The Journal of Supercomputing

, Volume 59, Issue 1, pp 469–485 | Cite as

Task dispatching approach to reduce the number of waiting tasks in grid environments

Article

Abstract

In this paper, a mathematical solution for reducing the mean number of the tasks waiting to be processed in a grid environment is proposed. The approach uses queuing theory and models the grid environment in the form of an open queuing network (QN). Applying the steady state analysis to the proposed QN and minimizing the mean number of waiting tasks within the grid environment, an equality and inequality system is obtained. Solving the equality and inequality system, subtasks arrival rates at each of the resources within the grid environment can be estimated. Applying the obtained subtasks arrival rates at each of the grid resources, the mean number of the waiting tasks in the grid environment could be minimized.

To evaluate the results obtained from the proposed QN and provide a graphical representation of the grid environment a formal description of the environment in terms of generalized stochastic Petri nets (GSPNs) is presented. Steady state analyzing of the GSPN model and finding the subtask dispatching weights at each of the grid resources, subtask arrival rates can be estimated. Comparing the results obtained from two proposed approaches shows that the subtasks arrival rates achieved from QNs and GSPNs are the same.

Keywords

Grid environment Waiting tasks Queuing networks Generalize stochastic Petri nets 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Foster I, Kesselman C (2003) The grid 2: blueprint for a new computing infrastructure. Morgan-Kauffman, San Mateo Google Scholar
  2. 2.
    Wang L, Jie W, Chen J (2009) Grid computing: infrastructure, service and applications. CRC Press/Taylor & Francis, Boca Raton CrossRefGoogle Scholar
  3. 3.
    Hsu Ch-H, Chen T-L, Li K-Ch (2007) Performance effective pre-scheduled strategy for heterogeneous grid systems in the master slave paradigm. J Future Gener Comput Syst 23:569–579 CrossRefGoogle Scholar
  4. 4.
    Kalantari M, Akbari MK (2008) Fault-aware grid scheduling using performance prediction by workload modeling. J Supercomput 46:15–39 CrossRefGoogle Scholar
  5. 5.
    Dai YS, Levitin G (2006) Reliability and performance of tree-structured grid services. IEEE Trans Reliab 55(2) Google Scholar
  6. 6.
    Levitin G, Dai YS, Ben-Haim H (2006) Reliability and performance of star topology grid service with precedence constraints on subtask execution. IEEE Trans Reliab 55(3) Google Scholar
  7. 7.
    He X, Sun X-He, Laszewski GV (2003) QoS guided min-min heuristic for grid task scheduling. J Comput Sci Technol 18:442–451 MATHCrossRefGoogle Scholar
  8. 8.
    Magoules F, Nguyen TMH, Yu L (2009) Grid resource management: towards virtual and services compliant grid computing. CRC Press/Taylor & Francis, Boca Raton Google Scholar
  9. 9.
    Elmroth E, Tordsson J (2008) Grid resource brokering algorithms enabling advanced reservations and resource selection based on performance prediction. J Future Gener Comput Syst 24:585–593 CrossRefGoogle Scholar
  10. 10.
    Gao Y, Rong H, Huang JZh (2005) Adaptive grid job scheduling with genetic algorithms. J Future Gener Comput Syst 21:151–161 CrossRefGoogle Scholar
  11. 11.
    Krauter K, Buyya R, Maheswaran M (2002) A taxonomy and survey of grid resource management systems for distributed computing. J Softw: Pract Experience 32(2): 135–164 MATHCrossRefGoogle Scholar
  12. 12.
    Iosup A, Epema DHJ, Franke C, Papaspyrou A, Schley L, Song B, Yahyapour R (2006) On grid performance evaluation using synthetic workloads. In: 12th international workshop on job scheduling strategies for parallel processing, France, 26 June 2006, pp. 232–255 Google Scholar
