Journal of Grid Computing

, 4:373 | Cite as

Entropic Grid Scheduling

  • Youcef Derbal


Computational Grids (CGs) are large scale dynamical networks of geographically distributed peer resource clusters. These clusters are independent but cooperating computing systems bound by a management framework for the provision of computing services, called Grid Services. In its basic form, the Grid scheduling problem consists in finding at least one cluster that has the capacity to handle, within the constraints of a specified quality of service, a user service request submitted to the CG. Since CGs span distinct management domains, the scheduling process has to be decentralized. Furthermore, it has to account for the ubiquitous uncertainty on the state of the CG. In this paper, we propose a scalable distributed Entropy-based scheduling approach that utilizes a Markov chain model to capture the dynamics of the service capacity state. An entropy-based quantification of the uncertainty on the service capacity information is developed and explicitly integrated within the proposed Grid scheduling approach. The performance of the proposed scheduling strategy is validated, through simulation, against a random delegation scheme and a load balancing-based scheduling strategy with respect to throughput, exploitation and convergence speed, respectively.

Key words

Computational Grid Decision Making Scheduling Entropy Markov Chain 


  1. 1.
    The Economist: One Grid to rule them all. The Economist 373, 94 (2004)Google Scholar
  2. 2.
    Gustafson, J.: Program of grand challenge problems: Expectations and results. In: Aizu International Symposium on Parallel Algorithms/Architecture Synthesis, pp. 2–7 (1997)Google Scholar
  3. 3.
    Buyya, R., Branson, K., Giddy J., Abramson, D.: The Virtual Laboratory: A toolset to enable distributed molecular modelling for drug design on the world-wide Grid. Concurr. Comput. Pract. Exp. 15, 1–25 (2003)zbMATHCrossRefGoogle Scholar
  4. 4.
    Tantoso, E., Wahab, H.A., Chan, H.Y.: Molecular docking: An example of Grid enabled applications. New Gener. Comput. 22, 189–190 (2004)zbMATHCrossRefGoogle Scholar
  5. 5.
    Ahmad, I., Kwok, Y.-K.: On parallelizing the multiprocessor scheduling problem. IEEE Trans. Parallel Distrib. Syst. 10, 414–432 (1999)CrossRefGoogle Scholar
  6. 6.
    Foster, I., Kesselman, C.: The Grid: Blueprint for a New Computing Infrastructure. Elsevier Science, San Francisco (2004)Google Scholar
  7. 7.
    Casavant, T.L., Kuhl, J.G.: A taxonomy of scheduling in general-purpose distributed computing systems. IEEE Trans. Softw. Eng. 14, 141–155 (1988)CrossRefGoogle Scholar
  8. 8.
    Buyya, R.: High Performance Cluster Computing. Prentice Hall PTR, Upper Saddle River, New Jersey (1999)Google Scholar
  9. 9.
    Braun, T.D., Siegel, H.J., Beck, N., Boloni, L., Maheswaran, M., Reuther, A.I., Robertson, J.P., Theys M.D., Yao, B.: Taxonomy for describing matching and scheduling heuristics for mixed-machine heterogeneous computing systems. In: Proceedings of the IEEE Symposium on Reliable Distributed Systems, pp. 330–335, 1998Google Scholar
  10. 10.
    Al-Mouhamed, M.A.: Lower bound on the number of processors and time for scheduling precedence graphs with communication costs. IEEE Trans. Softw. Eng. 16, 1317–1322 (1990)MathSciNetCrossRefGoogle Scholar
  11. 11.
