Batch Scheduling for Identical Multi-Tasks Jobs on Heterogeneous Platforms
|
|
- Ashlyn West
- 7 years ago
- Views:
Transcription
1 atch Scheduling for Identical Multi-Tasks Jobs on Heterogeneous Platforms Jean-Marc Nicod Sékou iakité, Laurent Philippe - 16/05/2008 Laboratoire d Informatique de l Université de Franche-omté - esançon 2nd Scheduling in ussois workshop
2 Presentation Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45
3 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45
4 Scheduling Problem efinitions Execution Platform: non oriented graph, G = (P, L) : P: processors p i, i [1, m] L: communication links l j, j [1, c] Jobs: Gs without fork (intrees), J = (T, ): T : tasks t k, k [1, n] : tasks dependencies d l, l [1, d] N instances of the same job. 2nd Scheduling in ussois workshop - 19/05/ / 45
5 Scheduling Problem haracteristics: Each task of a job must be performed by a specific function, F is the set of the functions needed to process a job, Each execution resource provides a subset of F, The execution resources are unrelated. Problem: Schedule a batch of N jobs J Objective function: max R m intrees, batch of identical jobs max 2nd Scheduling in ussois workshop - 19/05/ / 45
6 Scheduling Problem Problem illustration N instances of the same job: 1 platform for execution: Figure: Job Type p 1 p 2 p 3 p Table: Execution times 2nd Scheduling in ussois workshop - 19/05/ / 45
7 Scheduling Problem Use ases Grid: Image processing: filters, 2 or 3 reconstructions, Servers provides an application set. Micro-Factories: omposed of cells: assembly, treatments,... Less geographical constraints, Products are micro-metric easily buffered 2nd Scheduling in ussois workshop - 19/05/ / 45
8 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45
9 Possible solutions lassical (Off-line): schedule a G on an heterogeneous platform, max optimization NP-Hard, batch of jobs: no use of identical jobs. Steady state technics (Off-line): flow optimization: maximize the throughput optimal solution on heterogeneous platforms, use the identical job characteristic, does not take starting/ending into account. On-line: batch waiting queue, schedule ready tasks, no use of identical job characteristic, 2nd Scheduling in ussois workshop - 19/05/ / 45
10 Used algorithms On-line scheduling: simple, assign tasks on the fly, respect dependencies, used as reference. Genetic Meta-heuristic GTS[aoud05]: improves list scheduling, good results on G schedule, needs to be adapted to batches: period, performances of a standard heuristic on batches of jobs? Steady State[eaumont04]: optimal for batches of infinite size, performances on finite size batches? 2nd Scheduling in ussois workshop - 19/05/ / 45
11 Steady State Overview efinition and resolution of a linear program: define the constraints of the problem, flow: solutions are time ratios per resources. ompute a cyclic schedule: construct allocations with respect of the ratios, 1 port model: communication intervals. Execution: starting, cyclic schedule, ending. 2nd Scheduling in ussois workshop - 19/05/ / 45
12 Steady State linear system MXIMIZE ρ = p i=1 cons(p i, t f ), UNER THE ONSTRINTS (1)p i, t k T, α(p i, t k ) = cons(p i, t k ) c i,k (2)p i, t k T, 0 α(p i, t k ) 1 (3)p i, t k T α(p i, t k ) 1 2nd Scheduling in ussois workshop - 19/05/ / 45
13 Steady State Solution t 0 t 1 t 2 t 3 Type p 1 p 2 p 3 p Figure: Job Table: ost: c p 1 p 2 p 3 p 4 t0 7/ /200 t1 3/100 1/ t2-1/20 3/100 - t /100 1/100 Table: omsumption: cons, objective ρ = 2/25 2nd Scheduling in ussois workshop - 19/05/ / 45
14 Steady State Solution P1:0 0:1 1:1 4:1 Tbegin:0:0 8 :1:1 4 P2:1 1:1 2:1 3:1 8 8 :2:1 8 2 :3:1 P3:2 1:1 2:1 3:1 8 Tend:4:0 Figure: Platform Figure: Job 2nd Scheduling in ussois workshop - 19/05/ / 45
15 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45
16 Experiences Metric efficiency = makespan o /makespan r efficiency = N/(ρ makespan r ) makespan o : lower bound makespan o : N/ρ, reference time makespan r : makespan resulting from experience, Simulation results (SimGrid), ommunications neglected. 2nd Scheduling in ussois workshop - 19/05/ / 45
17 Figure: Job j 0 Type p 1 p 2 p 3 p 4 p 5 p Table: Grid G 0 Efficiency Steady state GTS On line atch size Figure: Execution of batches j 0 on G 0 Global results: Steady state tends toward optimal, GTS good for small batches, then collapses, on-line is constant. 2nd Scheduling in ussois workshop - 19/05/ / 45
18 Type p 1 p 2 p 3 p 4 p 5 p Figure: Job j 1 Table: Grid G 0 Efficiency Steady state GTS On line atch size Sames tasks as j 0, GTS collapses earlier (250 instances vs. 300). Figure: Execution of batches j 1 on G 0 2nd Scheduling in ussois workshop - 19/05/ / 45
19 Figure: Job j 2 Type p 1 p 2 p 3 p 4 p 5 p Table: Grid G 0 Efficiency Steady state GTS On line atch size Steady state uses p 6 (: 1000), Figure: Execution of batches j 2 on G 0 2nd Scheduling in ussois workshop - 19/05/ / 45
