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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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