Scheduling Monotone Moldable Jobs in Linear Time

A moldable job is a job that can be executed on an arbitrary number of processors, and whose processing time depends on the number of processors allotted to it. A moldable job is monotone if its work doesn't decrease for an increasing number of allotted processors. We consider the problem of scheduling monotone moldable jobs to minimize the makespan. We argue that for certain compact input encodings a polynomial algorithm has a running time polynomial in n and log(m), where n is the number of jobs and m is the number of machines. We describe how monotony of jobs can be used to counteract the increased problem complexity that arises from compact encodings, and give tight bounds on the approximability of the problem with compact encoding: it is NP-hard to solve optimally, but admits a PTAS. The main focus of this work are efficient approximation algorithms. We describe different techniques to exploit the monotony of the jobs for better running times, and present a (3/2+{\epsilon})-approximate algorithm whose running time is polynomial in log(m) and 1/{\epsilon}, and only linear in the number n of jobs

Schedulability analysis of timed CSP models using the PAT model checker

Timed CSP can be used to model and analyse real-time and concurrent behaviour of embedded control systems. Practical CSP implementations combine the CSP model of a real-time control system with prioritized scheduling to achieve efficient and orderly use of limited resources. Schedulability analysis of a timed CSP model of a system with respect to a scheduling scheme and a particular execution platform is important to ensure that the system design satisfies its timing requirements. In this paper, we propose a framework to analyse schedulability of CSP-based designs for non-preemptive fixed-priority multiprocessor scheduling. The framework is based on the PAT model checker and the analysis is done with dense-time model checking on timed CSP models. We also provide a schedulability analysis workflow to construct and analyse, using the proposed framework, a timed CSP model with scheduling from an initial untimed CSP model without scheduling. We demonstrate our schedulability analysis workflow on a case study of control software design for a mobile robot. The proposed approach provides non-pessimistic schedulability results

Workforce minimization for a mixed-model assembly line in the automotive industry

A paced assembly line consisting of several workstations is considered. This line is intended to assemble products of different types. The sequence of products is given. The sequence of technological tasks is common for all types of products. The assignment of tasks to the stations and task sequence on each station are known and cannot be modified, and they do not depend on the product type. Tasks assigned to the same station are performed sequentially. The processing time of a task depends on the number of workers performing this task. Workers are identical and versatile. If a worker is assigned to a task, he/she works on this task from its start till completion. Workers can switch between the stations at the end of each task and the time needed by any worker to move from one station to another one can be neglected. At the line design stage, it is necessary to know how many workers are necessary for the line. To know the response to this question we will consider each possible takt and assign workers to tasks so that the total number of workers is minimized, provided that a given takt time is satisfied. The maximum of minimal numbers of workers for all takts will be considered as the necessary number of workers for the line. Thus, the problem is to assign workers to tasks for a takt. We prove that this problem is NP-hard in the strong sense, we develop an integer linear programming formulation to solve it, and propose conventional and randomized heuristics

Modeling of an Adaptive Parallel System with Malleable Applications in a Distributed Computing Environment

Adaptive parallel applications that can change resources during execution, promise increased application performance and better system utilization. Furthermore, they open the opportunity for developing a new class of parallel applications driven by unpredictable data and events. The research issues in an adaptive parallel system are complex and interrelated. The nature and complexities of the relationships among these issues are not well researched and understood. Before developing adaptive applications or an infrastructure support for adaptive applications, these issues need to be investigated and studied in detail. One way of understanding and investigating these issues is by modeling and simulation. A model for adaptive parallel systems has been developed to enable the investigation of the impact of malleable workloads on its performance. The model can be used to determine how different model parameters impact the performance of the system and to determine the relationships among them Subsequently, a discrete event simulator has been developed to numerically simulate the model. Using the simulator, the impact of the variation in the number of malleable jobs in the workload, the flexibility, the negotiation cost, and the adaptation cost on system performance have been studied. The results and conclusions of these simulation experiments are presented in this dissertation. In general, the simulation results reveal that the performance improves with an increase in the number of malleable jobs in a workload, and that the performance saturates at a certain percentage of rigid to malleable jobs mix. A high percentage of malleable jobs is not necessary to achieve significant improvement in performance. The performance in general improves as the flexibility increases up to a certain point; then, it saturates. The negotiation cost impacts the performance, but not significantly. The number of negotiations for a given workload increases as number of malleable jobs increases up to a certain point, and then it decreases as number of malleable jobs increases further. The performance degrades as the application adaptation cost increases. The impact of the application adaptation cost on performance is much more significant compared to that of the negotiation cost

