Preemptive scheduling on uniform parallel machines with controllable job processing times

In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan

Computational dynamics for robotics systems using a non-strict computational approach

A Non-Strict computational approach for real-time robotics control computations is proposed. In contrast to the traditional approach to scheduling such computations, based strictly on task dependence relations, the proposed approach relaxes precedence constraints and scheduling is guided instead by the relative sensitivity of the outputs with respect to the various paths in the task graph. An example of the computation of the Inverse Dynamics of a simple inverted pendulum is used to demonstrate the reduction in effective computational latency through use of the Non-Strict approach. A speedup of 5 has been obtained when the processes of the task graph are scheduled to reduce the latency along the crucial path of the computation. While error is introduced by the relaxation of precedence constraints, the Non-Strict approach has a smaller error than the conventional Strict approach for a wide range of input conditions

Genetic Algorithms in Real-Time Imprecise Computing

This article describes the use of genetic algorithms in real-time systems that employ the imprecise computation paradigm. In real-time systems, the focus is on ensuring that a set of tasks each complete within their deadlines. Faults may occur in the computation or the environment that can cause missed deadlines. That is why the idea of using partial results, when exact ones cannot be produced within the deadline, has been introduced. This idea has been formalized using the concepts of anytime algorithms and imprecise computation and specific techniques have been developed for designing programs which can produce partial results and for developing systems that can support imprecise computation techniques. Genetic algorithms are methods that can be, without any adaptation, used in an imprecise computation system. They produce a solution that bears a certain measure of reliability. During the process of their execution, this solution is constant ly improving. They can be used as a part of a real-time system, especially for optimizing tasks where the classical algorithms are not applicable or its computational time proves to be too expensive

Partial servicing of on-line jobs

We consider the problem of scheduling jobs online, where jobs may be served partially in order to optimize the overall use of the machines. Service requests arrive online to be executed immediately;Every job must start immediately or be refused. the scheduler must decide how long and if it will run a job (that is, it must fix the Quality of Service level of the job) at the time of arrival of the job: preemption is not allowed. We give lower bounds on the competitive ratio and present algorithmsanalyze the competitive performance of algorithms for jobs with varying sizes and for jobs with uniform size, and for jobs that can be run for an arbitrary time or only for some fixed fraction of their full execution time

PSBS: Practical Size-Based Scheduling

Size-based schedulers have very desirable performance properties: optimal or near-optimal response time can be coupled with strong fairness guarantees. Despite this, such systems are very rarely implemented in practical settings, because they require knowing a priori the amount of work needed to complete jobs: this assumption is very difficult to satisfy in concrete systems. It is definitely more likely to inform the system with an estimate of the job sizes, but existing studies point to somewhat pessimistic results if existing scheduler policies are used based on imprecise job size estimations. We take the goal of designing scheduling policies that are explicitly designed to deal with inexact job sizes: first, we show that existing size-based schedulers can have bad performance with inexact job size information when job sizes are heavily skewed; we show that this issue, and the pessimistic results shown in the literature, are due to problematic behavior when large jobs are underestimated. Once the problem is identified, it is possible to amend existing size-based schedulers to solve the issue. We generalize FSP -- a fair and efficient size-based scheduling policy -- in order to solve the problem highlighted above; in addition, our solution deals with different job weights (that can be assigned to a job independently from its size). We provide an efficient implementation of the resulting protocol, which we call Practical Size-Based Scheduler (PSBS). Through simulations evaluated on synthetic and real workloads, we show that PSBS has near-optimal performance in a large variety of cases with inaccurate size information, that it performs fairly and it handles correctly job weights. We believe that this work shows that PSBS is indeed pratical, and we maintain that it could inspire the design of schedulers in a wide array of real-world use cases.Comment: arXiv admin note: substantial text overlap with arXiv:1403.599

Scheduling data flow program in xkaapi: A new affinity based Algorithm for Heterogeneous Architectures

Efficient implementations of parallel applications on heterogeneous hybrid architectures require a careful balance between computations and communications with accelerator devices. Even if most of the communication time can be overlapped by computations, it is essential to reduce the total volume of communicated data. The literature therefore abounds with ad-hoc methods to reach that balance, but that are architecture and application dependent. We propose here a generic mechanism to automatically optimize the scheduling between CPUs and GPUs, and compare two strategies within this mechanism: the classical Heterogeneous Earliest Finish Time (HEFT) algorithm and our new, parametrized, Distributed Affinity Dual Approximation algorithm (DADA), which consists in grouping the tasks by affinity before running a fast dual approximation. We ran experiments on a heterogeneous parallel machine with six CPU cores and eight NVIDIA Fermi GPUs. Three standard dense linear algebra kernels from the PLASMA library have been ported on top of the Xkaapi runtime. We report their performances. It results that HEFT and DADA perform well for various experimental conditions, but that DADA performs better for larger systems and number of GPUs, and, in most cases, generates much lower data transfers than HEFT to achieve the same performance