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Learning and backtracking in non-preemptive scheduling of tasks under timing constraints

Special issue on machine learning and cybernetics

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Abstract

We propose two novel heuristic search techniques to address the problem of scheduling tasks under hard timing constraints on a single processor architecture. The underlying problem is NP-hard in the strong sense and it is a fundamental challenge in feedback-control theory and automated cybernetics. The proposed techniques are a learning-based approaches and they take much less memory space. A partial feasible schedule is maintained and extended over a repeated problem solving trials, previously assigned priorities are refined according to the gained information about the problem to lead the convergence to a complete feasible schedule if one exists. First, we present the learning in hard-real-time with single learning (LHRTS-SL) algorithm where a single learning function is utilized, then we discuss its drawback and we propose the LHRTS with double learning algorithm in which a second learning function is integrated to cope up with LHRTS-SL drawback. Experimental results show the efficiency of the proposed techniques in terms of success ratio when used to schedule randomly generated problem instances.

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Notes

  1. It is assumed that there is no data dependencies between invocations of different tasks.

  2. we mean by urgent tasks that should be selected earlier.

  3. We mean by sound an algorithm which is able to find an existing feasible schedule.

  4. Supposed that tie situations are broken non-randomly.

  5. In the remainder of the paper we use g max set to lcm.

  6. To avoid the exponential time needed to schedule all task sets in dset1 and dset2 using the exhaustive method DFS, we added a time out to this algorithm to carry out an unknown decision about the input task set after that time. Further details are presented in Appendix.

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Authors and Affiliations

  1. National Computer Science School, 16309 Oued-Smar, Algiers, Algeria

    Yacine Laalaoui & Habiba Drias

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  1. Yacine Laalaoui
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  2. Habiba Drias
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Correspondence to Yacine Laalaoui.

Appendix

Appendix

  • dsets1 is a set of 5,000 task sets taken from the workload interval [0.5,1]. This interval is divided into 10 sub-intervals where each sub-interval includes 500 task sets. The minimum and the maximum task set sizes after dealing with the system periodicity are 4 and 33 tasks, respectively. The number of used lcms are three where each lcm is a set of three to five periods. This small number of periods were used because this parameter is related to the nature of interaction between the physical process and the control unit where, in general, a relatively small number of sensors and actuators are used. Table 8 describes the used periods and lcms. The minimum and the maximum accepted lcms during the generation process are 250 and 750, respectively. To increase the probability of generating task sets that are not schedulable using EDF, the ratio between r i and P i for each task is generated using uniform distribution over [0,0.2]. Computation times are generated using uniform distribution over [0.01,0.34] to select U i and implicitly the computation time C i for a task T i . We used uniform distribution over [0.9,1] to select the ratio between D i and P i for each task.

    Table 8 The used periods and lcms in dset1
    Full size table

  • dset2 contains also 5,000 task sets generated using the same procedure as dset1 (Table 8). The minimum and the maximum task set sizes after dealing with the system periodicity are 4 and 23 tasks, respectively. The used periods and lcms are described in Table 9. The maximum and the minimum accepted lcms are 4,000 and 8,000, respectively.

    Table 9 The used periods and lcms in dset2
    Full size table
    Table 10 Number of task sets schedulable preemptively, non-preemptively and task sets with and unknown decisions
    Full size table

The DFS traversal is used as an exhaustive algorithm to compare our proposed approaches. The long time that DFS takes to schedule dset1 and dset2 motivate us to integrate a time out to this algorithm. The number of schedulable task sets in dset1 and dset2 together with the associated time out are presented in Table 10. This table shows also the number of schedulable task sets by the preemptive EDF where this heuristic is used to disregarded task sets non-schedulable preemptively and non-preemptively. The last column of the table shows the number of task sets with unknown decision about their schedulability within the specified time-out.

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Laalaoui, Y., Drias, H. Learning and backtracking in non-preemptive scheduling of tasks under timing constraints. Soft Comput 15, 1071–1086 (2011). https://doi.org/10.1007/s00500-010-0582-2

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