Washington University in St. Louis Washington University Open Scholarship Engineering and Applied Science Theses & McKelvey School of Engineering Dissertations Summer 8-15-2017 Parallel Real-Time Scheduling for Latency-Critical Applications Jing Li Washington University in St. Louis Follow this and additional works at: https://openscholarship.wustl.edu/eng_etds Part of the Computer Engineering Commons Recommended Citation Li, Jing, "Parallel Real-Time Scheduling for Latency-Critical Applications" (2017). Engineering and Applied Science Theses & Dissertations. 302. https://openscholarship.wustl.edu/eng_etds/302 This Dissertation is brought to you for free and open access by the McKelvey School of Engineering at Washington University Open Scholarship. It has been accepted for inclusion in Engineering and Applied Science Theses & Dissertations by an authorized administrator of Washington University Open Scholarship. For more information, please contact [email protected]. WASHINGTON UNIVERSITY IN ST. LOUIS School of Engineering and Applied Science Department of Computer Science and Engineering Dissertation Examination Committee: Chenyang Lu, Chair Kunal Agrawal, Co-Chair Sameh Elnikety Christopher Gill Roch Gu´erin I-Ting Angelina Lee Parallel Real-Time Scheduling for Latency-Critical Applications by Jing Li A dissertation presented to The Graduate School of Washington University in partial fulfillment of the requirements for the degree of Doctor of Philosophy August 2017 St. Louis, Missouri Table of Contents List of Tables ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: vii List of Figures:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: viii Acknowledgments::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: xv Abstract ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::xviii Chapter 1: Introduction ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 1 1.1 Systems with Latency-Critical Applications :::::::::::::::::::::::::::::::::::::::::::::::: 3 1.2 Parallel Scheduling for Applications :::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 5 1.3 Thesis Statement :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 7 1.4 Thesis Contributions ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 8 Chapter 2: Preliminaries and Notation ::::::::::::::::::::::::::::::::::::::::::::::::::::::: 13 2.1 Parallel Job Model :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 13 2.2 Scheduling Parallel Jobs ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 15 2.2.1 Centralized Greedy Schedulers ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 16 2.2.2 Randomized Work-Stealing Schedulers :::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17 2.3 Parallel Languages and Runtime Systems::::::::::::::::::::::::::::::::::::::::::::::::::: 18 2.4 Classic Static Real-Time System Model ::::::::::::::::::::::::::::::::::::::::::::::::::::: 19 2.5 Classic Online Scheduling Model :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 22 Part I Static Real-Time Systems for Parallel Tasks with Deadlines :::::::::::: 25 Chapter 3: Global Scheduling for Parallel Real-Time Tasks::::::::::::::::::::::::: 29 3.1 Related Work on Hard Real-Time Systems ::::::::::::::::::::::::::::::::::::::::::::::::: 30 3.2 Canonical Form of a DAG Task ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 33 3.3 Capacity Augmentation Bound of Global EDF:::::::::::::::::::::::::::::::::::::::::::: 40 3.3.1 Upper Bound on Capacity Augmentation of GEDF:::::::::::::::::::::::::::::::::::::::::: 40 3.3.2 Lower Bound on Capacity Augmentation of GEDF :::::::::::::::::::::::::::::::::::::::::: 42 3.4 Capacity Augmentation of Global RM::::::::::::::::::::::::::::::::::::::::::::::::::::::: 44 3.5 Parallel GEDF Platform::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 46 ii 3.5.1 Background ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 47 3.5.2 PGEDF Programming Interface ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 50 3.5.3 PGEDF Operation :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 52 Chapter 4: Federated Scheduling for Parallel Real-Time Tasks:::::::::::::::::::: 56 4.1 Federated Scheduling Algorithm::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 57 4.2 Capacity Augmentation Bound of 2 for Federated Scheduling::::::::::::::::::::::::: 58 4.3 Lower Bound on Capacity Augmentation of Any