20 Type p 1 p 2 p Figure: Job j 2 Table: Grid G 1 Efficiency Steady state GTS On line atch size The efficiency of GTS decreases starting at 200 instances. Figure: Execution of batches j 2 on G 1 2nd Scheduling in ussois workshop - 19/05/ / 45
21 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45
22 Experiences Synthesis Small batches: 50 Medium batches: 100 Large batches: 500 On-line Steady GTS On-line Steady GTS On-line Steady GTS Table: Mean efficiency Synthesis: GTS: up to 200, Steady state: from 500. Time consumption for 1000 instances: steady state: 0.08s, on-line: 35.04s, GTS: s, 2nd Scheduling in ussois workshop - 19/05/ / 45
23 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45
24 Steady state for small batches Means of action im: improve (decrease) the global makespan for small batches, The steady state phase is optimal. Schedule starting/ending phases on the heterogeneous platform: NP-Hard find a good schedule, reduce the work in initialization/ending phases. What can be done on starting/ending phases? Keeping steady state optimal: re-organise affectations to reduce the period size, resolve dependencies inside the period. eterioration of steady state: reduce the number of instances per periods 2nd Scheduling in ussois workshop - 19/05/ / 45
25 Steady state schedule Type p 1 p 2 p 3 p Figure: Job j 3 Table: Grid G 2 Period 1 Period 2 Period N... 2nd Scheduling in ussois workshop - 19/05/ / 45
26 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45
27 Steady state for small batches Example t 0 t 1 t 2 t 3 Type p 1 p 2 p 3 p Figure: Job Table: ost p 1 p 2 p 3 p 4 t0 7/ /200 t1 3/100 1/ t2-1/20 3/100 - t /100 1/100 Period = 200. Table: onsumption 2nd Scheduling in ussois workshop - 19/05/ / 45
28 Steady state for small batches lgorithm p 1 p 2 p 3 p 4 t0 7/ /200 t1 3/100 1/ t2-1/20 3/100 - t /100 1/100 Table: onsumptions: cons p 1 p 2 p 3 p 4 t t t t Table: Integer consuptions: consint 2nd Scheduling in ussois workshop - 19/05/ / 45
29 Steady state for small batches Initial steady state schedule S P: period, P : LM of the matrix denominators, ρ: throughput, ρ = a/b, reduced fraction. Let P min be the minimum possible period P 0 = b, P min = α P 0, α [1, P/b] Find P min, that respect the constraints: For lines L j : P i L i cons(i, j) = ρ, For columns i : P j j cons(i, j) w ij < 1 2nd Scheduling in ussois workshop - 19/05/ / 45
30 Steady state for small batches Example t 0 t 1 t 2 t 3 Type p 1 p 2 p 3 p Figure: Job Table: ost p 1 p 2 p 3 p 4 t0 7/ /200 t1 3/100 1/ t2-1/20 3/100 - t /100 1/100 p 1 p 2 p 3 p 4 t0 1/ /25 t1 1/50 3/ t2-1/25 1/25 - t /50 1/50 Table: onsumption Table: Modified consumption 2nd Scheduling in ussois workshop - 19/05/ / 45
31 Steady state for small batches lgorithm im: maximize of the onsint matrix that respect the constraints, Optimisation problem with integers. onstraints programming with finite domains (swi-prolog) Exponential complexity but the problem is small lgorithm 1: reduceperiod(cons: Matrix, cost: Matrix ) : Matrix cd periodlength/throughputenominator; while cd > 1 do newons : Matrix; if newons reorganize(cons, cost, cd) then return newons; else cd cd 1; end end return cons; 2nd Scheduling in ussois workshop - 19/05/ / 45
32 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45
33 Steady state for small batches Metric efficiency = makespan o /makespan r efficiency = atch size/(rate makespan r ) Steady state rate is optimal time reference: N/ρ, lower bound for optimal makespan (makespan o ), makespan r : makespan of the algorithm. 2nd Scheduling in ussois workshop - 19/05/ / 45
34 Figure: Job j 3 Type p 1 p 2 p 3 p Table: Grid G 3 Efficiency Normal period Reduced period atch size Period: 16/200 4/50 (/4), Figure: Execution of batches j 3 on G 2 2nd Scheduling in ussois workshop - 19/05/ / 45
35 Figure: Job j 3 Type p 1 p 2 p 3 p Table: Grid G 4 Efficiency Normal period Reduced periode atch size 96/1200 4/50 (/24), Figure: Execution of batches j 3 on G 3 2nd Scheduling in ussois workshop - 19/05/ / 45
36 Type p 1 p 2 p 3 p Figure: Job j 4 Table: Grid G 3 Efficiency Normal period Reduced period atch size 48/1320 4/110 (/12), starting: 194 instances, never in steady state. Figure: Execution of batches j 4 on G 2 2nd Scheduling in ussois workshop - 19/05/ / 45
37 Type p 1 p 2 p 3 p Figure: Job j 4 Table: Grid G 4 Efficiency Normal period Reduced period atch size 12/330 4/110 (/3), starting: 38 instances, 2 full periods for a batch of 150 jobs, 10 Figure: Execution of batches j 4 on G 3 Max efficiency difference: 1%. 2nd Scheduling in ussois workshop - 19/05/ / 45
38 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45
39 onclusion and futur works onclusion: omparison of algorithms performances, Minimal period while keeping steady state, Large gain for small batches, Not always possible. Futur works: Keeping an optimal steady state: omparison of dependencies resolutions. eterioration of steady state: Reduce the number of instances per periods. 2nd Scheduling in ussois workshop - 19/05/ / 45
