Online Scheduling on Identical Machines Using SRPT

Due to its optimality on a single machine for the problem of minimizing average flow time, Shortest-Remaining-Processing-Time (SRPT) appears to be the most natural algorithm to consider for the problem of minimizing average flow time on multiple identical machines. It is known that SRPT achieves the best possible competitive ratio on multiple machines up to a constant factor. Using resource augmentation, SRPT is known to achieve total flow time at most that of the optimal solution when given machines of speed $2- 1/m$. Further, it is known that SRPT's competitive ratio improves as the speed increases; SRPT is $s$-speed $1/s$-competitive when $s \geq 2 - 1/m$. However, a gap has persisted in our understanding of SRPT. Before this work, we did not know the performance of SRPT when given machines of speed $1+\eps$ for any $0 < \eps < 1 - 1/m$. We answer the question in this thesis. We show that SRPT is scalable on $m$ identical machines. That is, we show SRPT is $(1+\eps)$-speed $O(1/\eps)$-competitive for any $\eps > 0$. We also show that SRPT is $(1+\eps)$-speed O(1/\eps²)-competitive for the objective of minimizing the l_k norms of flow time on $m$ identical machines. Both of our results rely on new potential functions that capture the structure of SRPT. Our results, combined with previous work, show that SRPT is the best possible online algorithm in essentially every aspect when migration is permissible.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Fox, Kyle J.

Contributors dc:contributor

• Erickson, Jeff G.

• scheduling
• competitive analysis
• resource augmentation

Statement dc:rights

• Copyright 2010 Kyle J. Fox

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/18275

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F18275