Advertisement

Cluster Computing

, Volume 12, Issue 3, pp 285–297 | Cite as

A general mathematical performance model for wormhole-switched irregular networks

  • Reza Moraveji
  • Parya Moinzadeh
  • Hamid Sarbazi-Azad
Article

Abstract

Irregular topologies are desirable network structures for building scalable cluster systems and very recently they have also been employed in SoC (system-on-chip) design. Many analytical models have been proposed in the literature to evaluate the performance of networks with different topologies such as hypercube, torus, mesh, hypermesh, Cartesian product networks, star graph, and k-ary n-cube; however, to the best of our knowledge, no mathematical model has been presented for irregular networks. Therefore, as an effort to fill this gap, this paper presents a comprehensive mathematical model for fully adaptive routing in wormhole-switched irregular networks. Moreover, since our approach holds no assumption for the network topology, the proposed analytical model covers all the aforementioned models (i.e. it covers both regular and irregular topologies). Furthermore, the model makes no preliminary assumption about the deadlock-free routing algorithm applied to the network. Finally, besides the generality of the model regarding the topology and routing algorithm, our analysis shows that the analytical model exhibits high accuracy which enables it to be used for almost all topologies with all traffic loads.

Keywords

Irregular networks Computing clusters Routing Performance evaluation Analytical modeling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dally, W.J.: Virtual channel flow control. IEEE Trans. Parallel Distrib. Syst. 3, 194–205 (1992) CrossRefGoogle Scholar
  2. 2.
    Draper, J.T., Ghosh, J.: A comprehensive analytical model for wormhole routing in multicomputer systems. J. Parallel Distrib. Comput. 32, 202–214 (1994) CrossRefGoogle Scholar
  3. 3.
    Duato, J., Pinkston, T.M.: A General Theory for Deadlock-free Adaptive Routing using a Mixed Set of Resources. IEEE Trans. Parallel Distrib. Syst. 12, 1219–1235 (2001) CrossRefGoogle Scholar
  4. 4.
    Duato, S.J., Yalamanchili, Ni, L.: Interconnection networks: an engineering approach. IEEE Comput. Soc., Los Alamitos (2003) Google Scholar
  5. 5.
    Flich, J., Duato, J.: Logic-based distributed routing for NoCs. IEEE Comput. Archit. Lett. 7 (2008) Google Scholar
  6. 6.
    Kiasari, A.E., Sarbazi-Azad, H., Ould-Khaoua, M.: Analytical performance modelling of adaptive wormhole routing in the star interconnection network. In: Parallel and Distributed Processing Symposium, pp. 25–29 (2006) Google Scholar
  7. 7.
    Koibuchi, M., Funahashi, A., Jouraku, A., Amano, H.: L-turn routing: an adaptive routing in irregular networks. In: International Parallel Processing Conference, pp. 383–392 (2001) Google Scholar
  8. 8.
    Lysne, O., Skeie, T., Reinemo, S., Theiss, I.: Layered routing in irregular networks. IEEE Trans. Parallel Distrib. Syst. 17, 51–65 (2006) CrossRefGoogle Scholar
  9. 9.
    Moraveji, R., Sarbazi-Azad, H.: Mathematical performance analysis of product networks. In: International Conference on Parallel and Distributed Systems, vol. 2, pp. 1–8 (2007) Google Scholar
  10. 10.
    Moraveji, R., Sarbazi-Azad, H., Tavakkol, A.: The effect of network topology and channel labels on the performance of label-based routing algorithms. In: International Conference on Computational Science, pp. 529–538 (2008) Google Scholar
  11. 11.
    Najaf-abadi, H.H., Sarbazi-Azad, H., Rajabzadeh, P.: Performance modeling of fully adaptive wormhole routing in 2-D mesh-connected multiprocessors. In: Modeling, Analysis, and Simulation of Computer and Telecommunications Systems Conference, pp. 528–534 (2004) Google Scholar
  12. 12.
    Nayebi, A., Meraji, S., Shamaei, A., Sarbazi-Azad, H.: Xmulator: A listener-based integrated simulation platform for interconnection networks. In: International Conference on Modeling and Simulation, pp. 128–132 (2007) Google Scholar
  13. 13.
    Nguyen, H., Ngo, V., Choi, H.: Assessing routing behavior on on-chip-network. In: International Conference on Computer Engineering and Systems, pp. 62–65 (2006) Google Scholar
  14. 14.
    Ould-Khaoua, M., Sarbazi-Azad, H.: An analytical model of adaptive wormhole routing in hypercubes in the presence of hot spot traffic. IEEE Trans. Parallel Distrib. Syst. 12, 283–292 (2001) CrossRefMathSciNetGoogle Scholar
  15. 15.
    Puente, V., Gregorio, J.A., Vallejo, F., Beivide, R., Izu, C.: High-performance adaptive routing for networks with arbitrary topology. J. Syst. Archit. 52, 345–358 (2006) CrossRefGoogle Scholar
  16. 16.
    Sancho, J.C., Robles, A., Duato, J.: An effective methodology to improve the performance of the up*/down* routing algorithm. IEEE Trans. Parallel Distrib. Syst. 15, 740–745 (2004) CrossRefGoogle Scholar
  17. 17.
    Sarbazi-Azad, H., Ould-Khaoua, M., Mackenzie, L.M.: An accurate analytical model of adaptive wormhole routing in k-ary n-cube interconnection networks. Perform. Eval. 43, 165–179 (2001) MATHCrossRefGoogle Scholar
  18. 18.
    Schroeder, M.D., : Autonet: a high-speed, self configuring local area network using point-to-point links. J. Sel. Areas Commun. 9, 1318–1335 (1991) CrossRefGoogle Scholar
  19. 19.
    Wu, J., Sheng, L.: Deadlock-free routing in irregular networks using prefix routing. DIMACS Technical Report, 99–19 (1999) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Reza Moraveji
    • 1
  • Parya Moinzadeh
    • 1
  • Hamid Sarbazi-Azad
    • 2
  1. 1.School of Computer ScienceIPMTehranIran
  2. 2.Dept. of Computer EngineeringSharif University of TechnologyTehranIran

Personalised recommendations