Static allocation of tasks on multiprocessor architectures with interprocessor communication delays
This paper deals with the problem of task allocation, subjected to precedence constraints, on multiprocessor architectures with interprocessor communication delays. Two kinds of scheduling are distinguished: the deterministic scheduling (the duration of each task and the duration of each communication delay are known and are constant) and the stochastic scheduling (the duration of each task and the duration of each communication delay is modelled by a probability law).
For each of these two scheduling problems, we propose several scheduling methods and we build several models in order first to estimate the efficiency of the obtained schedules and second to evaluate the multiprocessor architecture performances, such as the busy percentage of processors. These methods are based on the coupling between priority list algorithms and neighbourhood methods. Because neighbourhood methods are not suitable for stochastic scheduling problem, we have modified the simulated annealing algorithm in order to solve stochastic optimization problems.
For the deterministic scheduling, we use finite deterministic simulation models. In the case of stochastic scheduling, we built several models: a markovian model, a stochastic simulation model and a hybrid model (markovian analysis and simulation).
Although this scheduling problem is NP-complete, these methods compute satisfactory solutions in reasonable computing times. The mean improvement compared with classical list scheduling methods is about 10% in the deterministic case as well as in the stochastic case.
KeywordsStochastic scheduling Deterministic scheduling Task allocation on multiprocessor architectures
Unable to display preview. Download preview PDF.
- [Adam 74]T.L. Adam, K.M. Chandy, J.R. Dickson, “A comparison of list schedules for parallel processing systems”. Communications of the ACM, Vol 17 (n∘12), Dec 1974.Google Scholar
- [Bulgak 88]A.A. Bulgak, J.L. Sanders, “Integrating a modified simulated annealing algorithm with the simultion of a manufacturing system to optimize buffer sizes in automatic assembly systems”, Proceedings of the 1988 Winter Simulation Conference, pp. 684–690.Google Scholar
- [Chrétienne 89]
- [Chétienne 92]P. Chrétienne, C. Picouleau, “The basic scheduling problem with interprocessor communication delays”, Ecole d'été sur la théorie de l'ordonnancement et ses applications, 28 Sept–20 Octobre 1992, Château de Bonas (Gers), France, pp. 81–100.Google Scholar
- [Coffman 72]E. G. Coffman, R.L. Graham, “Optimal scheduling for two processor systems”, Acta Informatica, Vol 1, pp. 200–213, 1972.Google Scholar
- [Coffman 76]E.G. Coffman, “Computer and jobshop scheduling theory”, John Wiley and sons, 1987.Google Scholar
- [Fleury 93]G. Fleury, “Quelques méthodes de résolution de problèmes NP-complets”, Thèse d'université, Université Blaise Pascal, Clermont-Ferrand II, à paraître, 1993.Google Scholar
- [Garey 83]M.R. Garey, D.S. Johnson, “Computers and intractability: a guide to the theory of NP-completeness”, Freeman, New-York, 1983.Google Scholar
- [Gerasoulls 92]A. Gerasoulis, T. Yang, “A static macro-dataflow scheduling tool for scalable parallel architecture”. Ecole d'été sur la théorie de l'ordonnancement et ses applications, 28 Sept–20 Octobre 1992, Château de Bonas (Gers), France, pp. 382–417.Google Scholar
- [Hajeck 88]B. Hajeck, “Cooling schedules for optimal annealing”, Mathematics of Operations Research, 1988, pp.311–329, 1988.Google Scholar
- [Hu 61]T.C. Hu, “Parallel sequencing and assembly line problem”. Operational Research, Vol 9, pp. 841–843, Nov. 1961.Google Scholar
- [Hwang 89]J.J. Hwang, Y.C. Chow, F.D. Anger, C.Y. Lee, “Scheduling precedence graphs in systems with interprocessor communication times”, SIAM JComp, 18,2,April 1989, pp. 244–257.Google Scholar
- [Lewis 73]T.G. Lewis, W.H. Payne, “Generalized feedback shift register pseudo random number algorithm”, J. ACM, Vol 20, n∘3, pp.456–468. July 73.Google Scholar
- [Marsan 86]M.A. Marsan, G. Balbo, G. Conte, “Performance models of multiprocessor systems”, The MIT Press, USA, 1986.Google Scholar
- [Molloy 82]M.K. Molloy, “Performance analysis using Petri Nets”, IEEE Transactions on Computers, Vol C31. September 1984, pp. 913–917.Google Scholar
- [Mueller 85]B. Mueller, “NUMAS: a tool for the numerical modelling of computer systems”, in Modelling Techniques and Tools for Performance Analysis, North-Holland, 1985.Google Scholar
- [Natkin 80]S. Natkin, “Réseaux de Petri stochastiques”. Thèse de Docteur-Ingénieur, Cnam Paris. 1980.Google Scholar
- [Norre 93]S. Norre, “Affectation de tâches sur une architecture multiprocesseur — Méthodes stochastiques et évaluation des performances”. Thèse de doctorat,Université Clermont-Ferrand II.Google Scholar
- [Paul 85]D.W. Paul, “An approach toward a universal specification language for discrete stochastic systems”, in Modelling Techniques and Tools for Performance Analysis, North-Holland, 1985.Google Scholar
- [Picouleau 92]C. Picouleau, “New complexity results on the UET-UCT scheduling problems”, Ecole d'été sur la théorie de l'ordonnancement et ses applications, 28 Sept–20 Octobre 1992, Château de Bonas (Gers), France, pp. 487–502.Google Scholar
- [Potler 85]D. Potier, M. Véran, “The markovian solver of Qnap2 and applications”, Rapport Technique INRIA n∘49. Mars 1985, FranceGoogle Scholar
- [Qnap2 91]Qnap2 version8, manuel de référence, Société Simulog, 1991.Google Scholar
- [Siarry 88]P. Siarry, G. Dreyfus, “La méthode du recuit simulé: théorie et applications”, ISDET, Paris, 1988.Google Scholar
- [Stewart 78]W.J. Stewart, “A comparison of numerical techniques in markov modelling”, C. ACM 21, 2, 1978, pp. 144–152.Google Scholar
- [Van Laarhoven 89]P.J.M. Van Laarhoven, “Simulated annealing: theory and applications”, Kluwer Academic Publishors, The Netherlands, 1989.Google Scholar