Abstract
We consider a scheduling problem where machines need to be rented from the cloud in order to process jobs. There are two types of machines available which can be rented for machine-type dependent prices and for arbitrary durations. However, a machine-type dependent setup time is required before a machine is available for processing. Jobs arrive online over time, have deadlines and machine-type dependent sizes. The objective is to rent machines and schedule jobs so as to meet all deadlines while minimizing the rental cost. As we observe the slack of jobs to have a fundamental influence on the competitiveness, we parameterize instances by their (minimum) slack. An instance is called to have a slack of \(\beta \) if, for all jobs, the difference between the job’s release time and the latest point in time at which it needs to be started is at least \(\beta \). While for \(\beta < s\) no finite competitiveness is possible, our main result is an online algorithm for \(\beta = (1+\varepsilon )s\) with 
, where s denotes the largest setup time. Its competitiveness only depends on \(\varepsilon \) and the cost ratio of the machine types and is proven to be optimal up to a factor of 
.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abshoff S, Markarian C, Meyer auf der Heide F (2014) Randomized online algorithms for set cover leasing problems. In: Zhang Z, Wu L, Xu W, Du DZ (eds) COCOA 2014, LNCS, vol 8881. Springer, Berlin, pp 25–34
Amazon EC2. https://aws.amazon.com/ec2/. Accessed Nov 2017
Anthony MB, Gupta A (2007) Infrastructure leasing problems. In: Fischetti M, Williamson DP (eds) IPCO 2007, LNCS, vol 4513. Springer, Berlin, pp 424–438
Azar Y, Ben-Aroya N, Devanur N-R, Jain N (2013) Cloud scheduling with setup cost. In: Proceedings of the 25th ACM symposium on parallelism in algorithms and architectures (SPAA’13). ACM, pp 298–304
Bender MA, Bunde DP, Leung VJ, McCauley S, Phillips CA (2013) Efficient scheduling to minimize calibrations. In: Proceedings of the 25th ACM symposium on parallelism in algorithms and architectures (SPAA’13). ACM, pp 280–287
Chuzhoy J, Guha S, Khanna S, Naor J (2004) Machine minimization for scheduling jobs with interval constraints. In: Proceedings of the 45th symposium on foundations of computer science (FOCS’04). IEEE, pp 81–90
Devanur NR, Makarychev K, Panigrahi D, Yaroslavtsev G (2014) Online algorithms for machine minimization. CoRR. arXiv:1403.0486
Fineman TJ, Sheridan B (2015) Scheduling non-unit jobs to minimize calibrations. In: Proceedings of the 27th ACM symposium on parallelism in algorithms and architectures (SPAA’15). ACM, pp 161–170
Google Cloud. https://cloud.google.com/. Accessed Nov 2017
Kling P, Meyer auf der Heide F, Pietrzyk P (2012) An algorithm for online facility leasing. In: Even G, Halldórsson MM (eds) SIROCCO 2012, LNCS, vol 7355. Springer, Berlin, pp 61–72
Lee G, Chun B-G, Katz RH (2001) Heterogeneity-aware resource allocation and scheduling in the cloud. In: Proceedings of the 3rd USENIX workshop on hot topics in cloud computing (HotCloud’11). USENIX
Li S, Mäcker A, Markarian C, Meyer auf der Heide F, Riechers S (2015) Towards flexible demands in online leasing problems. In: Proceedings of the 21st international conference on computing and combinatorics (COCOON’15). Springer, Berlin, pp 277–288
Malik S, Huet F (2011) Virtual cloud: rent out the rented resources. In: Proceedings of the 2011 international conference on internet technology and secured transactions (ICITST’11). IEEE, pp 536–541
Mao M, Humphrey M (2012) A performance study on the VM startup time in the cloud. In: Proceedings of the 2012 IEEE 5th international conference on cloud computing (ICCC’12). IEEE, pp 423–430
Mao M, Li J, Humphrey M (2010) Cloud auto-scaling with deadline and budget constraints. In: Proceedings of the 2010 11th IEEE/ACM international conference on grid computing (GRID’10). IEEE, pp 41–48
Meyerson A (2005) The parking permit problem. In: Proceedings of the 46th annual symposium on foundations of computer science (FOCS’05). IEEE, pp 274–282
Raghavan P, Thompson CD (1987) Randomized rounding: a technique for provably good algorithms and algorithmic proofs. Combinatorica 7(4):365–374
Saha B (2013) Renting a cloud. In: Proceedings of the annual conference on foundations of software technology and theoretical computer science (FSTTCS’13). LIPIcs, pp 437–448
Sgall J (2014) Online bin packing: old algorithms and new results. In: Beckmann A, Csuhaj-Varjú E, Meer K (eds) CiE 2014, LNCS, vol 8493. Springer, Berlin, pp 362–372
Yu G, Zhang G (2009) Scheduling with a minimum number of machines. Oper Res Lett 37(2):97–101
Author information
Authors and Affiliations
Corresponding author
Additional information
A prior version of this work is published in the proceedings of the 10th Annual International Conference on Combinatorial Optimization and Applications (COCOA) available at Springer via https://dx.doi.org/10.1007/978-3-319-48749-6_42.
This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing” (SFB 901).
Rights and permissions
About this article
Cite this article
Mäcker, A., Malatyali, M., Meyer auf der Heide, F. et al. Cost-efficient scheduling on machines from the cloud. J Comb Optim 36, 1168–1194 (2018). https://doi.org/10.1007/s10878-017-0198-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-017-0198-x