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Cluster Computing

, Volume 10, Issue 2, pp 241–250 | Cite as

Analyzing the performance of optical multistage interconnection networks with limited crosstalk

  • Ajay K. KatangurEmail author
  • Somasheker Akkaladevi
  • Yi Pan
Article

Abstract

Analytical modeling techniques can be used to study the performance of optical multistage interconnection network (OMIN) effectively. MINs have assumed importance in recent times, because of their cost-effectiveness. An N×N MIN consists of a mapping from N processors to N memories, with log  2 N stages of 2×2 switches with N/2 switches per stage. The interest is on the study of the performance of unbuffered optical multistage interconnection network using the banyan network. The uniform reference model approach is assumed for the purpose of analysis. In this paper the analytical modeling approach is applied to an N×N OMIN with limited crosstalk (conflicts between messages) up to (log  2 N−1). Messages with switch conflicts satisfying the constraint of (log  2 N−1) are allowed to pass in the same group, but in case of a link conflict, the message is routed in a different group. The analysis is performed by calculating the bandwidth and throughput of the network operating under a load l and allowing random traffic and using a greedy routing strategy. A number of equations are derived using the theory of probability and the performance curves are plotted. The results obtained show that the performance of the network improves by allowing limited crosstalk in the network.

Keywords

Bandwidth Banyan network Crosstalk OMIN 

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References

  1. 1.
    Regis Bates, J.: Optical Switching and Networking Handbook. McGraw-Hill, New York (2001) Google Scholar
  2. 2.
    Berrnond, J.C., Fourneau, J.M., Jean-Marie, A.: Equivalence of multistage interconnection networks, Rapport LRI-217, Univ. de Paris-Sud, France, May 1985 Google Scholar
  3. 3.
    Bhuyan, L.N., Agrawal, D.P.: Design and performance of generalized interconnection networks. IEEE Trans. Comput. C-32(2), 1081–1090 (1983) Google Scholar
  4. 4.
    Bhuyan, L.N., Yang, Q., Agrawal, D.P.: Performance of multiprocessor interconnection networks. IEEE Comput. 22(2), 25–37 (1989) Google Scholar
  5. 5.
    Brenner, M., Tutsch, D., Hommel, G.: Measuring transient performance of a multistage interconnection network using ethernet networking equipment. In: Proceedings of the International Conference on Communications in Computing 2002 (CIC’02), Las Vegas, USA, 2002, pp. 211–216 Google Scholar
  6. 6.
    Cheemalavagu, S., Malek, M.: Analysis and simulation of Banyan interconnection networks with 2×2, 4×4 and 8×8 switching elements, IEEE Real-Time Systems Symposium, 1982, pp. 83–89 Google Scholar
  7. 7.
    Dias, D.M., Jump, J.R.: Analysis and simulation of buffered delta networks. IEEE Trans. Comput. C-30, 273–282 (1981) Google Scholar
  8. 8.
    Goke, L.R., Lipovski, G.J.: Banyan networks for partitioning multiprocessing systems. In: Proceedings of the First International Symposium on Computer Architecture, 1973, pp. 21–28 Google Scholar
  9. 9.
    Jiang, X., Khandker, M.M., Horiguchi, S.: Nonblocking optical MINs under crosstalk-free constraint. In: Proc. IEEE Workshop High Performance Switching and Routing, May 2001, pp. 307–311 Google Scholar
  10. 10.
    Kruskal, C.P., Snir, M.: The performance of multistage interconnection networks for multiprocessors. IEEE Trans. Comput. 32(12), 1091–1098 (1983) Google Scholar
  11. 11.
