Cluster Computing

, Volume 13, Issue 1, pp 31–46 | Cite as

PPDD: scheduling multi-site divisible loads in single-level tree networks

  • Xiaolin Li
  • Bharadwaj Veeravalli


This paper investigates scheduling strategies for divisible jobs/loads originating from multiple sites in hierarchical networks with heterogeneous processors and communication channels. In contrast, most previous work in the divisible load scheduling theory (DLT) literature mainly addressed scheduling problems with loads originating from a single processor. This is one of the first works that address scheduling multiple loads from multiple sites in the DLT paradigm. In addition, scheduling multi-site jobs is common in Grids and other general distributed systems for resource sharing and coordination. An efficient static scheduling algorithm PPDD (Processor-set Partitioning and Data Distribution Algorithm) is proposed to near-optimally distribute multiple loads among all processors so that the overall processing time of all jobs is minimized. The PPDD algorithm is applied to two cases: when processors are equipped with front-ends and when they are not equipped with front-ends. The application of the algorithm to homogeneous systems is also studied. Further, several important properties exhibited by the PPDD algorithm are proven through lemmas. To implement the PPDD algorithm, we propose a communication strategy. In addition, we compare the performance of the PPDD algorithm with a Round-robin Scheduling Algorithm (RSA), which is most commonly used. Extensive case studies through numerical analysis have been conducted to verify the theoretical findings.


Divisible load theory Heterogeneous computing Load scheduling Grid computing Single-level tree networks 


