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Optimality Aspects of Greedy Schemes in Parallel Processing of Random Graph-Structured Jobs

Published online by Cambridge University Press:  27 July 2009

Nicholas Bambos  and
Shou C. Chen
Nicholas Bambos
Affiliation:
Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, California 90024-1594
Shou C. Chen
Affiliation:
Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, California 90024-1594
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Abstract

Parallel processing systems with jobs structured as random graphs, where the nodes correspond to executable tasks and the directed edges to precedence constraints, are studied from a queueing theoretic point of view under general stationarity assumptions on the job flows. Jobs need to have their tasks processed non-preemptively by a set of uniform processors. Simple, natural greedy schemes of allocating processors to tasks are shown to asymptotically minimize the long-term average execution time per job. The stability condition for this queueing system is specified, and greedy allocation schemes are shown to stabilize the system under the maximum possible job arrival rate. Some recurrence properties of the system state are also established.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 2 , April 1994 , pp. 229 - 243
Copyright
Copyright © Cambridge University Press 1994

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References

1.Baccelli, F. & Liu, Z. (1989). On the stability condition of a precedence-based queueing discipline. Advances in Applied Probability 21(4): 883–898.CrossRefGoogle Scholar
2.Baccelli, F. & Liu, Z. (1990). Generalized precedence-based queueing systems. INRIA Research Report. Preprint.Google Scholar
3.Baccelli, F. & Liu, Z. (1990). On the execution of parallel programs on multiprocessor systems — A queueing theoretic approach. Journal of the Association of Computing Machinery 37(2): 373–414.CrossRefGoogle Scholar
4.Baccelli, F., Liu, Z., & Towsley, D. (1989). Optimal scheduling of parallel processing systems with real-time constraints. INRIA Research Report, No. 1113.Google Scholar
5.Bambos, N. & Walrand, J. (1991). On stability and performance of parallel processing systems. Journal of the Association of Computing Machinery 38(2): 429–452.CrossRefGoogle Scholar
6.Franken, P., Koenig, D., Arndt, U., & Schmidt, V. (1982). Queues and point processes. Berlin: Akademie Verlag.Google Scholar
7.Hu, T.C. (1961). Parallel sequencing and assembly line problems. Operations Research 9: 841–848.CrossRefGoogle Scholar
8.Kingman, J.F.C. (1973). Subadditive ergodic theory. Annals of Probability 1(6): 883–909.CrossRefGoogle Scholar
9.Loynes, R.M. (1962). The stability of a queue with non-independent inter-arrival and service times. Proceedings of the Cambridge Philosophical Society 58: 497–520.CrossRefGoogle Scholar
10.Papadimitriou, C. & Tsitsiklis, J. (1987). On stochastic scheduling with in-tree precedence constraints. SIAM Journal of Computing 16(1): 1–6.CrossRefGoogle Scholar
11.Tsitsiklis, J.N., Papadimitriou, C., & Humblet, P. (1986). The performance of a precedence-based queueing discipline. Journal of the Association of Computing Machinery 33(3): 593–602.CrossRefGoogle Scholar
12.Walters, P. (1982). An introduction to ergodic theory. New York: Springer-Verlag.CrossRefGoogle Scholar