40 The end Thanks for your attention.
41 Steady state for small batches Reminder Initialization prepares all the dependencies needed before entering in steady state: For each task or communication in the period: execute all the preceding tasks/communications in the graph Ending: finish all the remaining tasks/communications, ommon work with Loris Marchal (LIP) Reduce the number of tasks computed in the starting and ending phases. 2nd Scheduling in ussois workshop - 19/05/ / 45
42 ependencies resolution Period 1 Period 2 Period N Figure: Job j 3 Type p 1 p 2 p 3 p Table: Grid G 5 Figure: Execution of batches j 3 on G 5 2nd Scheduling in ussois workshop - 19/05/ / 45
43 ependencies resolution Initial Schedule: Period 1 Period 2 Period N... Schedule with less dependencies: Period 1 Period 2 Period N... 2nd Scheduling in ussois workshop - 19/05/ / 45
44 ependencies resolution P1:0 0:1 1:1 4:1 Tbegin:0:0 8 :1:1 4 P2:1 1:1 2:1 3:1 8 8 :2:1 8 2 :3:1 P3:2 1:1 2:1 3:1 8 Tend:4:0 Figure: Platform Figure: Job 2nd Scheduling in ussois workshop - 19/05/ / 45
45 ependencies resolution 8 1 suppressed dependency = 1 subgraph less, alance starting and ending, How to optimize dependencies resolution? How to mesure the gain? The more... the less re there better dependencies? Max number of dependencies: two-partition Reoganize the periodic schedule: heuristics Find a good scheduling algorithm for starting and ending phases. Link number of jobs <=> period size 2nd Scheduling in ussois workshop - 19/05/ / 45
5 INTEGER LINEAR PROGRAMMING (ILP) E. Amaldi Fondamenti di R.O. Politecnico di Milano 1
5 INTEGER LINEAR PROGRAMMING (ILP) E. Amaldi Fondamenti di R.O. Politecnico di Milano 1 General Integer Linear Program: (ILP) min c T x Ax b x 0 integer Assumption: A, b integer The integrality condition
More informationDiscrete Optimization
Discrete Optimization [Chen, Batson, Dang: Applied integer Programming] Chapter 3 and 4.1-4.3 by Johan Högdahl and Victoria Svedberg Seminar 2, 2015-03-31 Todays presentation Chapter 3 Transforms using
More informationIntroduction to Scheduling Theory
Introduction to Scheduling Theory Arnaud Legrand Laboratoire Informatique et Distribution IMAG CNRS, France arnaud.legrand@imag.fr November 8, 2004 1/ 26 Outline 1 Task graphs from outer space 2 Scheduling
More informationToday s topic: So far, we have talked about. Question. Task models
Overall Stucture of Real Time Systems So far, we have talked about Task...... Task n Programming Languages to implement the Tasks Run-TIme/Operating Systems to run the Tasks RTOS/Run-Time System Hardware
More informationFactors to Describe Job Shop Scheduling Problem
Job Shop Scheduling Job Shop A work location in which a number of general purpose work stations exist and are used to perform a variety of jobs Example: Car repair each operator (mechanic) evaluates plus
More informationClassification - Examples
Lecture 2 Scheduling 1 Classification - Examples 1 r j C max given: n jobs with processing times p 1,...,p n and release dates r 1,...,r n jobs have to be scheduled without preemption on one machine taking
More informationCHAPTER 6 MAJOR RESULTS AND CONCLUSIONS
133 CHAPTER 6 MAJOR RESULTS AND CONCLUSIONS The proposed scheduling algorithms along with the heuristic intensive weightage factors, parameters and ß and their impact on the performance of the algorithms
More informationThe Problem of Scheduling Technicians and Interventions in a Telecommunications Company
The Problem of Scheduling Technicians and Interventions in a Telecommunications Company Sérgio Garcia Panzo Dongala November 2008 Abstract In 2007 the challenge organized by the French Society of Operational
More informationAlgorithm Design and Analysis
Algorithm Design and Analysis LECTURE 27 Approximation Algorithms Load Balancing Weighted Vertex Cover Reminder: Fill out SRTEs online Don t forget to click submit Sofya Raskhodnikova 12/6/2011 S. Raskhodnikova;
More informationArena 9.0 Basic Modules based on Arena Online Help
Arena 9.0 Basic Modules based on Arena Online Help Create This module is intended as the starting point for entities in a simulation model. Entities are created using a schedule or based on a time between
More informationInteger Programming: Algorithms - 3
Week 9 Integer Programming: Algorithms - 3 OPR 992 Applied Mathematical Programming OPR 992 - Applied Mathematical Programming - p. 1/12 Dantzig-Wolfe Reformulation Example Strength of the Linear Programming
More informationReal-Time Scheduling (Part 1) (Working Draft) Real-Time System Example
Real-Time Scheduling (Part 1) (Working Draft) Insup Lee Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania www.cis.upenn.edu/~lee/ CIS 41,
More informationEfficient and Robust Allocation Algorithms in Clouds under Memory Constraints
Efficient and Robust Allocation Algorithms in Clouds under Memory Constraints Olivier Beaumont,, Paul Renaud-Goud Inria & University of Bordeaux Bordeaux, France 9th Scheduling for Large Scale Systems
More informationIEOR 4404 Homework #2 Intro OR: Deterministic Models February 14, 2011 Prof. Jay Sethuraman Page 1 of 5. Homework #2
IEOR 4404 Homework # Intro OR: Deterministic Models February 14, 011 Prof. Jay Sethuraman Page 1 of 5 Homework #.1 (a) What is the optimal solution of this problem? Let us consider that x 1, x and x 3
More informationPartitioned real-time scheduling on heterogeneous shared-memory multiprocessors
Partitioned real-time scheduling on heterogeneous shared-memory multiprocessors Martin Niemeier École Polytechnique Fédérale de Lausanne Discrete Optimization Group Lausanne, Switzerland martin.niemeier@epfl.ch
More information! Solve problem to optimality. ! Solve problem in poly-time. ! Solve arbitrary instances of the problem. !-approximation algorithm.
