Abstract
In this chapter, we consider the partitioned preemptive scheduling of implicit-deadline sporadic task systems on identical multiprocessor platforms.
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- 1.
Actually, the result in [108] was expressed in terms of minimizing the makespan—the duration of the schedule— of a given finite collection of nonpreemptive jobs; however, the makespan minimization problem considered in [108] is easily shown to essentially be equivalent to the problem of partitioning implicit-deadline sporadic task systems.
- 2.
We note that this “sacrifice” is only in terms of worst-case guarantees, as formalized in Theorem 6.2. It is quite possible that some of this sacrificed capacity can in fact be used during the partitioning of particular task systems.
- 3.
Note that this argument does not hold for actual utilizations—the u i in the figure—less than \(\varepsilon/(1+\varepsilon)\). If a task with utilization u i arbitrarily close to zero (\(u_i\rightarrow 0^+\)) were to have its utilization rounded up to \(\varepsilon/(1+\varepsilon)\), the inflation factor would be \((\varepsilon/(1+\varepsilon)) \div u_i\), which approaches ∞ as \(u_i\rightarrow 0\). We will see—Step 3 of the pseudo-code listed in Fig. 6.1—that our task-assignment procedure handles tasks with utilization \(<\varepsilon/(1+\varepsilon)\) differently.
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The \(\textsf{EDF}\) utilization bounds described in this chapter are to be found in Lopez et al. [141, 142]; the speedup bounds are from [32]. The PTAS described in Sect. 6.3 is from [68]; which applied the results in [108] concerning makespan minimization to come up with the LUT-based approach. Some of the FTP scheduling results are from [22].
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Baruah, S., Bertogna, M., Buttazzo, G. (2015). Partitioned Scheduling of L&L Tasks. In: Multiprocessor Scheduling for Real-Time Systems. Embedded Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-08696-5_6
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DOI: https://doi.org/10.1007/978-3-319-08696-5_6
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