    Kumar, M., Jump, J.R.: Performance of unbuffered shuffle-exchange networks. IEEE Trans. Comput. 35(6), 573–578 (1986) CrossRefGoogle Scholar
  12. 12.
    Maier, G., Pattavina, A.: Design of photonic rearrangeable networks with zero first-order switching-element-crosstalk. IEEE Trans. Commun. 49, 1268–1279 (2001) CrossRefGoogle Scholar
  13. 13.
    Padmanabhan, K., Netravali, A.N.: Dilated networks for photonic switching. IEEE Trans. Commun. 35(12), 1357–1365 (1987) CrossRefGoogle Scholar
  14. 14.
    Ozdaglar, A.E., Bertsekas, D.P.: Routing and wavelength assignment in optical networks, Lab. Information and Decision Systems, Mass. Inst. Technology, Cambridge, LIDS Rep., 2001 Google Scholar
  15. 15.
    Pan, Y., Qiao, C., Yang, Y., Wu, J.: Recent developments in optical multistage networks. In: Ruan, L., Du, D.-Z. (eds.) Optical Networks—Recent Advances, pp. 151–185. Kluwer Academic, Norwell (2001) Google Scholar
  16. 16.
    Patel, J.H.: Performance of processor-memory interconnections for multiprocessors. IEEE Trans. Comput. C-30, 771–780 (1981) Google Scholar
  17. 17.
    Gu, Q.P., Peng, S.: Wavelengths requirement for permutation routing in all-optical multistage interconnection networks. In: Proceedings of the 2000 International Parallel and Distributed Processing Symposium, Cancun, Mexico, May 1–5 2000, pp. 761–768 Google Scholar
  18. 18.
    Pan, Y., Qiao, C., Yang, Y.: Optical multistage interconnection networks: new challenges and approaches. IEEE Commun. Mag. Featur. Top. Opt. Netw. Commun. Syst. Devices 37(2), 50–56 (1999) Google Scholar
  19. 19.
    Qiao, C.: A universal analytic model for photonic banyan networks. IEEE Trans. Commun. 46(10), 1381–1389 (1998) CrossRefGoogle Scholar
  20. 20.
    Qiao, C., Zhou, L.: Scheduling switching element disjoint connections in stage-controlled photonic banyans. IEEE Trans. Commun. 47(1), 139–148 (1999) CrossRefGoogle Scholar
  21. 21.
    Qiao, C., Melhem, R., Chiarulli, D., Levitan, S.: A time domain approach for avoiding crosstalk in optical blocking multistage interconnection networks. J. Light. Technol. 12(10), 1854–1862 (1994) CrossRefGoogle Scholar
  22. 22.
    Shen, X., Yang, F., Pan, Y.: Equivalent permutation capabilities between time division optical omega networks and non-optical extra-stage omega networks. IEEE/ACM Trans. Netw. 9(4), 518–524 (2001) CrossRefGoogle Scholar
  23. 23.
    Vaez M.M., Lea, C.-T.: Strictly nonblocking directional-coupler-based switching networks under crosstalk constraint. IEEE Trans. Commun. 48, 316–323 (2000) CrossRefGoogle Scholar
  24. 24.
    Varma A., Raghavendra, C.S.: Interconnection Networks for Multiprocessors and Multicomputers, Theory and Practice. IEEE Computer Society Press, Los Alamitos (1994) Google Scholar
  25. 25.
    Yang Y., Wang, J.: A more accurate analytical model on blocking probability of multicast networks. IEEE Trans. Commun. 48(11), 1930–1935 (2000) CrossRefGoogle Scholar
  26. 26.
    Yang, Y., Wang, J., Pan, Y.: Permutation capability of optical multistage interconnection networks. J. Parallel Distr. Comput. (JPDC) 60(1), 72–91 (2000) zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Ajay K. Katangur
    • 1
    Email author
  • Somasheker Akkaladevi
    • 2
  • Yi Pan
    • 3
  1. 1.Computing & Mathematical Sciences DepartmentTexas A&M University-Corpus ChristiCorpus ChristiUSA
  2. 2.Department of Computer Information SystemsVirginia State UniversityPetersburgUSA
  3. 3.Department of Computer ScienceGeorgia State UniversityAtlantaUSA

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