Approximating Real-Time Scheduling on Identical Machines
We study the problem of assigning n tasks to m identical parallel machines in the real-time scheduling setting, where each task recurrently releases jobs that must be completed by their deadlines. The goal is to find a partition of the task set over the machines such that each job that is released by a task can meet its deadline. Since this problem is co-NP-hard, the focus is on finding α-approximation algorithms in the resource augmentation setting, i.e., finding a feasible partition on machines running at speed α ≥ 1, if some feasible partition exists on unit-speed machines.
Recently, Chen and Chakraborty gave a polynomial-time approximation scheme if the ratio of the largest to the smallest relative deadline of the tasks, λ, is bounded by a constant. However, their algorithm has a super-exponential dependence on λ and hence does not extend to larger values of λ. Our main contribution is to design an approximation scheme with a substantially improved running-time dependence on λ. In particular, our algorithm depends exponentially on logλ and hence has quasi-polynomial running time even if λ is polynomially bounded. This improvement is based on exploiting various structural properties of approximate demand bound functions in different ways, which might be of independent interest.
KeywordsTask System Earliest Deadline First Feasibility Test Identical Machine Sporadic Task
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- 1.Baker, T.P., Baruah, S.K.: Schedulability analysis of multiprocessor sporadic task systems. In: Handbook of Real-Time and Embedded Systems, ch. 3. CRC Press (2007)Google Scholar
- 3.Baruah, S., Fisher, N.: The partitioned multiprocessor scheduling of sporadic task systems. In: Proceedings of 26th IEEE Real-Time Systems Symposium, pp. 321–329. IEEE (2005)Google Scholar
- 4.Baruah, S., Goossens, J.: Scheduling real-time tasks: Algorithms and complexity. In: Leung, J.Y.-T. (ed.) Handbook of Scheduling: Algorithms, Models and Performance Evalution, ch. 28. CRC Press (2004)Google Scholar
- 5.Baruah, S., Mok, A., Rosier, L.: Preemptively scheduling hard-real-time sporadic tasks on one processor. In: Proceedings of 11th IEEE Real-Time Systems Symposium, pp. 182–190. IEEE (1990)Google Scholar
- 7.Chakraborty, S., Künzli, S., Thiele, L.: Approximate schedulability analysis. In: Proceedings of 23rd IEEE Real-Time Systems Symposium, pp. 159–168. IEEE (2002)Google Scholar
- 9.Chen, J.-J., Chakraborty, S.: Partitioned packing and scheduling for sporadic real-time tasks in identical multiprocessor systems. In: Proceedings of 24th Euromicro Conference on Real-Time Systems, pp. 24–33 (2012)Google Scholar
- 10.Eisenbrand, F., Rothvoß, T.: EDF-schedulability of synchronous periodic task systems is coNP-hard. In: Proceedings of 21st Symposium on Discrete Algorithms, pp. 1029–1034 (2010)Google Scholar