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  1. 1.
    Kesselman, C., Foster, I. (eds.): The Grid 2: Blueprint for a New Computing Infrastructure by. Morgan Kaufmann, San Mateo (2003) Google Scholar
  2. 2.
    Hennessy, J., Patterson, D.: Computer Architecture: A Quantitative Approach, 4th edn. Morgan Kaufmann, San Mateo (2006) zbMATHGoogle Scholar
  3. 3.
    Xu, K., Hwang, Z.: Scalable Parallel Computing: Technology, Architecture, Programming. McGraw-Hill, New York (1998) zbMATHGoogle Scholar
  4. 4.
    Eshaghian, M. (ed.): Heterogeneous Computing. Artech House, Norwood (1996) Google Scholar
  5. 5.
    Drozdowski, M.: Selected Problems of Scheduling Tasks in Multiprocessor Computer Systems. University of Technology Press, Poznan (1997) Google Scholar
  6. 6.
    Veeravalli, B., Ghose, D., Mani, V., Robertazzi, T. (eds.): Scheduling Divisible Loads in Parallel and Distributed Systems. IEEE Computer Society Press, Los Alamitos, (1996) Google Scholar
  7. 7.
    Shirazi, B., Hurson, A., Kavi, K. (eds.): Scheduling and Load Balancing in Parallel and Distributed Systems. IEEE Computer Society Press, Los Alamitos (1995) Google Scholar
  8. 8.
    Veeravalli, B., Ghose, D., Robertazzi, T.: Divisible load theory: a new paradigm for load scheduling in distributed systems. Clust. Comput. Div. Load Sched. 6(1), 7–18 (2003). Special Issue Google Scholar
  9. 9.
    Robertazzi, T., Sohn, J.: Optimal time-varying load sharing divisible jobs. IEEE Trans. Aerospace Electronic Syst. 34, 907–923 (1998) CrossRefGoogle Scholar
  10. 10.
    Sohn, J., Robertazzi, T., Luryi, S.: Optimizing computing costs using divisible load analysis. IEEE Trans. Parallel Distrib. Syst. 9(3), 225–234 (1998) CrossRefGoogle Scholar
  11. 11.
    Marchal, L., Yang, Y., Casanova, H., Robert, Y.: A realistic network/application model for scheduling divisible loads on large-scale platforms. In: International Parallel and Distributed Processing Symposium (IPDPS 2005), 2005 Google Scholar
  12. 12.
    Viswanathan, S., Veeravalli, B., Yu, D., Robertazzi, T.: Design and analysis of a dynamic scheduling strategy with resource estimation for large-scale grid systems. In: Proceedings of the 5th IEEE/ACM International Workshop on Grid Computing (held in conjunction with Supercomputing 2004), Pittsburgh, Pennsylvania, USA, Nov. 2004, pp. 163–171 Google Scholar
  13. 13.
    Li, X., Veeravalli, B., Ko, C.: Distributed image processing on a network of workstations. Int. J. Comput. Appl. 25(2), 1–10 (2003) zbMATHGoogle Scholar
  14. 14.
    Veeravalli, B., Ghose, D., Robertazzi, T.: A new paradigm for load scheduling in distributed systems. Divisible Load Sched. Clust. Comput. 6(1), 7–18 (2003). Special issue Google Scholar
  15. 15.
    Robertazzi, T.: Ten reasons to use divisible load theory. IEEE Comput. 36(5), 63–68 (2003) Google Scholar
  16. 16.
    Ghose, D., Kim, H.J.: Load partitioning and trade-off study for large matrix-vector computations in multicast bus networks with communication delays. J. Parallel Distrib. Comput. 55(1), 32–59 (1998) zbMATHCrossRefGoogle Scholar
  17. 17.
    Veeravalli, B., Barlas, G.: Efficient scheduling strategies for processing multiple divisible loads on bus networks. J. Parallel Distrib. Comput. 62(1), 132–151 (2002) zbMATHCrossRefGoogle Scholar
  18. 18.
    Wong, H., Veeravalli, B.: Scheduling divisible loads on heterogeneous linear daisy chain networks with arbitrary processor release times. IEEE Trans. Parallel Distrib. Syst. 15(3), 273–288 (2005) Google Scholar
  19. 19.
    Drozdowski, M., Blazewicz, J.: Distributed processing of divisible jobs with communication startup costs. Discrete Appl. Math. 76(1–3), (1997) Google Scholar
  20. 20.
    Veeravalli, B., Li, X., Ko, C.C.: On the influence of start-up costs in scheduling divisible loads on bus networks. IEEE Trans. Parallel Distrib. Syst. 11(12), 1288–1305 (2000) CrossRefGoogle Scholar
  21. 21.
    Li, X., Veeravalli, B., Ko, C.: Divisible load scheduling on single-level tree networks with buffer constraints. IEEE Trans. Aerospace Electronic Syst. 36(4), 1298–1308 (2000) CrossRefGoogle Scholar
  22. 22.
    Chan, S., Veeravalli, B., Ghose, D.: Large matrix-vector products on distributed bus networks with communication delays using the divisible load paradigm: Performance analysis and simulation. Math. Comput. Simul. 58, 71–79 (2001) zbMATHCrossRefGoogle Scholar
  23. 23.
    Wolniewicz, P., Drozdowski, M.: Experiments with scheduling divisible tasks in clusters of workstations. In: Proceedings of the Parallel Processing, 6th International Euro-Par Conference, Munich, Germany, August 2000, pp. 311–319 Google Scholar
  24. 24.
    Ghose, D., Kim, H.J., Kim, T.H.: Adaptive divisible load scheduling strategies for workstation clusters with unknown network resources. IEEE Trans. Parallel Distrib. Syst. 16(10), 897–907 (2005) CrossRefGoogle Scholar
  25. 25.
    Beaumont, O., Casanova, H., Legrand, A., Robert, Y., Yang, Y.: Scheduling divisible loads on star and tree networks: results and open problems. IEEE Trans. Parallel Distrib. Syst. 16(3), 207–218 (2005) CrossRefGoogle Scholar
  26. 26.
    Min, W.H., Veeravalli, B.: Aligning biological sequences on distributed bus networks: a divisible load scheduling approach. IEEE Trans. Inf. Technol. Biomed. 9(4), 489–501 (2005) CrossRefGoogle Scholar
  27. 27.
    Yao, J., Guo, J., Bhuyan, L., Xu, Z.: Scheduling real-time multimedia tasks in network processors. In: IEEE Global Telecommunications Conference (GLOBECOM’04), vol. 3, 2004 Google Scholar
  28. 28.
    Li, X., Cao, J.: Coordinated workload scheduling in hierarchical sensor networks for data fusion applications. J. Comput. Sci. Technol. 23(3), 355–364 (2008) CrossRefGoogle Scholar
  29. 29.
    Moges, M., Robertazzi, T.G.: Wireless sensor networks: scheduling for measurement and data reporting. IEEE Trans. Aerospace Electronic Syst. 42(1), 327–340 (2006) CrossRefGoogle Scholar
  30. 30.
    Carroll, T.E., Grosu, D.: A strategyproof mechanism for scheduling divisible loads in tree networks. In: Proc. of the 20th IEEE Intl. Parallel and Distributed Processing Symp. (IPDPS 2006), 2006 Google Scholar
  31. 31.
    Carroll, T.E., Grosu, D.: Strategyproof mechanisms for scheduling divisible loads in Bus-Networked distributed systems. IEEE Trans. Parallel Distrib. Syst. 19(8), 1124–1135 (2008) CrossRefGoogle Scholar
  32. 32.
    Robertazzi, T., Sohn, J.: A multi-job load sharing strategy for divisible jobs on bus networks. In: Proceedings of the Conference on Information Sciences and Systems, Princeton, NJ, March 1994 Google Scholar
  33. 33.
    Veeravalli, B., Yao, J.: Design and performance analysis of divisible load scheduling strategies on arbitrary graphs. Clust. Comput. 7(2), 841–865 (2004) Google Scholar
  34. 34.
    Haddad, E.: Real-time optimization of distributed load balancing. In: Proceedings of the Second Workshop on Parallel and Distributed Real-Time Systems, 1994, pp. 52–57 Google Scholar
  35. 35.
    Robertazzi, T., Lammie, T.: A linear daisy chain with two divisible load sources. In: 2005 Conference on Information Sciences and Systems, The Johns Hopkins University, Baltimore, Maryland, March 2005 Google Scholar
  36. 36.
    Wong, H.M., Yu, D., Veeravalli, B., Robertazzi, T.: Data intensive grid scheduling: multiple sources with capacity constraints. In: Fifteenth IASTED International Conference on Parallel and Distributed Computing and Systems, vol. 1, 2003, pp. 7–11 Google Scholar
  37. 37.
    Chervenak, A., Foster, I., Kesselman, C., Salisbury, C., Tuecke, S.: The data grid: Towards an architecture for the distributed management and analysis of arge scientific datasets. J. Netw. Comput. Appl. 23, 187–200 (2001) CrossRefGoogle Scholar
  38. 38.
    Shivaratri, N., Krueger, P., Singhal, M.: Load distributing for locally distributed systems. Computer 25(12), 33–44 (1992) CrossRefGoogle Scholar
  39. 39.
    Gallager, D., Bertsekas, R. (eds.): Data Networks, 2nd edn. Prentice Hall, New York (1992) zbMATHGoogle Scholar
  40. 40.
    Luszczek, P., Dongarra, J.: Introduction to the hpcchallenge benchmark suite. University of Tennessee, Tech. Rep. ICL-UT-05-01 (2005) Google Scholar
  41. 41.
    Lee, C., Hamdi, M.: Parallel image processing applications on a network of workstations. Parallel Comput. 21, 137–160 (1995) zbMATHCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Computer Science DepartmentOklahoma State UniversityStillwaterUSA
  2. 2.Department of Electrical and Computer EngineeringThe National University of SingaporeSingaporeRepublic of Singapore

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