Approximation Algorithms Chapter Approximation Algorithms Q Suppose I need to solve an NP-hard problem What should I do? A Theory says you're unlikely to find a poly-time algorithm Must sacrifice one of
More informationCPU Scheduling. Core Definitions
CPU Scheduling General rule keep the CPU busy; an idle CPU is a wasted CPU Major source of CPU idleness: I/O (or waiting for it) Many programs have a characteristic CPU I/O burst cycle alternating phases
More informationPerformance Analysis of a Telephone System with both Patient and Impatient Customers
Performance Analysis of a Telephone System with both Patient and Impatient Customers Yiqiang Quennel Zhao Department of Mathematics and Statistics University of Winnipeg Winnipeg, Manitoba Canada R3B 2E9
More informationChapter 11. 11.1 Load Balancing. Approximation Algorithms. Load Balancing. Load Balancing on 2 Machines. Load Balancing: Greedy Scheduling
Approximation Algorithms Chapter Approximation Algorithms Q. Suppose I need to solve an NP-hard problem. What should I do? A. Theory says you're unlikely to find a poly-time algorithm. Must sacrifice one
More informationTHROUGHPUT OPTIMIZATION IN ROBOTIC CELLS
Contents Preface xv 1. ROBOTIC CELLS IN PRACTICE 1 1.1 Cellular Manufacturing 2 1.2 Robotic Cell Flowshops 3 1.3 Throughput Optimization 7 1.4 Historical Overview 9 1.5 Applications 11 2. A CLASSIFICATION
More informationTwo objective functions for a real life Split Delivery Vehicle Routing Problem
International Conference on Industrial Engineering and Systems Management IESM 2011 May 25 - May 27 METZ - FRANCE Two objective functions for a real life Split Delivery Vehicle Routing Problem Marc Uldry
More informationOptimal shift scheduling with a global service level constraint
Optimal shift scheduling with a global service level constraint Ger Koole & Erik van der Sluis Vrije Universiteit Division of Mathematics and Computer Science De Boelelaan 1081a, 1081 HV Amsterdam The
More informationReal Time Scheduling Basic Concepts. Radek Pelánek
Real Time Scheduling Basic Concepts Radek Pelánek Basic Elements Model of RT System abstraction focus only on timing constraints idealization (e.g., zero switching time) Basic Elements Basic Notions task
More informationFault-Tolerant Application Placement in Heterogeneous Cloud Environments. Bart Spinnewyn, prof. Steven Latré
Fault-Tolerant Application Placement in Heterogeneous Cloud Environments Bart Spinnewyn, prof. Steven Latré Cloud Application Placement Problem (CAPP) Application Placement admission control: decide on
More informationScheduling Shop Scheduling. Tim Nieberg
Scheduling Shop Scheduling Tim Nieberg Shop models: General Introduction Remark: Consider non preemptive problems with regular objectives Notation Shop Problems: m machines, n jobs 1,..., n operations
More informationOffline sorting buffers on Line
Offline sorting buffers on Line Rohit Khandekar 1 and Vinayaka Pandit 2 1 University of Waterloo, ON, Canada. email: rkhandekar@gmail.com 2 IBM India Research Lab, New Delhi. email: pvinayak@in.ibm.com
More informationHYBRID GENETIC ALGORITHMS FOR SCHEDULING ADVERTISEMENTS ON A WEB PAGE
HYBRID GENETIC ALGORITHMS FOR SCHEDULING ADVERTISEMENTS ON A WEB PAGE Subodha Kumar University of Washington subodha@u.washington.edu Varghese S. Jacob University of Texas at Dallas vjacob@utdallas.edu
More informationUNIT 2 QUEUING THEORY
UNIT 2 QUEUING THEORY LESSON 24 Learning Objective: Apply formulae to find solution that will predict the behaviour of the single server model II. Apply formulae to find solution that will predict the
More informationObjective Criteria of Job Scheduling Problems. Uwe Schwiegelshohn, Robotics Research Lab, TU Dortmund University
Objective Criteria of Job Scheduling Problems Uwe Schwiegelshohn, Robotics Research Lab, TU Dortmund University 1 Jobs and Users in Job Scheduling Problems Independent users No or unknown precedence constraints
More informationPlanning and Scheduling in the Digital Factory
Institute for Computer Science and Control Hungarian Academy of Sciences Berlin, May 7, 2014 1 Why "digital"? 2 Some Planning and Scheduling problems 3 Planning for "one-of-a-kind" products 4 Scheduling
More informationOptimization Modeling for Mining Engineers
