Abstract
Pfair scheduling is characterized by the fact that tasks are explicitly required to make progress at steady rates. Consider a task in which both the parameters Ci and Ti are positive integers, and suppose that a job of this task is released at time-instant to. In a pfair schedule, scheduling decisions are made at integer time boundaries; hence, jobs are scheduled for execution an integer unit at a time (to, too, is assumed to be an integer).
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- 1.
Here is an informal description of the technique; for further detail, please see [79, p. 116]. Let δ denote an arbitrarily small positive real number, and \([t,t+\delta]\) a time interval during which the processor shares assigned to the tasks do not change. Each task τ i that is active during this interval needs to execute for an amount \(u_i\cdot\delta\). Considering the tasks sequentially in any order, we simply begin assigning them to the first processor starting at time-instant t until we have reached time-instant \(t+\delta\), at which point we would “wrap around” and proceed to the next processor beginning again at time-instant t, and so on until all the tasks have been assigned. If a task has only been assigned a part of its execution requirement upon a processor, we assign it the remainder of its execution requirement upon the next processor: the fact that \(u_i \le 1\) for each task guarantees that the allocation to a task upon two consecutive processors will not overlap in time.
- 2.
Actually, the potentially tighter bound of \(\min(C_i/\text{gcd}(C_i,T_i), C_j/\text{gcd}(C_j,T_j))\) on the number of comparisons is easily seen to hold.
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© 2015 Springer International Publishing Switzerland
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Baruah, S., Bertogna, M., Buttazzo, G. (2015). Global Dynamic-Priority 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_7
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DOI: https://doi.org/10.1007/978-3-319-08696-5_7
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