    El-Rewini, H., Lewis, T.G., Ali, H.H.: Task Scheduling in Parallel and Distributed Systems. Prentice Hall, Englewood Cliffs, New Jersey (1994)Google Scholar
  12. 12.
    Hwang, J.-J., Chow, Y.-C., Anger, F.D., Lee, C.-Y.: Scheduling precedence graphs in systems with interprocessor communication times. SIAM J. Comput. 18, 244–257 (1989)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Cosnard, M., Loi, M.: Automatic task graph generation techniques. Parallel Process. Lett. 54, 527–538 (1995)CrossRefGoogle Scholar
  14. 14.
    Kwok, Y.-K., Ahmad, I.: Benchmarking the task graph scheduling algorithms. In: Proceedings of the International Parallel Processing Symposium, IPPS, p. 531, 1998Google Scholar
  15. 15.
    Kwok, Y.-K., Ahmad, I.: Static scheduling algorithms for allocating directed task graphs to multiprocessors. ACM Comput. Surv. 31, 406–471 (1999)CrossRefGoogle Scholar
  16. 16.
    Kwok, Y.-K., Ahmad, I.: Dynamic critical-path scheduling: An effective technique for allocating task graphs to multiprocessors. IEEE Trans. Parallel Distrib. Syst. 7, 506–521 (1996)CrossRefGoogle Scholar
  17. 17.
    Ahmad, I., Kwok, Y.-K.: Parallel program scheduling techniques. In: Buyya, R. (ed.), High Performance Cluster Computing, pp. 553–578. Prentice Hall PTR, New Jersey (1999)Google Scholar
  18. 18.
    Gary, R., Johnson, D.: Computers and Intractability – A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)Google Scholar
  19. 19.
    He, X., Sun, X., Von Laszewski, G.: QoS guided Min-Min heuristic for Grid task scheduling. J. Comput. Sci. Technol. 18, 442–451 (2003)zbMATHCrossRefGoogle Scholar
  20. 20.
    Berman, F., Wolski, R., Casanova, H., Cirne, W., Dail, H., Faerman, M., Figueira, S., Hayes, J., Obertelli, G., Schopf, J., Shao, G., Smallen, S., Spring, N., Su A., Zagorodnov, D.: Adaptive computing on the Grid using AppLeS. IEEE Trans. Parallel Distrib. Syst. 14, 369–382 (2003)CrossRefGoogle Scholar
  21. 21.
    Weng, C., Lu, X.: Heuristic scheduling for bag-of-tasks applications in combination with QoS in the computational Grid. Future Gener. Comput. Syst. 21, 271–280 (2005)CrossRefGoogle Scholar
  22. 22.
    Berman, F., Casanova, H., Chien, A., Cooper, K., Dail, H., Dasgupta, A., Deng, W., Dongarra, J., Johnsson, L., Kennedy, K., Koelbel, C., Liu, B., Liu, X., Mandal, A., Marin, G., Mazina, M., Mellor-Crummey, J., Mendes, C., Olugbile, A., Patel, M., Reed, D., Shi, Z., Sievert, O., Xia, H., Yarkhan, A.: New Grid scheduling and rescheduling methods in the GrADS project. Int. J. Parallel Program. 33, 209–229 (2005)CrossRefGoogle Scholar
  23. 23.
    Nakada, H., Sato, M., Sekiguchi, S.: Design and implementations of Ninf: Towards a global computing infrastructure. Future Gener. Comput. Syst. 15, 649–658 (1999)CrossRefGoogle Scholar
  24. 24.
    Cao, J., Jarvis, S.A., Saini, S., Kerbyson, D.J., Nudd, G.R.: ARMS: An agent-based resource management system for Grid computing. Sci. Program. 10, 135–148 (2002)Google Scholar
  25. 25.
    Sun, X.-H., Wu, M.: Grid Harvest Service: A system for long-term, application-level task scheduling. In: Parallel and Distributed Processing Symposium, pp. 25–33, 2003Google Scholar
  26. 26.
    Gao, Y., Rong, H., Huang, J.Z.: Adaptive Grid job scheduling with genetic algorithms. Future Gener. Comput. Syst. 21, 151–161 (2005)CrossRefGoogle Scholar
  27. 27.
