now, we present the first analysis which considers mode changes in multicore systems, which use global EDF to schedule a set of mode independent (MI) and mode specific (MS) tasks. In such systems, only the set of MS tasks has to be replaced during mode changes, without jeopardizing the schedulability of the MI tasks. Of prime concern is that the mode change is safe and efficient: i.e. the mode change needs to be performed in a predefined time window and no deadlines may be missed as a function of the mode change.

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.

A capacity sharing and stealing strategy for open real-time systems

This paper focuses on the scheduling of tasks with hard and soft real-time constraints in open and dynamic real-time systems. It starts by presenting a capacity sharing and stealing (CSS) strategy that supports the coexistence of guaranteed and non-guaranteed bandwidth servers to efficiently handle soft-tasks’ overloads by making additional capacity available from two sources: (i) reclaiming unused reserved capacity when jobs complete in less than their budgeted execution time and (ii) stealing reserved capacity from inactive non-isolated servers used to schedule best-effort jobs. CSS is then combined with the concept of bandwidth inheritance to efficiently exchange reserved bandwidth among sets of inter-dependent tasks which share resources and exhibit precedence constraints, assuming no previous information on critical sections and computation times is available. The proposed Capacity Exchange Protocol (CXP) has a better performance and a lower overhead when compared against other available solutions and introduces a novel approach to integrate precedence constraints among tasks of open real-time systems.

A compositional scheduling framework for digital avionics systems

ARINC specification 653-2 describes the interface between application software and underlying middleware in a distributed real-time avionics system. The real-time workload in this system comprises of partitions, where each partition consists of one or more processes. Processes incur blocking and preemption overheads and can communicate with other processes in the system. In this work we develop compositional techniques for automated scheduling of such partitions and processes. At present, system designers manually schedule partitions based on interactions they have with the partition vendors. This approach is not only time consuming, but can also result in under utilization of resources. In contrast, the technique proposed in this paper is a principled approach for scheduling ARINC-653 partitions and therefore should facilitate system integration.

Assigning real-time tasks on heterogeneous multiprocessors with two types of processors

Consider the problem of scheduling a set of implicitdeadline sporadic tasks on a heterogeneous multiprocessor so as to meet all deadlines. Tasks cannot migrate and the platform is restricted in that each processor is either of type-1 or type-2 (with each task characterized by a different speed of execution upon each type of processor). We present an algorithm for this problem with a timecomplexity of O(n·m), where n is the number of tasks and m is the number of processors. It offers the guarantee that if a task set can be scheduled by any non-migrative algorithm to meet deadlines then our algorithm meets deadlines as well if given processors twice as fast. Although this result is proven for only a restricted heterogeneous multiprocessor, we consider it significant for being the first realtime scheduling algorithm to use a low-complexity binpacking approach to schedule tasks on a heterogeneous multiprocessor with provably good performance.

Sporadic multiprocessor Linux scheduler

The advent of multicore systems has renewed the interest of research community on real-time scheduling on multiprocessor systems. Real-time scheduling theory for uniprocessors is considered a mature research field, but real-time scheduling theory for multiprocessors is an emerging research field. Being part of this research community I have decided to implement the Sporadic Multiprocessor Linux Scheduler that implements a new real-time scheduling algorithm, which was designed to schedule real-time sporadic tasks on multiprocessor systems. This technical reports describes the implementation of the SMLS.

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.

Competitive analysis of partitioned scheduling on uniform multiprocessors

Consider the problem of scheduling a set of sporadically arriving tasks on a uniform multiprocessor with the goal of meeting deadlines. A processor p has the speed Sp. Tasks can be preempted but they cannot migrate between processors. We propose an algorithm which can schedule all task sets that any other possible algorithm can schedule assuming that our algorithm is given processors that are three times faster.

Competitive analysis of static-priority partitioned scheduling on uniform multiprocessors

Consider the problem of scheduling a set of sporadically arriving tasks on a uniform multiprocessor with the goal of meeting deadlines. A processor p has the speed Sp. Tasks can be preempted but they cannot migrate between processors. On each processor, tasks are scheduled according to rate-monotonic. We propose an algorithm that can schedule all task sets that any other possible algorithm can schedule assuming that our algorithm is given processors that are √2 / √2−1 ≈ 3.41 times faster. No such guarantees are previously known for partitioned static-priority scheduling on uniform multiprocessors.

Capacity sharing and stealing in dynamic server-based real-time systems

This paper proposes a dynamic scheduler that supports the coexistence of guaranteed and non-guaranteed bandwidth servers to efficiently handle soft-tasks’ overloads by making additional capacity available from two sources: (i) residual capacity allocated but unused when jobs complete in less than their budgeted execution time; (ii) stealing capacity from inactive non-isolated servers used to schedule best-effort jobs. The effectiveness of the proposed approach in reducing the mean tardiness of periodic jobs is demonstrated through extensive simulations. The achieved results become even more significant when tasks’ computation times have a large variance.