Scheduler for Parallel Tasks :::: 62 4.4 Practical Considerations ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 62 4.5 Implementation of a Federated Scheduling Platform ::::::::::::::::::::::::::::::::::::: 64 4.6 Empirical Comparison Between PGEDF and RTCG::::::::::::::::::::::::::::::::::::: 66 4.6.1 Task Generation ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 67 4.6.2 Baseline Platform:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 68 4.6.3 Experimental Results::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 70 Chapter 5: Mixed-Criticality Federated Scheduling::::::::::::::::::::::::::::::::::::: 72 5.1 System Model and Background :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 74 5.1.1 Mixed-Criticality Parallel Real-Time Tasks Model ::::::::::::::::::::::::::::::::::::::::::: 74 5.1.2 System Model for Dual-Criticality System:::::::::::::::::::::::::::::::::::::::::::::::::::::: 75 5.1.3 Schedulability Conditions for Dual-Criticality Systems:::::::::::::::::::::::::::::::::::::: 76 5.1.4 Dual-Criticality Capacity Augmentation Bound :::::::::::::::::::::::::::::::::::::::::::::: 77 5.1.5 Background ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 77 5.2 Related Work on Mixed-Criticality Scheduling :::::::::::::::::::::::::::::::::::::::::::: 80 5.3 Scheduling Dual-Criticality High-Utilization Tasks :::::::::::::::::::::::::::::::::::::: 81 5.3.1 Mapping Algorithm ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 82 5.3.2 Schedulability Conditions of MCFS :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 83 5.3.3 MCFS Runtime Execution :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 84 5.4 Proof of Correctness and Capacity Augmentation Bound :::::::::::::::::::::::::::::: 85 5.4.1 LH tasks under MCFS ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 85 5.4.2 HVH tasks under MCFS::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 86 5.4.3 HMH tasks under MCFS :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 89 5.4.4 Proof of Correctness :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 93 p 5.4.5 Proof of Capacity Augmentation Bound 2 + 2 :::::::::::::::::::::::::::::::::::::::::::::: 94 iii 5.4.6 Lower Bound on Capacity Augmentation for High-Utilization Tasks :::::::::::::::::::: 97 5.5 MCFS for Multi-Criticality Systems:::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 98 5.5.1 Multi-Criticality System Model :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 98 5.5.2 Multi-Criticality MCFS Algorithm and Bound ::::::::::::::::::::::::::::::::::::::::::::::::100 5.6 Improve MCFS Algorithm for High-Utilization Tasks ::::::::::::::::::::::::::::::::::: 104 5.7 General Case for Dual-Criticality MCFS :::::::::::::::::::::::::::::::::::::::::::::::::::: 109 5.8 Implementation of a MCFS Runtime System :::::::::::::::::::::::::::::::::::::::::::::: 112 5.9 Numerical Evaluation :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 119 5.10 Empirical Evaluation ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 130 Chapter 6: Federated Scheduling for Stochastic Parallel Real-time Tasks :::: 135 6.1 Related Work on Soft Real-Time Scheduling::::::::::::::::::::::::::::::::::::::::::::::: 136 6.2 System Model for Stochastic Parallel Real-Time Tasks:::::::::::::::::::::::::::::::::: 137 6.3 Stochastic Federated Scheduling Guarantees Bounded Tardiness ::::::::::::::::::::: 139 6.3.1 Stochastic Federated Scheduling Strategy:::::::::::::::::::::::::::::::::::::::::::::::::::::::139 6.3.2 Mapping Algorithms Guarantee Bounded Tardiness :::::::::::::::::::::::::::::::::::::::::140 6.3.3 Calculating Expected Tardiness :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::142 6.3.4 A Mapping Algorithm for Stochastic Federated Scheduling ::::::::::::::::::::::::::::::::144 6.3.5 BASIC Federated Mapping Algorithm :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::144 6.3.6 FAIR Federated Mapping Algorithm :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::146 6.3.7 ILP-Based Federated Mapping Algorithm ::::::::::::::::::::::::::::::::::::::::::::::::::::::147 6.4 Stochastic Capacity Augmentation of 2 for Stochastic Federated Scheduling:::::: 151 6.4.1 Stochastic Capacity Augmentation Bound for BASIC :::::::::::::::::::::::::::::::::::::::151 6.4.2 Stochastic Capacity Augmentation Bound for FAIR :::::::::::::::::::::::::::::::::::::::::153