Optimization Modeling for Mining Engineers Alexandra M. Newman Division of Economics and Business Slide 1 Colorado School of Mines Seminar Outline Linear Programming Integer Linear Programming Slide 2
More informationAn Energy-aware Multi-start Local Search Metaheuristic for Scheduling VMs within the OpenNebula Cloud Distribution
An Energy-aware Multi-start Local Search Metaheuristic for Scheduling VMs within the OpenNebula Cloud Distribution Y. Kessaci, N. Melab et E-G. Talbi Dolphin Project Team, Université Lille 1, LIFL-CNRS,
More informationA Genetic Algorithm to Schedule Workflow Collections on a SOA-Grid with Communication Costs
LABORATOIRE D INFORMATIQUE DE L UNIVERSITE DE FRANCHE-COMTE EA 4269 A Genetic Algorithm to Schedule Workflow Collections on a SOA-Grid with Communication Costs Jean-Marc Nicod and Laurent Philippe and
More informationOptimal Hiring of Cloud Servers A. Stephen McGough, Isi Mitrani. EPEW 2014, Florence
Optimal Hiring of Cloud Servers A. Stephen McGough, Isi Mitrani EPEW 2014, Florence Scenario How many cloud instances should be hired? Requests Host hiring servers The number of active servers is controlled
More informationAlgorithms for Assigning Substrate Network Resources to Virtual Network Components
Algorithms for Assigning Substrate Network Resources to Virtual Network Components Yong Zhu and Mostafa Ammar Networking and Telecommunications Group Georgia Institute of Technology, Atlanta, Georgia Email:
More informationPart 2: Community Detection
Chapter 8: Graph Data Part 2: Community Detection Based on Leskovec, Rajaraman, Ullman 2014: Mining of Massive Datasets Big Data Management and Analytics Outline Community Detection - Social networks -
More informationA Constraint Programming Application for Rotating Workforce Scheduling
A Constraint Programming Application for Rotating Workforce Scheduling Markus Triska and Nysret Musliu Database and Artificial Intelligence Group Vienna University of Technology {triska,musliu}@dbai.tuwien.ac.at
More informationCommon Approaches to Real-Time Scheduling
Common Approaches to Real-Time Scheduling Clock-driven time-driven schedulers Priority-driven schedulers Examples of priority driven schedulers Effective timing constraints The Earliest-Deadline-First
More informationWarshall s Algorithm: Transitive Closure
CS 0 Theory of Algorithms / CS 68 Algorithms in Bioinformaticsi Dynamic Programming Part II. Warshall s Algorithm: Transitive Closure Computes the transitive closure of a relation (Alternatively: all paths
More informationSupplement to Call Centers with Delay Information: Models and Insights
Supplement to Call Centers with Delay Information: Models and Insights Oualid Jouini 1 Zeynep Akşin 2 Yves Dallery 1 1 Laboratoire Genie Industriel, Ecole Centrale Paris, Grande Voie des Vignes, 92290
More informationLecture 3. Linear Programming. 3B1B Optimization Michaelmas 2015 A. Zisserman. Extreme solutions. Simplex method. Interior point method
Lecture 3 3B1B Optimization Michaelmas 2015 A. Zisserman Linear Programming Extreme solutions Simplex method Interior point method Integer programming and relaxation The Optimization Tree Linear Programming
More informationOptimal Dynamic Resource Allocation in Multi-Class Queueing Networks
Imperial College London Department of Computing Optimal Dynamic Resource Allocation in Multi-Class Queueing Networks MEng Individual Project Report Diagoras Nicolaides Supervisor: Dr William Knottenbelt
More informationLargest Fixed-Aspect, Axis-Aligned Rectangle
Largest Fixed-Aspect, Axis-Aligned Rectangle David Eberly Geometric Tools, LLC http://www.geometrictools.com/ Copyright c 1998-2016. All Rights Reserved. Created: February 21, 2004 Last Modified: February
More informationTime-line based model for software project scheduling
Time-line based model for software project scheduling with genetic algorithms Carl K. Chang, Hsin-yi Jiang, Yu Di, Dan Zhu, Yujia Ge Information and Software Technology(IST), 2008 2010. 3. 9 Presented
More informationEmbedded Systems 20 BF - ES
Embedded Systems 20-1 - Multiprocessor Scheduling REVIEW Given n equivalent processors, a finite set M of aperiodic/periodic tasks find a schedule such that each task always meets its deadline. Assumptions:
More information! Solve problem to optimality. ! Solve problem in poly-time. ! Solve arbitrary instances of the problem. #-approximation algorithm.
