Algorithmes d'approximation pour l'ordonnancement multi-objectif. Application aux systèmes parallèles et embarqués. (Approximation algorithms for multi-objective scheduling. Application to parallel and embedded systems)

L'informatique moderne n'est plus uniquement composee de machines personnelles et de super calculateurs. De nombreux supports de calcul sont maintenant disponibles et chacun pose des contraintes particulieres amenant a de nombreux objectifs. Ainsi, la notion de performance d'une application est devenue multi-dimensionnelle. Par exemple, ordonnancer optimalement (en temps) une application sur une grille de calcul est inutile si elle ne fournit pas de resultat parce qu'une machine tombe en panne. Fournir une solution a ces problemes est un defi algorithmique actuel. Dans ce manuscrit, nous etudions l'ordonnancement multi-objectif a l'aide des outils de la theorie de l'approximation. Nous traitons ainsi quatre problemes. Les deux premiers sont inspires des systemes embarques, tandis que les deux derniers sont inspires des problematiques que l'on retrouve sur les grilles et les \textit{clusters}. Le premier probleme etudie est l'optimisation des performances d'une application sur une machine disposant de peu de memoire de stockage. Nous montrons que l'utilisation de l'optimisation multi-objectif permet de fournir une solution et des informations sur le probleme que la theorie mono-objectif de l'approximation ne pouvait pas obtenir. Les deux problemes suivants concernent l'optimisation des performances d'une application lorsque les machines ne sont pas entierement fiables. Les differents modeles de defaillances amenent a des problemes d'optimisation radicalement differents. C'est pourquoi le deuxieme probleme traite de la surete de fonctionnement des systemes embarques alors que le troisieme considere la fiabilite des grilles et \textit{clusters}. Le dernier probleme concerne l'utilisation simultanee d'une plate-forme de calcul parallele par de nombreux utilisateurs. Nous montrons comment l'utilisation de l'optimisation multi-objectif peut permettre de prendre en compte les besoins utilisateurs au sein du processus d'optimisation.

[1]  Hamoudi Kalla,et al.  Génération automatique de distributions/ordonnancements temps réel, fiables et tolérants aux fautes , 2004 .

[2]  Mark J. Clement,et al.  Core Algorithms of the Maui Scheduler , 2001, JSSPP.

[3]  Arnaud Legrand,et al.  Non-Cooperative Scheduling of Multiple Bag-of-Task Applications , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[4]  W. Stromquist.  How to Cut a Cake Fairly , 1980 .

[5]  S. Tse.  Online Bicriteria Load Balancing for Distributed File Servers , 2007, 2007 Second International Conference on Communications and Networking in China.

[6]  Niraj K. Jha,et al.  Safety and Reliability Driven Task Allocation in Distributed Systems , 1999, IEEE Trans. Parallel Distributed Syst..

[7]  Björn Lisper.  Trends in Timing Analysis , 2006, DIPES.

[8]  H. Kellerer.  Algorithms for multiprocessor scheduling with machine release times , 1998 .

[9]  Frank Thomson Leighton,et al.  Tight bounds on the size of fault-tolerant merging and sorting networks with destructive faults , 1993, SPAA '93.

[10]  Jan Karel Lenstra,et al.  Approximation algorithms for scheduling unrelated parallel machines , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[11]  Chung-Yee Lee,et al.  Parallel machines scheduling with nonsimultaneous machine available time , 1991, Discret. Appl. Math..

[12]  Edward A. Lee,et al.  A Compile-Time Scheduling Heuristic for Interconnection-Constrained Heterogeneous Processor Architectures , 1993, IEEE Trans. Parallel Distributed Syst..

[13]  Fred B. Schneider,et al.  Implementing fault-tolerant services using the state machine approach: a tutorial , 1990, CSUR.

[14]  Xiao Qin,et al.  An efficient fault-tolerant scheduling algorithm for real-time tasks with precedence constraints in heterogeneous systems , 2002, Proceedings International Conference on Parallel Processing.

[15]  Reinhold Heckmann,et al.  Computing the Worst Case Execution Time of an Avionics Program by Abstract Interpretation , 2007 .

[16]  Ishfaq Ahmad,et al.  Benchmarking the task graph scheduling algorithms , 1998, Proceedings of the First Merged International Parallel Processing Symposium and Symposium on Parallel and Distributed Processing.

[17]  Michael P. Wellman,et al.  Auction Protocols for Decentralized Scheduling , 2001, Games Econ. Behav..

[18]  David B. Shmoys,et al.  Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms , 1997, Math. Oper. Res..

[19]  Kishor S. Trivedi,et al.  Reliability and Performability Modeling Using SHARPE 2000 , 2000, Computer Performance Evaluation / TOOLS.

[20]  Myron Lipow,et al.  Reliability: Management, Methods, and Mathematics , 1977 .

