Multiprocessor Task Scheduling with Probabilistic Task Duration

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System Dependability - Theory and Applications (DepCoS-RELCOMEX 2024)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 1026))

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Abstract

Article concentrate on so-called multiprocessor task scheduling problem with uncertain (random) time of tasks duration. Multiprocessor scheduling can be perceived as a tool for improving dependability of the system by hardware and software redundancy. Our overall aim is develop more precise description of various configuration of embedded systems). Our aim is to evaluate the model of task duration distribution on the result of scheduling. We compare two models of the task: normal distribution and Erlang distribution. The latter model is considered as more suitable for multiprocessor scheduling, which reflects more accurately reality. We use MVA (Mean Value Analysis) methodology in the research with the application of modified Muntz-Coffman algorithm. The article is an extension of previous research of the author, considering uncertain task duration in different models. Computational experiments compared results obtained for both distributions in this stochastic model.

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References

  1. Behnamian, J.: Survey on fuzzy shop scheduling. Fuzzy Optim. Decis. Making 15(3), 331–366 (2016)

    Article  MathSciNet  Google Scholar 

  2. Behnamian, J., Fatemi Ghomi, S.: A survey of multi-factory scheduling. J. Intell. Manuf. 27, 231–249 (2016)

    Article  Google Scholar 

  3. Blazewicz, J., Drabowski, M., Weglarz, J.: Scheduling multiprocessor tasks to minimize schedule length. IEEE Trans. Comput. 5, 389–393 (1986)

    Article  MathSciNet  Google Scholar 

  4. Błażewicz, J., Drozdowski, M., Ecker, K.: Management of resources in parallel systems. In: Błażewicz, J., Ecker, K., Plateau, B., Trystram, D. (eds.) Handbook on Parallel and Distributed Processing, pp. 263–341. Springer, Heidelberg (2000). https://doi.org/10.1007/978-3-662-04303-5_6

    Chapter  Google Scholar 

  5. Blazewicz, J., et al.: Communication delays and multiprocessor tasks. In: Handbook on Scheduling: From Theory to Practice, pp. 199–241 (2019)

    Google Scholar 

  6. Błażewicz, J., Liu, Z.: Scheduling multiprocessor tasks with chain constraints. Eur. J. Oper. Res. 94(2), 231–241 (1996)

    Article  Google Scholar 

  7. Bozejko, W., Hejducki, Z., Wodecki, M.: Flowshop scheduling of construction processes with uncertain parameters. Arch. Civil Mech. Eng. 19(1), 194–204 (2019)

    Article  Google Scholar 

  8. Bozejko, W., Hejducki, Z., Wodecki, M.: Flowshop scheduling of construction processes with uncertain parameters. Arch. Civil Mech. Eng. 19, 194–204 (2019)

    Article  Google Scholar 

  9. Caplan, J., Al-Bayati, Z., Zeng, H., Meyer, B.H.: Map** and scheduling mixed-criticality systems with on-demand redundancy. IEEE Trans. Comput. 67(4), 582–588 (2017)

    Article  MathSciNet  Google Scholar 

  10. Chin, M.K., Kek, S.L., Sim, S.Y., Seow, T.W.: Probabilistic completion time in project scheduling. Int. J. Eng. Res. Sci. 3(4), 44–48 (2017)

    Google Scholar 

  11. Davis, R.I., Cucu-Grosjean, L.: A survey of probabilistic timing analysis techniques for real-time systems. LITES: Leibniz Trans. Embed. Syst. 1–60 (2019)

    Google Scholar 

  12. Dorota, D.P.: Szeregowanie zadań wieloprocesorowych w warunkach niepewności (2023)

    Google Scholar 

  13. Drozdowski, M.: On the complexity of multiprocessor task scheduling. Bull. Polish Acad. Sci. Techn. Sci. 43(3), 1–12 (1995)

    Google Scholar 

  14. Drozdowski, M.: Scheduling multiprocessor tasks-an overview. Eur. J. Oper. Res. 94(2), 215–230 (1996)

    Article  MathSciNet  Google Scholar 

  15. Drozdowski, M.: Scheduling for Parallel Processing. Springer, London (2009). https://doi.org/10.1007/978-1-84882-310-5

    Book  Google Scholar 

  16. Graham, R.L., Lawler, E.L., Lenstra, J.K., Kan, A.R.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Disc. Math. 5, 287–326 (1979)

    Article  MathSciNet  Google Scholar 

  17. Ibrahim, H., Salih, M.H.: Design and implementation of embedded true parallelism jammer system using FPGA-SOC for low design complexity. ARPN J. Eng. Appl. Sci. 13(24), 9410–9420 (2018)

    Google Scholar 

  18. Jiang, X., Lee, K., Pinedo, M.L.: Ideal schedules in parallel machine settings. Eur. J. Oper. Res. 290(2), 422–434 (2021)

