{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/18275"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/18275","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Online Scheduling on Identical Machines Using SRPT","abstract":"Item withdrawn by Alexis Thompson (athmpsn1@illinois.edu) on 2010-12-03T19:33:24Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 4 jeffe.sty: 24412 bytes, checksum: 7ff608a5b6c12b98320e3fb918b076e5 (MD5) SRPTidentical.tex: 41117 bytes, checksum: bd7473306ef8d1fb5f6ba4d3b108f6f1 (MD5) SRPT.bib: 36493 bytes, checksum: 2a6ddf7d79f5527e39fdf1baf15e7c44 (MD5) Fox_Kyle.pdf: 251847 bytes, checksum: 79cd877ddb4000e33f51e201b9c19703 (MD5)","abstract_html":"Item withdrawn by Alexis Thompson (athmpsn1@illinois.edu) on 2010-12-03T19:33:24Z Item was in collections: University of Illinois Theses &amp; Dissertations (ID: 1) No. of bitstreams: 4 jeffe.sty: 24412 bytes, checksum: 7ff608a5b6c12b98320e3fb918b076e5 (MD5) SRPTidentical.tex: 41117 bytes, checksum: bd7473306ef8d1fb5f6ba4d3b108f6f1 (MD5) SRPT.bib: 36493 bytes, checksum: 2a6ddf7d79f5527e39fdf1baf15e7c44 (MD5) Fox_Kyle.pdf: 251847 bytes, checksum: 79cd877ddb4000e33f51e201b9c19703 (MD5)","abstract_has_math":false,"creators":["Fox, Kyle J."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Erickson, Jeff G."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-14T22:43:35Z","date_published":"2011-01-14T22:43:35Z","updated_at":"2026-07-22T22:25:11Z","subjects":["scheduling","competitive analysis","resource augmentation"],"languages":["en"],"rights":["Copyright 2010 Kyle J. Fox"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/18275","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Erickson, Jeff G."]},{"key":"dc:creator","label":"Author","values":["Fox, Kyle J."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-01-14T22:43:35Z","2010-12"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["scheduling","competitive analysis","resource augmentation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2010 Kyle J. Fox"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/18275"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Item withdrawn by Alexis Thompson (athmpsn1@illinois.edu) on 2010-12-03T19:33:24Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 4 jeffe.sty: 24412 bytes, checksum: 7ff608a5b6c12b98320e3fb918b076e5 (MD5) SRPTidentical.tex: 41117 bytes, checksum: bd7473306ef8d1fb5f6ba4d3b108f6f1 (MD5) SRPT.bib: 36493 bytes, checksum: 2a6ddf7d79f5527e39fdf1baf15e7c44 (MD5) Fox_Kyle.pdf: 251847 bytes, checksum: 79cd877ddb4000e33f51e201b9c19703 (MD5)","Made available in DSpace on 2011-01-14T22:43:35Z (GMT). No. of bitstreams: 5 Fox_Kyle.pdf: 251847 bytes, checksum: 79cd877ddb4000e33f51e201b9c19703 (MD5) license.txt: 4058 bytes, checksum: 41960e5160f64bdf15db3f46583cc26c (MD5) SRPT.bib: 36493 bytes, checksum: 2a6ddf7d79f5527e39fdf1baf15e7c44 (MD5) SRPTidentical.tex: 41117 bytes, checksum: bd7473306ef8d1fb5f6ba4d3b108f6f1 (MD5) jeffe.sty: 24412 bytes, checksum: 7ff608a5b6c12b98320e3fb918b076e5 (MD5)","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 $O(1/\\eps^2)$-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."]},{"key":"dc:title","label":"Title","values":["Online Scheduling on Identical Machines Using SRPT"]}]}],"canonical_facts":{"dc:contributor":["Erickson, Jeff G."],"dc:creator":["Fox, Kyle J."],"dc:date":["2011-01-14T22:43:35Z","2010-12"],"dc:description":["Item withdrawn by Alexis Thompson (athmpsn1@illinois.edu) on 2010-12-03T19:33:24Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 4 jeffe.sty: 24412 bytes, checksum: 7ff608a5b6c12b98320e3fb918b076e5 (MD5) SRPTidentical.tex: 41117 bytes, checksum: bd7473306ef8d1fb5f6ba4d3b108f6f1 (MD5) SRPT.bib: 36493 bytes, checksum: 2a6ddf7d79f5527e39fdf1baf15e7c44 (MD5) Fox_Kyle.pdf: 251847 bytes, checksum: 79cd877ddb4000e33f51e201b9c19703 (MD5)","Made available in DSpace on 2011-01-14T22:43:35Z (GMT). No. of bitstreams: 5 Fox_Kyle.pdf: 251847 bytes, checksum: 79cd877ddb4000e33f51e201b9c19703 (MD5) license.txt: 4058 bytes, checksum: 41960e5160f64bdf15db3f46583cc26c (MD5) SRPT.bib: 36493 bytes, checksum: 2a6ddf7d79f5527e39fdf1baf15e7c44 (MD5) SRPTidentical.tex: 41117 bytes, checksum: bd7473306ef8d1fb5f6ba4d3b108f6f1 (MD5) jeffe.sty: 24412 bytes, checksum: 7ff608a5b6c12b98320e3fb918b076e5 (MD5)","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 $O(1/\\eps^2)$-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."],"dc:identifier":["http://hdl.handle.net/2142/18275"],"dc:language":["en"],"dc:rights":["Copyright 2010 Kyle J. Fox"],"dc:subject":["scheduling","competitive analysis","resource augmentation"],"dc:title":["Online Scheduling on Identical Machines Using SRPT"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:11Z"}