Approximation Algorithms 11 Approximation Algorithms Q Suppose I need to solve an NP-hard problem What should I do? A Theory says you're unlikely to find a poly-time algorithm Must sacrifice one of three
More informationLift-based search for significant dependencies in dense data sets
Lift-based search for significant dependencies in dense data sets W. Hämäläinen epartment of omputer Science University of Helsinki Finland whamalai@cs.helsinki.fi StReio 09 (K 09) p.1/48 1 Problem Find
More informationFinding Liveness Errors with ACO
Hong Kong, June 1-6, 2008 1 / 24 Finding Liveness Errors with ACO Francisco Chicano and Enrique Alba Motivation Motivation Nowadays software is very complex An error in a software system can imply the
More informationComplexity Theory. IE 661: Scheduling Theory Fall 2003 Satyaki Ghosh Dastidar
Complexity Theory IE 661: Scheduling Theory Fall 2003 Satyaki Ghosh Dastidar Outline Goals Computation of Problems Concepts and Definitions Complexity Classes and Problems Polynomial Time Reductions Examples
More informationEmbedded Systems 20 REVIEW. Multiprocessor Scheduling
Embedded Systems 0 - - Multiprocessor Scheduling REVIEW Given n equivalent processors, a finite set M of aperiodic/periodic tasks find a schedule such that each task always meets its deadline. Assumptions:
More informationA Review on Load Balancing In Cloud Computing 1
www.ijecs.in International Journal Of Engineering And Computer Science ISSN:2319-7242 Volume 4 Issue 6 June 2015, Page No. 12333-12339 A Review on Load Balancing In Cloud Computing 1 Peenaz Pathak, 2 Er.Kamna
More informationScheduling Algorithms in MapReduce Distributed Mind
Scheduling Algorithms in MapReduce Distributed Mind Karthik Kotian, Jason A Smith, Ye Zhang Schedule Overview of topic (review) Hypothesis Research paper 1 Research paper 2 Research paper 3 Project software
More informationOptimal Scheduling for Dependent Details Processing Using MS Excel Solver
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 8, No 2 Sofia 2008 Optimal Scheduling for Dependent Details Processing Using MS Excel Solver Daniela Borissova Institute of
More informationPolynomial Neural Network Discovery Client User Guide
Polynomial Neural Network Discovery Client User Guide Version 1.3 Table of contents Table of contents...2 1. Introduction...3 1.1 Overview...3 1.2 PNN algorithm principles...3 1.3 Additional criteria...3
More informationUniversity Dortmund. Robotics Research Institute Information Technology. Job Scheduling. Uwe Schwiegelshohn. EPIT 2007, June 5 Ordonnancement
University Dortmund Robotics Research Institute Information Technology Job Scheduling Uwe Schwiegelshohn EPIT 2007, June 5 Ordonnancement ontent of the Lecture What is ob scheduling? Single machine problems
More informationAI: A Modern Approach, Chpts. 3-4 Russell and Norvig
AI: A Modern Approach, Chpts. 3-4 Russell and Norvig Sequential Decision Making in Robotics CS 599 Geoffrey Hollinger and Gaurav Sukhatme (Some slide content from Stuart Russell and HweeTou Ng) Spring,
More informationLecture Outline Overview of real-time scheduling algorithms Outline relative strengths, weaknesses
Overview of Real-Time Scheduling Embedded Real-Time Software Lecture 3 Lecture Outline Overview of real-time scheduling algorithms Clock-driven Weighted round-robin Priority-driven Dynamic vs. static Deadline
More informationA Genetic Algorithm Approach for Solving a Flexible Job Shop Scheduling Problem
A Genetic Algorithm Approach for Solving a Flexible Job Shop Scheduling Problem Sayedmohammadreza Vaghefinezhad 1, Kuan Yew Wong 2 1 Department of Manufacturing & Industrial Engineering, Faculty of Mechanical
More informationSDMX technical standards Data validation and other major enhancements
SDMX technical standards Data validation and other major enhancements Vincenzo Del Vecchio - Bank of Italy 1 Statistical Data and Metadata exchange Original scope: the exchange Statistical Institutions
More informationApplied Algorithm Design Lecture 5
Applied Algorithm Design Lecture 5 Pietro Michiardi Eurecom Pietro Michiardi (Eurecom) Applied Algorithm Design Lecture 5 1 / 86 Approximation Algorithms Pietro Michiardi (Eurecom) Applied Algorithm Design
More informationA Bi-Objective Approach for Cloud Computing Systems
A Bi-Objective Approach for Cloud Computing Systems N.Geethanjali 1, M.Ramya 2 Assistant Professor, Department of Computer Science, Christ The King Engineering College 1, 2 ABSTRACT: There are Various
More informationImproved Algorithms for Data Migration
Improved Algorithms for Data Migration Samir Khuller 1, Yoo-Ah Kim, and Azarakhsh Malekian 1 Department of Computer Science, University of Maryland, College Park, MD 20742. Research supported by NSF Award
More informationPopulation-based Metaheuristics for Tasks Scheduling in Heterogeneous Distributed Systems
Population-based Metaheuristics for Tasks Scheduling in Heterogeneous Distributed Systems Flavia Zamfirache, Marc Frîncu, Daniela Zaharie Department of Computer Science, West University of Timişoara, Romania
More informationW4118 Operating Systems. Instructor: Junfeng Yang
W4118 Operating Systems Instructor: Junfeng Yang Outline Introduction to scheduling Scheduling algorithms 1 Direction within course Until now: interrupts, processes, threads, synchronization Mostly mechanisms
More informationMulti-core real-time scheduling
Multi-core real-time scheduling Credits: Anne-Marie Déplanche, Irccyn, Nantes (many slides come from her presentation at ETR, Brest, September 2011) 1 Multi-core real-time scheduling! Introduction: problem
More informationSingle machine parallel batch scheduling with unbounded capacity
Workshop on Combinatorics and Graph Theory 21th, April, 2006 Nankai University Single machine parallel batch scheduling with unbounded capacity Yuan Jinjiang Department of mathematics, Zhengzhou University
More informationJoint Optimization of Overlapping Phases in MapReduce
Joint Optimization of Overlapping Phases in MapReduce Minghong Lin, Li Zhang, Adam Wierman, Jian Tan Abstract MapReduce is a scalable parallel computing framework for big data processing. It exhibits multiple
More informationNear Optimal Solutions
Near Optimal Solutions Many important optimization problems are lacking efficient solutions. NP-Complete problems unlikely to have polynomial time solutions. Good heuristics important for such problems.
