Advertisement

Analysis of dynamic load balancing strategies using a combination of stochastic petri nets and queueing networks

  • C. R. M. Sundaram
  • Y. Narahari
Full Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 691)

Abstract

This paper is concerned with the analytical evaluation of two well known dynamic load balancing strategies, namely, shortest queue routing (SQR) and shortest expected delay routing (SEDR). We overcome the limitations of existing analysis methodologies, using a well known hybrid performance model that combines generalized stochastic Petri nets and product form queueing networks. Our methodology is applicable to both open queueing network and closed queueing network models of load balancing in distributed computing systems. The results show that for homogeneous distributed systems, SQR outperforms all other policies. For heterogeneous systems, SEDR surprisingly performs worse than SQR at low levels of imbalance in loads. However, with increase in imbalance in load, SEDR expectedly performs better than SQR.

Keywords

Queue Length Average Response Time High Level Model Queueing Network Queue Length Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M.Ajmone Marsan, G.Balbo and G.Conte, A Class of Generalized Stochastic Petri Nets for the Performance Evaluation of Multiprocessor Systems, ACM Transactions of Computer Systems, Vol. 2, No.2, May 1984, pp. 93–122.Google Scholar
  2. [2]
    I.F.Akyildiz, Central Server Models with Multiple Job Classes, State Dependent Routing, and Rejection Blocking, IEEE Transactions on Software Engineering, Vol. 15, No.10, October 1989, pp. 1305–1312.Google Scholar
  3. [3]
    G.Balbo, S.C.Bruell and S.Ghanta, Combining Queueing Networks and Generalized Stochastic Petri Nets for the Solution of Complex Models of Computer Systems, IEEE Transactions On Computers, Vol. 17, No.10, October 1988, pp. 1251–1268.Google Scholar
  4. [4]
    S.A.Banawan and J.Zahorjan, Load Sharing in Heterogeneous Queueing Systems, Proceedings of the IEEE INFOCOM'89, 1989, pp.731–739.Google Scholar
  5. [5]
    J.P.C.Blanc, A Note on Waiting Times in Systems with Queues in Parallel, Journal of Applied Probability, Vol. 24, 1987, pp. 540–546.Google Scholar
  6. [6]
    F.Bonomi and A.Kumar, Adaptive Optimal Load Balancing in a Heterogeneous Multiserver System with a Central Job Scheduler, IEEE Transactions on Computers, Vol. 39, No.10, October 1990, pp. 1232–1250.Google Scholar
  7. [7]
    J.P.Buzen, Computational Algorithms for Closed Queueing Networks with Exponential Servers, Communications of the ACM, Vol. 16, No.9, September 1973, pp. 527–531.Google Scholar
  8. [8]
    L.Flatto and H.P.Mckean, Two Queues in Parallel, Communications on Pure and Applied Mathematics, Vol. 30, 1977, pp. 255–263.Google Scholar
  9. [9]
    B.W.Conolly, An Autostrada Queueing Problem, Journal of Applied Probability, Vol. 21, 1984, pp. 394–403.Google Scholar
  10. [10]
    D.L.Eager, D.Edward, E.D.Lazowska, and John Zahorjan, Adaptive Load Sharing in Homogeneous Distributed Systems, IEEE Transactions on Software Engineering, Vol. 12, No.5, May 1986, pp. 662–675.Google Scholar
  11. [11]
    G.Foschini and J.Salz, A Basic Dynamic Routing Problem and Diffusion, IEEE Transactions on Communications, Vol.26, No.3, March 1978.Google Scholar
  12. [12]
    J.A.Gubner, B.Gopinath, and S.R.S.Varadhan, Bounding Functions of a Markov Process and the Shortest Queue Problem, Technical Report, Department of Computer Science, University of Maryland, U.S.A., 1988.Google Scholar
  13. [13]
    S.Halfin, The Shortest Queue Problem, Journal of Applied Probability, Vol. 22, 1985, pp. 865–878.Google Scholar
  14. [14]
    J.F.C.Kingman, Two Similar Queues in Parallel, Biometrika, Vol. 48, 1961, pp. 306–310.Google Scholar
  15. [15]
    G.Knessl, B.J.Mattowsky, Z.Schuss and C.Tier, Two Parallel M/G/1 Queues where Arrivals Join the System with the Smaller Buffer Content, IEEE Transactions on Communications, Vol. 35, No.11, November 1987, pp. 1153–1158.Google Scholar
  16. [16]
    A.E.Krzesinski, Multiclass Queueing Networks with State Dependent Routing, Performance Evaluation, Vol. 7, No.2, June 1987, pp. 125–145.Google Scholar
  17. [17]
    R.D.Nelson and T.K.Philips, An Approximation to the Response Time for Shortest Queue Routing, Performance Evaluation Review, Vol. 17, No.1, May 1989, pp. 181–189.Google Scholar
  18. [18]
    M.Reiser and S.S.Lavenberg, Mean Value Analysis of Closed Mutichain Queueing Networks, Journal of ACM, Vol. 27, No.2, April 1980, pp. 313–322.Google Scholar
  19. [19]
    R.Meenakshi Sundaram, Integrated Analytical Models for Parallel and Distributed Systems, M.S. Thesis, Department of Computer Sciene and Automation, Indian Institute of Science, Bangalore, October 1990.Google Scholar
  20. [20]
    A.N.Tantawi and D.Towsley, Optimal Static Load Balancing in Distributed Computer Systems, Journal of the ACM, Vol. 32, No.2, April 1985, pp. 445–465.Google Scholar
  21. [21]
    D.Towsley, Queueing Models with State Dependent Routing, Journal of the ACM, Vol. 27, No.2, April 1980, pp. 323–337.Google Scholar
  22. [22]
    YuanChow and Walter H.Kohler, Models for Dynamic Load Balancing in a Heterogeneous Multiprocessor System, IEEE Transactions on Computers, Vol. 28, No.5, May 1979, pp. 354–361.Google Scholar
  23. [23]
    T.Yung Wang and R.J.T.Morris, Load Sharing in Distributed Systems, IEEE Transactions on Computers, Vol. 34, No.3, March 1985, pp. 204–217.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • C. R. M. Sundaram
    • 1
  • Y. Narahari
    • 2
  1. 1.Department of Computational ScienceUniversity os SaskatchewanSaskatoonCanada
  2. 2.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia

Personalised recommendations