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The Computer Journal Advance Access originally published online on August 29, 2007
The Computer Journal 2008 51(2):216-226; doi:10.1093/comjnl/bxm059
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© The Author 2007. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved.For Permissions, please email: journals.permissions@oxfordjournals.org

Average-Case Performance Analysis Of Online Non-Clairvoyant Scheduling Of Parallel Tasks With Precedence Constraints

Keqin Li*

Department of Computer Science, State University of New York, New Paltz, New York 12561, USA

* Corresponding author: lik{at}newpaltz.edu

Received 10 January 2007; revised 21 June 2007

We evaluate the average-case performance of three approximation algorithms for online non-clairvoyant scheduling of parallel tasks with precedence constraints. We show that for a class of wide task graphs, when task sizes are uniformly distributed in the range [1...C], the online non-clairvoyant scheduling algorithm LL-SIMPLE has an asymptotic average-case performance bound of M/(M – (3 – (1 + 1/C)C+1)C – 1), where M is the number of processors. For uniform probability distributions of task sizes, we present numerical and simulation data to demonstrate the accuracy of our general asymptotic average-case performance bound. We also report extensive experimental results on the average-case performance of online non-clairvoyant scheduling algorithms LL-GREEDY and LS. Algorithm LL-GREEDY has better performance than LL-SIMPLE using an improved algorithm to schedule independent tasks in the same level. Algorithm LS produces even better schedules due to a break of boundaries among levels.

Key Words: Approximation algorithm • average-case performance ratio • non-clairvoyant scheduling • online scheduling • parallel task • precedence constraint • probabilistic analysis • simulation • worst case performance ratio


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