Abstract
We consider the online problem of scheduling real-time jobs with hard deadlines on m parallel machines. Each job has a processing time and a deadline, and the objective is to schedule jobs so that they complete before their deadline. It is known that even when the instance is feasible it may not be possible to meet all deadlines when jobs arrive online over time. We therefore consider the setting when the algorithm has available machines with speed s > 1.
We present a new online algorithm that finds a feasible schedule on machines of speed e/(e − 1) ≈ 1.58 for any instance that is feasible on unit speed machines. This improves on the previously best known result which requires a speed of 2 − 2/(m + 1). Our algorithm only uses the relative order of job deadlines and is oblivious of the actual deadline values. It was shown earlier that the minimum speed required for such algorithms is e/(e − 1), and thus, our analysis is tight. We also show that our new algorithm outperforms two other well-known algorithms by giving the first lower bounds on their minimum speed requirement.
Research supported by the Indo-German Max Planck Center for Computer Science (IMPECS).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cho, S., Lee, S.K., Ahn, S., Lin, K.-J.: Efficient real-time scheduling algorithms for multiprocessor systems. IEICE Transactions on Communications E85-B(12), 2859–2867 (2002)
Dertouzos, M.L.: Control robotics: The procedural control of physical processes. In: IFIP Congress, pp. 807–813 (1974)
Dertouzos, M.L., Mok, A.K.: Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Transactions on Software Engineering 15(12), 1497–1506 (1989)
Horn, W.A.: Some simple scheduling algorithms. Naval Research Logistics Quarterly 21(1), 177–185 (1974)
Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. Journal of the ACM 47(4), 617–643 (2000)
Lam, T.W., To, K.-K.: Trade-offs between speed and processor in hard-deadline scheduling. In: Proc. of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 623–632 (1999)
Park, M., Han, S., Kim, H., Cho, S., Cho, Y.: Comparison of deadline-based scheduling algorithms for periodic real-time tasks on multiprocessor. IEICE Transactions 88-D(3), 658–661 (2005)
Phillips, C.A., Stein, C., Torng, E., Wein, J.: Optimal time-critical scheduling via resource augmentation. Algorithmica 32(2), 163–200 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Anand, S., Garg, N., Megow, N. (2011). Meeting Deadlines: How Much Speed Suffices?. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22006-7_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-22006-7_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22005-0
Online ISBN: 978-3-642-22006-7
eBook Packages: Computer ScienceComputer Science (R0)