    Cao, J., Spooner, D.P., Jarvis, S.A., Nudd, G.R.: Grid load balancing using intelligent agents. Future Gener. Comput. Syst. 21, 135–149 (2005)CrossRefGoogle Scholar
  28. 28.
    Spooner, D.P., Jarvis, S.A., Cao, J., Saini, S., Nudd, G.R.: Local Grid scheduling techniques using performance prediction. IEE Proc. E 150, 87–96 (2003)Google Scholar
  29. 29.
    Yang, L., Schopf, J.M., Foster, I.: Conservative Scheduling: Using Predicted Variance to Improve Scheduling Decisions in Dynamic Environments. In: Proceedings of the 2003 ACM/IEEE conference on Supercomputing, pp. 31–47, 2003Google Scholar
  30. 30.
    Krothapalli, N., Deshmukh, A.V.: Dynamic allocation of communicating tasks in computational grids. IIE Trans. (Institute of Industrial Engineers) 36, 1037–4053 (2004)Google Scholar
  31. 31.
    Krauter, K., Buyya, R., Maheswaran, M.: A taxonomy and survey of Grid resource management systems for distributed computing. Softw. Pract. Exp. 32, 135–164 (2002)zbMATHCrossRefGoogle Scholar
  32. 32.
    Maheswaran, M., Ali, S., Siegel, H.J., Hensgen, D., Freund, R.F.: Dynamic matching and scheduling of a class of independent tasks onto heterogeneous computing systems. Proceedings of the Heterogeneous Computing Workshop, HCW, pp. 30–44, 1999Google Scholar
  33. 33.
    Hamscher, V., Schwiegelshohn, U., Streit, A., Yahyapour, R.: Evaluation of Job-Scheduling Strategies for Grid Computing. In: Proceedings of the 1st IEEE/ACM International Workshop on Grid Computing (Grid 2000), pp. 191–202, 2000Google Scholar
  34. 34.
    Adzigogov, L., Soldatos, J., Polymenakos, L.: EMPEROR: An OGSA Grid meta-scheduler based on dynamic resource predictions. Journal of Grid Computing 3, 19–37 (2005)CrossRefGoogle Scholar
  35. 35.
    Sanyal, S., Das, S.K.: MaTCH: Mapping Data-Parallel Tasks on a Heterogeneous Computing Platform Using the Cross Entropy Heuristic. In: Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium, pp. 64–74, 2005Google Scholar
  36. 36.
    Casanova, H., Bartol, T.M., Stiles, J., Berman, F.: Distributing MCell simulations on the Grid. Int. J. High Perform. Comput. Appl. 15, 243–257 (2001)CrossRefGoogle Scholar
  37. 37.
    Yang, L., Foster, I., Schopf, J.M.: Homeostatic and Tendency-based CPU Load Predictions. In: Procedings of the Parallel and Distributed Processing Symposium, 2003Google Scholar
  38. 38.
    He, L., Jarvis, S.A., Spooner, D.P., Chen, X., Nudd, G.R.: Hybrid performance-based workload management for multiclusters and grids. IEE Proc. Softw. 151, 224–231 (2004)CrossRefGoogle Scholar
  39. 39.
    Goldman, A., Queiroz, C.: A model for parallel job scheduling on dynamical computer Grids. Concurr. Comput. Pract. Exp. 16, 461–468 (2004)CrossRefGoogle Scholar
  40. 40.
    Abramson, D., Buyya, R., Giddy, J.: A computational economy for Grid computing and its implementation in the Nimrod-G resource broker. Future Gener. Comput. Syst. 18, 1061–1074 (2002)zbMATHGoogle Scholar
  41. 41.
    Chunlin, L., Layuan, L.: A distributed utility-based two level market solution for optimal resource scheduling in computational Grid. Parallel Comput. 31, 332–351 (2005)CrossRefGoogle Scholar
  42. 42.
    Buyya, R., Abramson, D., Venugopal, S.: The Grid economy. Proc. IEEE 93, 698–714 (2005)CrossRefGoogle Scholar
  43. 43.
    Buyya, R., Abramson, D., Giddy, J., Stockinger, H.: Economic models for resource management and scheduling in Grid computing. Concurr. Comput. Pract. Exp. 14, 1507–1542 (2002)zbMATHCrossRefGoogle Scholar