[21]  Jean-Claude Laprie.  Surete de fonctionnement des systemes: concepts de base et terminologie , 2004 .

[22]  D. Powell,et al.  The Delta-4 Approach to Dependability in Open Distributed Computing Systems , 1995, Twenty-Fifth International Symposium on Fault-Tolerant Computing, 1995, ' Highlights from Twenty-Five Years'..

[23]  C. Siva Ram Murthy,et al.  Task Allocation Algorithms for Maximizing Reliability of Distributed Computing Systems , 1997, IEEE Trans. Computers.

[24]  Shuvra S. Bhattacharyya,et al.  A Comparison of Clustering and Scheduling Techniques for Embedded Multiprocessor Systems , 2003 .

[25]  Vincent T'Kindt,et al.  Counting and enumeration complexity with application to multicriteria scheduling , 2005, 4OR.

[26]  Alan Burns,et al.  Guest Editorial: A Review of Worst-Case Execution-Time Analysis , 2000, Real-Time Systems.

[27]  Éva Tardos,et al.  Scheduling unrelated machines with costs , 1993, SODA '93.

[28]  Frédéric Vivien,et al.  Minimizing the stretch when scheduling flows of biological requests , 2006, SPAA '06.

[29]  Petru Eles,et al.  Scheduling and voltage scaling for energy/reliability trade-offs in fault-tolerant time-triggered embedded systems , 2007, 2007 5th IEEE/ACM/IFIP International Conference on Hardware/Software Codesign and System Synthesis (CODES+ISSS).

[30]  Z Liu,et al.  Scheduling Theory and its Applications , 1997 .

[31]  Rizos Sakellariou,et al.  An Experimental Investigation into the Rank Function of the Heterogeneous Earliest Finish Time Scheduling Algorithm , 2003, Euro-Par.

[32]  David B. Shmoys,et al.  A Polynomial Approximation Scheme for Scheduling on Uniform Processors: Using the Dual Approximation Approach , 1988, SIAM J. Comput..

[33]  David B. Shmoys,et al.  Using dual approximation algorithms for scheduling problems: practical and theoretical results , 1987 .

[34]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[35]  Jean C. Walrand,et al.  Fair end-to-end window-based congestion control , 2000, TNET.

[36]  Henrik Theiling,et al.  Fast and Precise WCET Prediction by Separated Cache and Path Analyses , 2000, Real-Time Systems.

[37]  J.-P. Wang,et al.  Task Allocation for Maximizing Reliability of Distributed Computer Systems , 1992, IEEE Trans. Computers.

[38]  Krzysztof Rzadca,et al.  Cooperation in Multi-organization Scheduling , 2009, Euro-Par.

[39]  Mihalis Yannakakis,et al.  On the approximability of trade-offs and optimal access of Web sources , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[40]  Soonhoi Ha,et al.  A Static Scheduling Heuristic for Heterogeneous Processors , 1996, Euro-Par, Vol. II.

[41]  Mark Voorneveld,et al.  Characterization of Pareto dominance , 2003, Oper. Res. Lett..

[42]  Oscar H. Ibarra,et al.  Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors , 1977, JACM.

[43]  Howard Jay Siegel,et al.  A dynamic matching and scheduling algorithm for heterogeneous computing systems , 1998, Proceedings Seventh Heterogeneous Computing Workshop (HCW'98).

[44]  David P. Williamson,et al.  Scheduling Parallel Machines On-Line , 1995, SIAM J. Comput..

[45]  Clifford Stein,et al.  On the existence of schedules that are near-optimal for both makespan and total weighted completion time , 1997, Oper. Res. Lett..

[46]  Henri Casanova,et al.  A realistic network/application model for scheduling divisible loads on large-scale platforms , 2005, 19th IEEE International Parallel and Distributed Processing Symposium.

[47]  Salim Hariri,et al.  Task scheduling algorithms for heterogeneous processors , 1999, Proceedings. Eighth Heterogeneous Computing Workshop (HCW'99).

[48]  Marc Despontin,et al.  Multiple Criteria Optimization: Theory, Computation, and Application, Ralph E. Steuer (Ed.). Wiley, Palo Alto, CA (1986) , 1987 .

[49]  Samir Jafar,et al.  Programmation des systèmes parallèles distribués : tolérance aux pannes, résilience et adaptabilité. (Parallel and distributed systems programming: Fault-Tolerance, resilience and adaptability) , 2006 .

[50]  Anand Sivasubramaniam,et al.  Fault-aware job scheduling for BlueGene/L systems , 2004, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings..

[51]  Rajmohan Rajaraman,et al.  Approximation algorithms for multiprocessor scheduling under uncertainty , 2007, SPAA.

[52]  Anand Sivasubramaniam,et al.  BlueGene/L Failure Analysis and Prediction Models , 2006, International Conference on Dependable Systems and Networks (DSN'06).

[53]  Martin Skutella,et al.  Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem , 1997, Math. Oper. Res..