  13. 13.
    Lai Zh, Yang J, Shan H (2003) A resource allocation method in the neural computation platform. In: Second international workshop on grid and cooperative computing, China, December 7–10, 2003, pp. 166–169 Google Scholar
  14. 14.
    Li Y, Yang Y, Ma M, Zhou L (2009) A hybrid load balancing strategy of sequential tasks for grid computing environments. J Future Gener Comput Syst 25(8): 819–828 CrossRefGoogle Scholar
  15. 15.
    Caron E, Garonne V, Tsaregorodtsev A (2007) Definition, modeling and simulation of a grid computing scheduling system for high throughput computing. J Future Gener Comput Syst 23:968–976 CrossRefGoogle Scholar
  16. 16.
    Van der Aalst WMP (2005) Petri net based scheduling. J OR Spectr 18(4):219–229 Google Scholar
  17. 17.
    Fei Y, Changjun J, Rong D, Jianjun Y (2009) Grid resource management policies for load-balancing and energy-saving by vacation queuing theory. J Comput Electr Eng 35:966–979 MATHCrossRefGoogle Scholar
  18. 18.
    Bolch G, Greiner S, de Meer H, Trivedi KS (2006) Queueing networks and Markov chains, 2nd edn. Wiley, New York MATHCrossRefGoogle Scholar
  19. 19.
    Cooper RB (1981) Introduction to queueing theory, 2nd edn. Elsevier/North-Holland, Amsterdam Google Scholar
  20. 20.
    Ajmone Marsan M, Balbo G, Conte G, Donatelli S, Franceschinis G (1995) Modeling with generalized stochastic Petri nets. Wiley, New York Google Scholar
  21. 21.
    Bause F, Kritzinger PS (2002) Stochastic Petri nets: an introduction to the theory, 2nd edn. Vieweg, Wiesbaden MATHGoogle Scholar
  22. 22.
    Afzal A, McGough A Stephen, Darlington J (2008) Capacity planning and scheduling in grid computing environment. J Future Gener Comput Syst 24:404–414 CrossRefGoogle Scholar
  23. 23.
    Kalantari M, Akbari MK (2009) A parallel solution for scheduling of real time applications on grid environments. J Future Gener Comput Syst 25(7):704–716 CrossRefGoogle Scholar
  24. 24.
    Li L, FangChun Y (2006) Modeling and performance analysis of a priority-based scheduling scheme in service grid. In: Proceedings of the fifth international conference on grid and cooperative computing, China, October 21–23, 2006, pp. 327–330 Google Scholar
  25. 25.
    Han Y, Jiang Ch, Luo X (2005) Resource scheduling model for grid computing based on sharing synthesis of Petri net. In: The 9th international conference on computer supported cooperative work in design proceedings, UK, May 24–26, 2005, pp. 367–372 Google Scholar
  26. 26.
    Han Y, Luo X (2006) Modeling and performance analysis of grid task scheduling based on composition and reduction of Petri nets. In: Proceedings of the fifth international conference on grid and cooperative computing, IEEE, China, October 21–23, 2006, pp. 331–334 Google Scholar
  27. 27.
    Palmer J, Mitrani I (2005) Optimal and heuristic policies for dynamic server allocation. J Parallel Distrib Comput 65:1204–1211 MATHCrossRefGoogle Scholar
  28. 28.
    Burke PJ (1956) The output of a queueing system. Oper Res 4(6):699–704 MathSciNetCrossRefGoogle Scholar
  29. 29.
    Horst R, Pardalos PM, Thoai NV (2002) Introduction to global optimization (nonconvex optimization and its applications). Springer, Berlin Google Scholar
  30. 30.
    http://www.lindo.com/ – Lingo section
  31. 31.
    Sahner R, Trivedi KS, Puliafito A (1996) Performance and reliability analysis of computer systems - an example - based approach using the SHARPE software package. Kluwer, Boston MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Parallel Processing & Concurrent Systems Laboratory, Department of Computer EngineeringIran University of Science and Technology (IUST)TehranIran

Personalised recommendations