Scheduling Distributed Clusters of Parallel Machines: Primal-Dual and LP-based Approximation Algorithms

The Map-Reduce computing framework rose to prominence with datasets of such size that dozens of machines on a single cluster were needed for individual jobs. As datasets approach the exabyte scale, a single job may need distributed processing not only on multiple machines, but on multiple clusters. We consider a scheduling problem to minimize weighted average completion time of n jobs on m distributed clusters of parallel machines. In keeping with the scale of the problems motivating this work, we assume that (1) each job is divided into m "subjobs" and (2) distinct subjobs of a given job may be processed concurrently. When each cluster is a single machine, this is the NP-Hard concurrent open shop problem. A clear limitation of such a model is that a serial processing assumption sidesteps the issue of how different tasks of a given subjob might be processed in parallel. Our algorithms explicitly model clusters as pools of resources and effectively overcome this issue. Under a variety of parameter settings, we develop two constant factor approximation algorithms for this problem. The first algorithm uses an LP relaxation tailored to this problem from prior work. This LP-based algorithm provides strong performance guarantees. Our second algorithm exploits a surprisingly simple mapping to the special case of one machine per cluster. This mapping-based algorithm is combinatorial and extremely fast. These are the first constant factor approximations for this problem

Concurrency Platforms for Real-Time and Cyber-Physical Systems

Parallel processing is an important way to satisfy the increasingly demanding computational needs of modern real-time and cyber-physical systems, but existing parallel computing technologies primarily emphasize high-throughput and average-case performance metrics, which are largely unsuitable for direct application to real-time, safety-critical contexts. This work contrasts two concurrency platforms designed to achieve predictable worst case parallel performance for soft real-time workloads with millisecond periods and higher. One of these is then the basis for the CyberMech platform, which enables parallel real-time computing for a novel yet representative application called Real-Time Hybrid Simulation (RTHS). RTHS combines demanding parallel real-time computation with real-time simulation and control in an earthquake engineering laboratory environment, and results concerning RTHS characterize a reasonably comprehensive survey of parallel real-time computing in the static context, where the size, shape, timing constraints, and computational requirements of workloads are fixed prior to system runtime. Collectively, these contributions constitute the first published implementations and evaluations of general-purpose concurrency platforms for real-time and cyber-physical systems, explore two fundamentally different design spaces for such systems, and successfully demonstrate the utility and tradeoffs of parallel computing for statically determined real-time and cyber-physical systems

실시간 멀티코어 플루이드 스케줄링에서 전체 시스템의 시간 · 밀도 트레이드오프

학위논문 (박사)-- 서울대학교 대학원 공과대학 전기·컴퓨터공학부, 2017. 8. 이창건.Recent parallel programming frameworks such as OpenCL and OpenMP allow us to enjoy the parallelization freedom for real-time tasks. The parallelization freedom creates the time vs. density tradeoff problem in fluid scheduling, i.e., more parallelization reduces thread execution times but increases the density. By system-widely exercising this tradeoff, this dissertation proposes a parameter tuning of real-time tasks aiming at maximizing the schedulability of multicore fluid scheduling. The experimental study by both simulation and actual implementation shows that the proposed approach well balances the time and the density, and results in up to 80% improvement of the schedulability.1 Introduction 1 1.1 Motivation and Objective 1 1.2 Approach 3 1.3 Organization 4 2 Related Work 6 2.1 Real-Time Scheduling 6 2.1.1 Workload Model 6 2.1.2 Scheduling on Multicore Systems 7 2.1.3 Period Control 9 2.1.4 Real-Time Operating System 10 2.2 Parallel Computing 10 2.2.1 Parallel Computing Framework 10 2.2.2 Shared Resource Management 12 3 System-wide Time vs. Density Tradeoff with Parallelizable Periodic Single Segment Tasks 14 3.1 Introduction 14 3.2 Problem Description 14 3.3 Motivating Example 21 3.4 Proposed Approach 26 3.4.1 Per-task Optimal Tradeoff of Time and Density 26 3.4.2 Peak Density Minimization for a Task Group with the Same Period 27 3.4.3 Heuristic Algorithm for System-wide Time vs. Density Tradeoff 38 3.5 Experimental Results 45 3.5.1 Simulation Study 45 3.5.2 Actual Implementation Results 51 4 System-wide Time vs. Density Tradeoff with Parallelizable Periodic Multi-segment Tasks 64 4.1 Introduction 64 4.2 Problem Description 64 4.3 Extension to Parallelizable Periodic Multi-segment Task Model 70 4.3.1 Peak Density Minimization for a Task Group of Multi-segment Tasks with Same Period 71 4.3.2 Heuristic Algorithm for System-wide Time vs. Density Tradeoff 78 5 Conclusion 81 5.1 Summary 81 5.2 Future Work 82 References 84 Appendices 100 A Period Harmonization 100Docto