Optimized Scheduling in Real-Time Environments with Column Generation

Transcription

1 JG U JOHANNES GUTENBERG UNIVERSITAT 1^2 Optimized Scheduling in Real-Time Environments with Column Generation Dissertation zur Erlangung des Grades,.Doktor der Naturwissenschaften" am Fachbereich Physik, Mathematik und Informatik der Johannes Gutenberg-Universitat in Mainz Sebastian Hoffmann geboren in Bad Homburg v.d.h. Mainz,

2 Abstract Zusammenfassung Acknowledgments v vii ix 1 Introduction Motivation 2 ~ 1.2 Related Work Contributions and Objectives Assessing Quality of Solutions by Providing Lower Bounds Providing Global Optimal Allocations Development of Hybrid Approaches Context Outline 6 2 Preliminaries General Preliminaries Computational Complexity Linear Algebra Linear Programming Canonical Form Standard Form " Algebra and Geometry Duality Degeneracy Simplex Method Dantzig-Wolfe Decomposition 29 xi

3 2.5 Integer Linear Programming Introduction Exact Algorithms Approximation Algorithms Heuristic Algorithms Real-Time Scheduling Real-Time Embedded Systems Electronical Control Units (ECUs) and ECU types Communication Buses Tasks Messages Task Networks Task Scheduling Policies and Analyses Processor Utilization Analysis Processor Demand Analysis Response Time Analysis Workload Analysis Earliest Deadline First (EDF) Fixed Priority Scheduling (FPS) Rate Monotonic Scheduling (RMS) Deadline Monotonic Scheduling (DMS) Message Scheduling Policies and Analyses Token Ring Local Area Network (TAN) Controller Area Network (CAN) Time Division Multiple Access (TDMA) 49 3 Problem Definition Hardware Architecture Task Network Assignments Additional Constraints Objective Function Feasibility Characterization of Problems 59 4 Column Generation Approach for the Distributed Scheduling Problem Computational Complexity ILP formulation LP relaxation Branch and Bound Framework Upper Bounds on the Objective Function Lower Bounds on the Objective Function Evaluation of Solutions Branching Rules 70 xii

4 TabJe of Contents Best First Search Strategy Column Generation Approach Algebraic Derivation Master Problem Pricing Problems Task Pricing Problems Message Pricing Problem Implementation Strategies Integrality of the Objective Function Multiple Columns Generation Heuristic Phase 79 5 Formulations for Different Scenarios Task Pricing Formulations Simplifications Formulations for the Additional Constraints Cost of Hardware Memory Consumption Scheduling Processor Utilization Analysis Response Time Analysis Workload Analysis Message Pricing Formulations Analysis for TAN buses Response Time Analysis for CAN buses Analysis for a simple TDMA bus Combined Formulations Analysis for Chains Modifications of the Master Problem Modifications of the Pricing Problems New ILP formulation for Computing Response Times Experiments and Evaluation Progress and Comparison Charts Experimental Setup Problem Instances Ill 6.4 Objectives and Evaluation Assessing Quality of Solutions by Providing Lower Bounds Providing Global Optimal Allocations DSP-GF with the DMS policy ColGen DSP-GF with WCRT computation ColGen-e and ColGen-n DSP-CF with WCRT computation ColGen-e and ColGen-n 121 xiii

5 6.4.3 Development of Hybrid Approaches Including heuristic start solutions Additional presolve phase Heuristic start solutions and presolve phase Conclusion Summary of the Results Assessing Quality of Solutions by Providing Lower Bounds Providing Global Optimal Allocations Development of Hybrid Approaches Discussion Algorithm Design Scalability Symmetry Parallelization Parameter Tuning 138 Bibliography 139 xiv