    Article  MathSciNet  Google Scholar 

  19. Mao, H., Chen, Y., Jaeger, M., Nielsen, T.D., Larsen, K.G., Nielsen, B.: Learning deterministic probabilistic automata from a model checking perspective. Mach. Learn. 105, 255–299 (2016)

    Article  MathSciNet  Google Scholar 

  20. Maxim, D., Davis, R.I., Cucu-Grosjean, L., Easwaran, A.: Probabilistic analysis for mixed criticality systems using fixed priority preemptive scheduling. In: Proceedings of the 25th International Conference on Real-Time Networks and Systems, pp. 237–246 (2017)

    Google Scholar 

  21. Miedema, L., Rouxel, B., Grelck, C.: Task-level redundancy vs instruction-level redundancy against single event upsets in real-time dag scheduling. In: 2021 IEEE 14th International Symposium on Embedded Multicore/Many-core Systems-on-Chip (MCSoC), pp. 373–380. IEEE (2021)

    Google Scholar 

  22. Moselhi, O., Lorterapong, P.: Fuzzy vs probabilistic scheduling. In: Proceedings of the 12th Conference “Automation and Robotics in Construction" (ISARC), pp. 441–448 (1995)

    Google Scholar 

  23. Ning, C., You, F.: Optimization under uncertainty in the era of big data and deep learning: when machine learning meets mathematical programming. Comput. Chem. Eng. 125, 434–448 (2019)

    Article  Google Scholar 

  24. Pathan, R.M.: Real-time scheduling algorithm for safety-critical systems on faulty multicore environments. Real-Time Syst. 53, 45–81 (2017)

    Article  Google Scholar 

  25. Pinedo, M.: Scheduling. Springer, New York (2015). https://doi.org/10.1007/978-3-319-26580-3

    Book  Google Scholar 

  26. Raj, M.D., Gogul, I., Thangaraja, M., Kumar, V.S.: Static gesture recognition based precise positioning of 5-dof robotic arm using FPGA. In: 2017 Trends in Industrial Measurement and Automation (TIMA), pp. 1–6. IEEE (2017)

    Google Scholar 

  27. Saint-Guillain, M., Vaquero, T., Chien, S., Agrawal, J., Abrahams, J.: Probabilistic temporal networks with ordinary distributions: theory, robustness and expected utility. J. Artif. Intell. Res. 71, 1091–1136 (2021)

    Article  MathSciNet  Google Scholar 

  28. Santinelli, L., Cucu-Grosjean, L.: A probabilistic calculus for probabilistic real-time systems. ACM Trans. Embed. Comput. Syst. (TECS) 14(3), 1–30 (2015)

    Article  Google Scholar 

  29. Shoval, S., Efatmaneshnik, M.: A probabilistic approach to the stochastic job-shop scheduling problem. Procedia Manuf. 21, 533–540 (2018)

    Article  Google Scholar 

  30. Sriram, S., Bhattacharyya, S.S.: Embedded Multiprocessors: Scheduling and Synchronization. CRC Press, Boca Raton (2018)

    Book  Google Scholar 

  31. Terekhov, D., Down, D.G., Beck, J.C.: Queueing-theoretic approaches for dynamic scheduling: a survey. Surv. Oper. Res. Manag. Sci. 19(2), 105–129 (2014)

    MathSciNet  Google Scholar 

  32. **n, X., Mou, M., Mu, G.: A polynomially solvable case of scheduling multiprocessor tasks in a multi-machine environment. In: 2017 2nd International Conference on Materials Science, Machinery and Energy Engineering (MSMEE 2017), pp. 1746–1749. Atlantis Press (2017)

    Google Scholar 

  33. Xu, M., Kashyap, S., Zhao, H., Kim, T.: Krace: data race fuzzing for kernel file systems. In: 2020 IEEE Symposium on Security and Privacy (SP), pp. 1643–1660. IEEE (2020)

    Google Scholar 

  34. Ye, D., Chen, D.Z., Zhang, G.: Online scheduling of moldable parallel tasks. J. Sched. 21(6), 647–654 (2018)

    Article  MathSciNet  Google Scholar 

  35. Zahid, Y., Khurshid, H., Memon, Z.A.: On improving efficiency and utilization of last level cache in multicore systems. Inf. Technol. Control 47(3), 588–607 (2018)

    Google Scholar 

  36. Zhao, L., Ren, Y., Sakurai, K.: Reliable workflow scheduling with less resource redundancy. Parallel Comput. 39(10), 567–585 (2013)

    Article  MathSciNet  Google Scholar 

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Correspondence to Dariusz Dorota .

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Dorota, D. (2024). Multiprocessor Task Scheduling with Probabilistic Task Duration. In: Zamojski, W., Mazurkiewicz, J., Sugier, J., Walkowiak, T., Kacprzyk, J. (eds) System Dependability - Theory and Applications. DepCoS-RELCOMEX 2024. Lecture Notes in Networks and Systems, vol 1026. Springer, Cham. https://doi.org/10.1007/978-3-031-61857-4_5

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