  44. 44.
    Czajkowski, K., Foster, I., Kesselman, C.: Agreement-based resource management. Proc. IEEE 93, 631–643 (2005)CrossRefGoogle Scholar
  45. 45.
    Smith, W., Foster, I., Taylor, V.: Scheduling with advanced reservations. Proceedings of the International Parallel Processing Symposium, IPPS, pp. 127–132, 2000Google Scholar
  46. 46.
    McGough, A.S., Afzal, A., Darlington, J., Furmento, N., Mayer, A., Young, L.: Making the Grid predictable through reservations and performance modelling. Comput. J. 48, 358–368 (2005)CrossRefGoogle Scholar
  47. 47.
    Czajkowski, K., Fitzgerald, S., Foster, I., Kesselman, C.: Grid information services for distributed resource sharing. In: IEEE International Symposium on High Performance Distributed Computing, Proceedings,pp. 181–194, 2001Google Scholar
  48. 48.
    Tuecke, S., Czajkowski, K., Foster, I., Frey, J., Graham, S., Kesselman, C., Maquire, T., Sandholm, T., Snelling D., Vanderbilt, P.: Open Grid Services Infrastructure (OGSI), Global Grid Forum (2003)Google Scholar
  49. 49.
    Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the Internet topology. Comput. Commun. Rev. 29, 251–262 (1999)CrossRefGoogle Scholar
  50. 50.
    Barabási, A., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)MathSciNetCrossRefGoogle Scholar
  51. 51.
    Al-Ali, R., Hafid, A., Rana, O., Walker, D.: An approach for quality of service adaptation in service-oriented Grids. Concurr. Comput. Pract. Exp. 16, 401–412 (2004)CrossRefGoogle Scholar
  52. 52.
    Singh, M.P., Huhns, M.N.: Service-Oriented Computing: Semantics, Processes, Agents. Wiley (2005)Google Scholar
  53. 53.
    Derbal, Y.: Service oriented Grid resource modeling and management. In: Proceedings of the 1st International Conference on Web Information Systems and Technologies (WEBIST 2005), Miami, Florida, pp. 146–153, 2005Google Scholar
  54. 54.
    Ross, S.M.: Introduction to Probability Models. Academic, San Diego, California (1989)zbMATHGoogle Scholar
  55. 55.
    Zhang, X., Schopf, J.M.: Performance analysis of the globus toolkit monitoring and discovery service, MDS2. In: Proceedins of the IEEE International Performance, Computing and Communications Conference, pp. 843–849, 2004Google Scholar
  56. 56.
    Fast, J.D.: Entropy. The Significance of the Concept of Entropy and its Applications in Science and Technology. [Translated by M.E. Mulder-Woolcock]. Macmillan, [London] (1970)Google Scholar
  57. 57.
    Saridis, G.N.: Analytic formulation of the principle of increasing precision with decreasing intelligence for intelligent machines. Automatica 25, 461–467 (1989)zbMATHCrossRefGoogle Scholar
  58. 58.
    Shannon, C.E., Weaver, W.: The mathematical theory of communication. University of Chicago, Urbana (1978)zbMATHGoogle Scholar
  59. 59.
    Saridis, G.N.: Entropy formulation of optimal and adaptive control. IEEE Trans. Automat. Contr. 33, 713–721 (1988)zbMATHMathSciNetCrossRefGoogle Scholar
  60. 60.
    Conant, R.C.: Laws of information which govern systems. IEEE Trans. Syst. Man Cybern. SMC-6, 240–255 (1976)MathSciNetGoogle Scholar
  61. 61.
    Gray, J.: Distributed Computing Economics. Microsoft Research (2003)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.School of Information Technology ManagementRyerson UniversityTorontoCanada

Personalised recommendations