Shelby Funk

Priority-driven scheduling of periodic task systems on multiprocessors

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.

Bounding energy consumption in large-scale MPI programs

Power is now a first-order design constraint in large-scale parallel computing. Used carefully, dynamic voltage scaling can execute parts of a program at a slower CPU speed to achieve energy savings with a relatively small (possibly zero) time delay. However, the problem of when to change frequencies in order to optimize energy savings is NP-complete, which has led to many heuristic energy-saving algorithms. To determine how closely these algorithms approach optimal savings, we developed a system that determines a bound on the energy savings for an application. Our system uses a linear programming solver that takes as inputs the application communication trace and the cluster power characteristics and then outputs a schedule that realizes this bound. We apply our system to three scientific programs, two of which exhibit load imbalance---particle simulation and UMT2K. Results from our bounding technique show particle simulation is more amenable to energy savings than UMT2K.

On-line scheduling on uniform 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.

DP-FAIR: A Simple Model for Understanding Optimal Multiprocessor Scheduling

We consider the problem of optimal real-time scheduling of periodic and sporadic tasks for identical multiprocessors. A number of recent papers have used the notions of fluid scheduling and deadline partitioning to guarantee optimality and improve performance. In this paper, we develop a unifying theory with the DP-FAIR scheduling policy and examine how it overcomes problems faced by greedy scheduling algorithms. We then present a simple DP-FAIR scheduling algorithm, DP-WRAP, which serves as a least common ancestor to many recent algorithms. We also show how to extend DP-FAIR to the scheduling of sporadic tasks with arbitrary deadlines.

Task assignment on uniform heterogeneous multiprocessors

The partitioning of periodic task systems upon uniform multiprocessors is considered. In the partitioned approach to scheduling periodic tasks upon multiprocessors, each task is assigned to a specific processor and all jobs generated by a task are required to execute upon the processor to which the task is assigned. A uniform heterogeneous multiprocessor is a multiprocessor in which each processor has an associated speed - a processor of speed s operating for t units of time will perform s /spl times/ t units of work. Partitioning of periodic task systems requires solving the bin-packing problem, which is known to be intractable (NP-hard in the strong sense). This paper presents methods for finding an approximate utilization bound for partitioned scheduling on uniform heterogeneous multiprocessors.

Robustness results concerning EDF scheduling upon uniform 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 earliest deadline first (EDF) scheduling of hard-real-time systems upon 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 in general (EDF in particular) to perform better than may be expected given these inherent limitations. It is shown that EDF scheduling upon uniform multiprocessors is robust with respect to both job execution requirements and processor computing capacity.

LRE-TL: an optimal multiprocessor algorithm for sporadic task sets with unconstrained deadlines

This article presents a detailed discussion of LRE-TL (Local Remaining Execution-TL-plane), an algorithm that schedules hard real-time periodic and sporadic task sets with unconstrained deadlines on identical multiprocessors. The algorithm builds upon important concepts such as the TL-plane construct used in the development of the LLREF algorithm (Largest Local Remaining Execution First). This article identifies the fundamental TL-plane scheduling principles used in the construction of LLREF . These simple principles are examined, identifying methods of simplifying the algorithm and allowing it to handle a more general task model. For example, we identify the principle that total local utilization can never increase within any TL-plane as long as a minimal number of tasks are executing. This observation leads to a straightforward approach for scheduling task arrivals within a TL-plane. In this manner LRE-TL can schedule sporadic tasks and tasks with unconstrained deadlines. Like LLREF, the LRE-TL scheduling algorithm is optimal for task sets with implicit deadlines. In addition, LRE-TL can schedule task sets with unconstrained deadlines provided they satisfy the density test for multiprocessor systems. While LLREF has a O(n2) runtime per TL-plane, LRE-TL’s runtime is O(nlog n) per TL-plane.

GART: A genetic algorithm based real-time system scheduler

Hard real-time systems require that all jobs are assigned a deadline and the system is deemed to be correct only if all jobs complete execution at or before their deadlines. Such strict timing requirements add to the complexity of the scheduling problem. This complexity is exacerbated when the system is executed on a multiprocessor platform. Even so, scheduling overheads must be kept to a minimum in order for the runtime behavior to be predictable. Thus, real-time scheduling algorithms have the dual requirement of satisfying complex requirements while using fairly simple and straightforward logic. One way an algorithm may achieve this goal is to reduce the overhead due to preemption and migration by rearranging the schedule so as to increase the duration between preemptions. Unfortunately, determining how best to rearrange the jobs is an NP-Complete problem. Hence, we need to use heuristics when scheduling such systems. This leads us to ask a couple of questions. First, what is the best heuristic? Second, is the same heuristic best for all real-time systems? This paper uses a Genetic Algorithm to help us answer these questions. Our genetic algorithm based real-time system scheduler (GART) is based on the DP-Wrap scheduling algorithm. The genetic algorithm searches through a variety of candidate heuristics to determine the best heuristic for a given task set. Experimental results demonstrate that this approach is able to efficiently identify the best heuristic for all the systems we consider. Moreover, we find that the “best” heuristic does, in fact, depend of various system parameters.

Characteristics of EDF schedulability on uniform multiprocessors

In uniform multiprocessor platforms, the various processors comprising the multiprocessor platform may have different computing capacities. The focus of this paper is the design of efficient tests for determining whether the earliest deadline first scheduling algorithm (EDF) can successfully schedule a given real-time task system to meet all deadlines upon a specified uniform multiprocessor platform. Upon uniform multiprocessor platforms, we show that it is often far easier (from a computational complexity perspective) to determine feasibility than it is to check for EDF-schedulability. In designing an EDF-schedulability test for uniform multiprocessors, therefore, our approach is as follows: for a given uniform multiprocessor platform, we attempt to efficiently identify all those uniform multiprocessor platforms such that any real-time instance feasible upon these platforms is guaranteed to be EDF-schedulable upon the platform under consideration. EDF-schedulability upon the given platform can then be determined by ascertaining whether the real-time system is feasible upon any of these platforms.

Group note-taking in a large lecture class

Large introductory-level classes provide a cost-efficient approach for universities to serve many students at once, but also present several challenges to learning (e.g., poor visual angles). In addition, more students with declared, undeclared, or undiagnosed learning disabilities are entering the college and university systems. In the spirit of universal design, we created a group note-taking system in our large introductory computer science course to increase interaction amongst students, promote good note-taking strategies, and provide study resources to all students while also fulfilling the role of accommodating for students with learning disabilities. We show that the section of the course taught with our intervention performed significantly better on their final examination compared to a course taught without the intervention. We report that students enjoyed increased interactions with their peers, and that one third of the class self-reported an increase in their note-taking skills. Furthermore, our intervention only required minimal cost to the institution, and no financial cost to students, and is easily implemented in any size class.