More informationDimensioning an inbound call center using constraint programming
Dimensioning an inbound call center using constraint programming Cyril Canon 1,2, Jean-Charles Billaut 2, and Jean-Louis Bouquard 2 1 Vitalicom, 643 avenue du grain d or, 41350 Vineuil, France ccanon@fr.snt.com
More informationCyber-Security Analysis of State Estimators in Power Systems
Cyber-Security Analysis of State Estimators in Electric Power Systems André Teixeira 1, Saurabh Amin 2, Henrik Sandberg 1, Karl H. Johansson 1, and Shankar Sastry 2 ACCESS Linnaeus Centre, KTH-Royal Institute
More informationModeling and Performance Evaluation of Computer Systems Security Operation 1
Modeling and Performance Evaluation of Computer Systems Security Operation 1 D. Guster 2 St.Cloud State University 3 N.K. Krivulin 4 St.Petersburg State University 5 Abstract A model of computer system
More informationIRMA: Integrated Routing and MAC Scheduling in Multihop Wireless Mesh Networks
IRMA: Integrated Routing and MAC Scheduling in Multihop Wireless Mesh Networks Zhibin Wu, Sachin Ganu and Dipankar Raychaudhuri WINLAB, Rutgers University 2006-11-16 IAB Research Review, Fall 2006 1 Contents
More informationApproximation Algorithms
Approximation Algorithms or: How I Learned to Stop Worrying and Deal with NP-Completeness Ong Jit Sheng, Jonathan (A0073924B) March, 2012 Overview Key Results (I) General techniques: Greedy algorithms
More informationChapter 5. Linear Inequalities and Linear Programming. Linear Programming in Two Dimensions: A Geometric Approach
Chapter 5 Linear Programming in Two Dimensions: A Geometric Approach Linear Inequalities and Linear Programming Section 3 Linear Programming gin Two Dimensions: A Geometric Approach In this section, we
More information11. APPROXIMATION ALGORITHMS
11. APPROXIMATION ALGORITHMS load balancing center selection pricing method: vertex cover LP rounding: vertex cover generalized load balancing knapsack problem Lecture slides by Kevin Wayne Copyright 2005
More informationBatch Scheduling of Deteriorating Products
Decision Making in Manufacturing and Services Vol. 1 2007 No. 1 2 pp. 25 34 Batch Scheduling of Deteriorating Products Maksim S. Barketau, T.C. Edwin Cheng, Mikhail Y. Kovalyov, C.T. Daniel Ng Abstract.
More informationA Hardware-Software Cosynthesis Technique Based on Heterogeneous Multiprocessor Scheduling
A Hardware-Software Cosynthesis Technique Based on Heterogeneous Multiprocessor Scheduling ABSTRACT Hyunok Oh cosynthesis problem targeting the system-on-chip (SOC) design. The proposed algorithm covers
More informationRECIFE: a MCDSS for Railway Capacity
RECIFE: a MCDSS for Railway Capacity Xavier GANDIBLEUX (1), Pierre RITEAU (1), and Xavier DELORME (2) (1) LINA - Laboratoire d Informatique de Nantes Atlantique Universite de Nantes 2 rue de la Houssiniere
More informationResource Scheduling in Cloud using Bacterial Foraging Optimization Algorithm
Resource Scheduling in Cloud using Bacterial Foraging Optimization Algorithm Liji Jacob Department of computer science Karunya University Coimbatore V.Jeyakrishanan Department of computer science Karunya
More informationCoding and decoding with convolutional codes. The Viterbi Algor
Coding and decoding with convolutional codes. The Viterbi Algorithm. 8 Block codes: main ideas Principles st point of view: infinite length block code nd point of view: convolutions Some examples Repetition
More informationStructure Preserving Model Reduction for Logistic Networks
Structure Preserving Model Reduction for Logistic Networks Fabian Wirth Institute of Mathematics University of Würzburg Workshop on Stochastic Models of Manufacturing Systems Einhoven, June 24 25, 2010.
