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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.175
URN: urn:nbn:de:0030-drops-53028
URL: http://drops.dagstuhl.de/opus/volltexte/2015/5302/
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Chen, Lin ; Megow, Nicole ; Rischke, Roman ; Stougie, Leen

Stochastic and Robust Scheduling in the Cloud

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Abstract

Users of cloud computing services are offered rapid access to computing resources via the Internet. Cloud providers use different pricing options such as (i) time slot reservation in advance at a fixed price and (ii) on-demand service at a (hourly) pay-as-used basis. Choosing the best combination of pricing options is a challenging task for users, in particular, when the instantiation of computing jobs underlies uncertainty. We propose a natural model for two-stage scheduling under uncertainty that captures such resource provisioning and scheduling problem in the cloud. Reserving a time unit for processing jobs incurs some cost, which depends on when the reservation is made: a priori decisions, based only on distributional information, are much cheaper than on-demand decisions when the actual scenario is known. We consider both stochastic and robust versions of scheduling unrelated machines with objectives of minimizing the sum of weighted completion times and the makespan. Our main contribution is an (8+eps)-approximation algorithm for the min-sum objective for the stochastic polynomial-scenario model. The same technique gives a (7.11+eps)-approximation for minimizing the makespan. The key ingredient is an LP-based separation of jobs and time slots to be considered in either the first or the second stage only, and then approximately solving the separated problems. At the expense of another epsilon our results hold for any arbitrary scenario distribution given by means of a black-box. Our techniques also yield approximation algorithms for robust two-stage scheduling.

BibTeX - Entry

@InProceedings{chen_et_al:LIPIcs:2015:5302,
  author =	{Lin Chen and Nicole Megow and Roman Rischke and Leen Stougie},
  title =	{{Stochastic and Robust Scheduling in the Cloud}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{175--186},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Naveen Garg and Klaus Jansen and Anup Rao and Jos{\'e} D. P. Rolim},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5302},
  URN =		{urn:nbn:de:0030-drops-53028},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.175},
  annote =	{Keywords: Approximation Algorithms, Robust Optimization, Stochastic Optimization, Unrelated Machine Scheduling, Cloud Computing}
}

Keywords: Approximation Algorithms, Robust Optimization, Stochastic Optimization, Unrelated Machine Scheduling, Cloud Computing
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)
Issue Date: 2015
Date of publication: 28.07.2015


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