Modeling of an Adaptive Parallel System with Malleable Applications in a Distributed Computing Environment

Adaptive parallel applications that can change resources during execution, promise increased application performance and better system utilization. Furthermore, they open the opportunity for developing a new class of parallel applications driven by unpredictable data and events. The research issues in an adaptive parallel system are complex and interrelated. The nature and complexities of the relationships among these issues are not well researched and understood. Before developing adaptive applications or an infrastructure support for adaptive applications, these issues need to be investigated and studied in detail. One way of understanding and investigating these issues is by modeling and simulation. A model for adaptive parallel systems has been developed to enable the investigation of the impact of malleable workloads on its performance. The model can be used to determine how different model parameters impact the performance of the system and to determine the relationships among them Subsequently, a discrete event simulator has been developed to numerically simulate the model. Using the simulator, the impact of the variation in the number of malleable jobs in the workload, the flexibility, the negotiation cost, and the adaptation cost on system performance have been studied. The results and conclusions of these simulation experiments are presented in this dissertation. In general, the simulation results reveal that the performance improves with an increase in the number of malleable jobs in a workload, and that the performance saturates at a certain percentage of rigid to malleable jobs mix. A high percentage of malleable jobs is not necessary to achieve significant improvement in performance. The performance in general improves as the flexibility increases up to a certain point; then, it saturates. The negotiation cost impacts the performance, but not significantly. The number of negotiations for a given workload increases as number of malleable jobs increases up to a certain point, and then it decreases as number of malleable jobs increases further. The performance degrades as the application adaptation cost increases. The impact of the application adaptation cost on performance is much more significant compared to that of the negotiation cost

Mixed Data-Parallel Scheduling for Distributed Continuous Integration

International audienceIn this paper, we consider the problem of schedul- ing a special kind of mixed data-parallel applications arising in the context of continuous integration. Continuous integration (CI) is a software engineering technique, which consists in re- building and testing interdependent software components as soon as developers modify them. The CI tool is able to provide quick feedback to the developers, which allows them to fix the bug soon after it has been introduced. The CI process can be described as a DAG where nodes represent package build tasks, and edges represent dependencies among these packages; build tasks themselves can in turn be run in parallel. Thus, CI can be viewed as a mixed data-parallel application. A crucial point for a successful CI process is its ability to provide quick feedback. Thus, makespan minimization is the main goal. Our contribution is twofold. First we provide and analyze a large dataset corresponding to a build DAG. Second, we compare the performance of several scheduling heuristics on this dataset

Theory and Engineering of Scheduling Parallel Jobs

Scheduling is very important for an efficient utilization of modern parallel computing systems. In this thesis, four main research areas for scheduling are investigated: the interplay and distribution of decision makers, the efficient schedule computation, efficient scheduling for the memory hierarchy and energy-efficiency. The main result is a provably fast and efficient scheduling algorithm for malleable jobs. Experiments show the importance and possibilities of scheduling considering the memory hierarchy

Approximation Algorithms for Demand Strip Packing

In the Demand Strip Packing problem (DSP), we are given a time interval and a collection of tasks, each characterized by a processing time and a demand for a given resource (such as electricity, computational power, etc.). A feasible solution consists of a schedule of the tasks within the mentioned time interval. Our goal is to minimize the peak resource consumption, i.e. the maximum total demand of tasks executed at any point in time. It is known that DSP is NP-hard to approximate below a factor 3/2, and standard techniques for related problems imply a (polynomial-time) 2-approximation. Our main result is a (5/3+?)-approximation algorithm for any constant ? > 0. We also achieve best-possible approximation factors for some relevant special cases