More informationD1.1 Service Discovery system: Load balancing mechanisms
D1.1 Service Discovery system: Load balancing mechanisms VERSION 1.0 DATE 2011 EDITORIAL MANAGER Eddy Caron AUTHORS STAFF Eddy Caron, Cédric Tedeschi Copyright ANR SPADES. 08-ANR-SEGI-025. Contents Introduction
More informationThe Multi-Item Capacitated Lot-Sizing Problem With Safety Stocks In Closed-Loop Supply Chain
International Journal of Mining Metallurgy & Mechanical Engineering (IJMMME) Volume 1 Issue 5 (2013) ISSN 2320-4052; EISSN 2320-4060 The Multi-Item Capacated Lot-Sizing Problem Wh Safety Stocks In Closed-Loop
More informationA hierarchical multicriteria routing model with traffic splitting for MPLS networks
A hierarchical multicriteria routing model with traffic splitting for MPLS networks João Clímaco, José Craveirinha, Marta Pascoal jclimaco@inesccpt, jcrav@deecucpt, marta@matucpt University of Coimbra
More informationRandom access protocols for channel access. Markov chains and their stability. Laurent Massoulié.
Random access protocols for channel access Markov chains and their stability laurent.massoulie@inria.fr Aloha: the first random access protocol for channel access [Abramson, Hawaii 70] Goal: allow machines
More informationDefinition 11.1. Given a graph G on n vertices, we define the following quantities:
Lecture 11 The Lovász ϑ Function 11.1 Perfect graphs We begin with some background on perfect graphs. graphs. First, we define some quantities on Definition 11.1. Given a graph G on n vertices, we define
More informationLinear smoother. ŷ = S y. where s ij = s ij (x) e.g. s ij = diag(l i (x)) To go the other way, you need to diagonalize S
Linear smoother ŷ = S y where s ij = s ij (x) e.g. s ij = diag(l i (x)) To go the other way, you need to diagonalize S 2 Online Learning: LMS and Perceptrons Partially adapted from slides by Ryan Gabbard
More informationMinimal Cost Reconfiguration of Data Placement in a Storage Area Network
Minimal Cost Reconfiguration of Data Placement in a Storage Area Network Hadas Shachnai Gal Tamir Tami Tamir Abstract Video-on-Demand (VoD) services require frequent updates in file configuration on the
More informationAnalyzing Mission Critical Voice over IP Networks. Michael Todd Gardner
Analyzing Mission Critical Voice over IP Networks Michael Todd Gardner Organization What is Mission Critical Voice? Why Study Mission Critical Voice over IP? Approach to Analyze Mission Critical Voice
More informationBatch Production Scheduling in the Process Industries. By Prashanthi Ravi
Batch Production Scheduling in the Process Industries By Prashanthi Ravi INTRODUCTION Batch production - where a batch means a task together with the quantity produced. The processing of a batch is called
More informationa 11 x 1 + a 12 x 2 + + a 1n x n = b 1 a 21 x 1 + a 22 x 2 + + a 2n x n = b 2.
Chapter 1 LINEAR EQUATIONS 1.1 Introduction to linear equations A linear equation in n unknowns x 1, x,, x n is an equation of the form a 1 x 1 + a x + + a n x n = b, where a 1, a,..., a n, b are given
More informationBotticelli: A Supply Chain Management Agent
Botticelli: A Supply Chain Management Agent M. Benisch, A. Greenwald, I. Grypari, R. Lederman, V. Naroditskiy, and M. Tschantz Department of Computer Science, Brown University, Box 1910, Providence, RI
More informationAperiodic Task Scheduling
Aperiodic Task Scheduling Jian-Jia Chen (slides are based on Peter Marwedel) TU Dortmund, Informatik 12 Germany Springer, 2010 2014 年 11 月 19 日 These slides use Microsoft clip arts. Microsoft copyright
More informationApproximability of Two-Machine No-Wait Flowshop Scheduling with Availability Constraints
Approximability of Two-Machine No-Wait Flowshop Scheduling with Availability Constraints T.C. Edwin Cheng 1, and Zhaohui Liu 1,2 1 Department of Management, The Hong Kong Polytechnic University Kowloon,
More informationTowards an understanding of oversubscription in cloud
IBM Research Towards an understanding of oversubscription in cloud Salman A. Baset, Long Wang, Chunqiang Tang sabaset@us.ibm.com IBM T. J. Watson Research Center Hawthorne, NY Outline Oversubscription
More informationContinued Fractions and the Euclidean Algorithm
Continued Fractions and the Euclidean Algorithm Lecture notes prepared for MATH 326, Spring 997 Department of Mathematics and Statistics University at Albany William F Hammond Table of Contents Introduction
More informationHigh-Mix Low-Volume Flow Shop Manufacturing System Scheduling
Proceedings of the 14th IAC Symposium on Information Control Problems in Manufacturing, May 23-25, 2012 High-Mix Low-Volume low Shop Manufacturing System Scheduling Juraj Svancara, Zdenka Kralova Institute
More informationScheduling Single Machine Scheduling. Tim Nieberg
Scheduling Single Machine Scheduling Tim Nieberg Single machine models Observation: for non-preemptive problems and regular objectives, a sequence in which the jobs are processed is sufficient to describe
More informationTraffic Engineering for Multiple Spanning Tree Protocol in Large Data Centers
Traffic Engineering for Multiple Spanning Tree Protocol in Large Data Centers Ho Trong Viet, Yves Deville, Olivier Bonaventure, Pierre François ICTEAM, Université catholique de Louvain (UCL), Belgium.
More informationResource Reservation & Resource Servers. Problems to solve
Resource Reservation & Resource Servers Problems to solve Hard-deadline tasks may be Periodic or Sporadic (with a known minimum arrival time) or Non periodic (how to deal with this?) Soft-deadline tasks
More information