Real-Time Systems

, Volume 46, Issue 3, pp 332–359 | Cite as

LRE-TL: an optimal multiprocessor algorithm for sporadic task sets with unconstrained deadlines

  • Shelby FunkEmail author


This article presents a detailed discussion of LRE-TL (Local Remaining Execution-TL-plane), an algorithm that schedules hard real-time periodic and sporadic task sets with unconstrained deadlines on identical multiprocessors. The algorithm builds upon important concepts such as the TL-plane construct used in the development of the LLREF algorithm (Largest Local Remaining Execution First). This article identifies the fundamental TL-plane scheduling principles used in the construction of LLREF . These simple principles are examined, identifying methods of simplifying the algorithm and allowing it to handle a more general task model. For example, we identify the principle that total local utilization can never increase within any TL-plane as long as a minimal number of tasks are executing. This observation leads to a straightforward approach for scheduling task arrivals within a TL-plane. In this manner LRE-TL can schedule sporadic tasks and tasks with unconstrained deadlines. Like LLREF, the LRE-TL scheduling algorithm is optimal for task sets with implicit deadlines. In addition, LRE-TL can schedule task sets with unconstrained deadlines provided they satisfy the density test for multiprocessor systems. While LLREF has a O(n 2) runtime per TL-plane, LRE-TL’s runtime is O(nlog n) per TL-plane.


Multiprocessor scheduling Hard real-time systems Periodic tasks Sporadic tasks Unconstrained deadlines 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Baker T (2003) Multiprocessor EDF and deadline monotonic schedulability analysis. In: 24th real-time systems symposium Google Scholar
  2. Baker T (2005) An analysis of EDF schedulability on a multiprocessor. IEEE Trans Parallel Distrib Syst 16(8):760–768 CrossRefGoogle Scholar
  3. Baruah SK, Cohen N, Plaxton CG, Varvel D (1996) Proportionate progress: a notion of fairness in resource allocation. Algorithmica 15(6):600–625 zbMATHCrossRefMathSciNetGoogle Scholar
  4. Chen SY, Hsueh CW (2008) Optimal dynamic-priority real-time scheduling algorithms for uniform multiprocessors. In: Proceedings of the 2008 real-time systems symposium, pp 147–156 CrossRefGoogle Scholar
  5. Cho H, Ravindran B, Jensen ED (2006) An optimal real-time scheduling algorithm for multiprocessors. In: Proceedings the 27th IEEE real-time system symposium (RTSS). IEEE Comput. Sci., Los Alamitos, pp 101–110 Google Scholar
  6. Cirinei M, Baker T (2007) EDZL scheduling analysis. In: Euromicro conference on real-time systems. ECRTS, pp 9–18. Google Scholar
  7. Davari S, Dhall SK (1985) On a real-time task allocation problem. In: Proceedings of the international conference on system science, pp 133–141 Google Scholar
  8. Dertouzos M (1974) Control robotics: the procedural control of physical processors. In: Proceedings of the IFIP congress, pp 807–813 Google Scholar
  9. Dertouzos M, Mok AK (1989) Multiprocessor scheduling in a hard real-time environment. IEEE Trans Softw Eng 15(12):1497–1506 CrossRefGoogle Scholar
  10. Devi UC, Anderson JH (2010) A schedulable utilization bound for the multiprocessor pfair algorithm. Real-Time Syst 38(3):237–288 CrossRefGoogle Scholar
  11. Fisher N, Goossens J, Baruah S (2010) Optimal online multiprocessor scheduling of sporadic real-time tasks is impossible. Real-Time Syst 45(1):26–71 zbMATHCrossRefGoogle Scholar
  12. Funk S, Nadadur V (2009) LRE-TL: An optimal multiprocessor algorithm for sporadic task sets. In: International conference on real-time and network systems (RTNS), Paris, France, pp 159–168 Google Scholar
  13. Hong KS, Leung JYT (1988) On-line scheduling of real-time tasks. In: Proceedings of the real-time systems symposium, pp 244–250 CrossRefGoogle Scholar
  14. Hong KS, Leung JYT (1992) On-line scheduling of real-time tasks. IEEE Trans Comput 41(10):1326–1331 CrossRefGoogle Scholar
  15. Kato S, Yamasaki N, Ishikawa Y (2009) Semi-partitioned scheduling of sporadic task systems on multiprocessors. In: Euromicro Conference onReal-Time Systems (ECRTS), Ireland, Dublin, pp 249–258 CrossRefGoogle Scholar
  16. Liu CL, Layland JW (1973) Scheduling algorithms for multiprogramming in a hard real-time environment. J ACM 20(1):46–61 zbMATHCrossRefMathSciNetGoogle Scholar
  17. Phillips CA, Stein C, Torng E, Wein J (1997) Optimal time-critical scheduling via resource augmentation. In: Proceedings of the twenty-ninth annual acm symposium on theory of computing. El Paso, Texas, pp 140–149 CrossRefGoogle Scholar
  18. Srinivasan A, Anderson JH (2005) Fair scheduling of dynamic task systems on multiprocessors. J Syst Softw 77(1):67–80 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.University of GeorgiaAthensUSA

Personalised recommendations