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An Analytic Model or Communication Latency in Wormhole-Switched k -Ary n -Cube Interconnection Networks with Digit-Reversal Traffic

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High Performance Computing (ISHPC 2000)

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Abstract

Several analytical models of fully adaptive routing in wormhole-routed k -ary n -cubes under the uniform traffic pattern have recently been proposed in the literature. This paper describes the first analytical model of fully adaptive routing in k -ary n -cubes in the presence of non-uniform traffic generated by the digit-reversal permutation,which is an important communication operation found in many matrix computation problems. Results obtained through simulation experiments confirm that the model predicts message latency with a good degree of accuracy under different working conditions.

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References

  1. Agarwal A.:Limits on interconnection network performance.IEEE TPDS 2 (4 )(1991) 398–412.

    Google Scholar 

  2. Anderson, E. Brooks, J. Grass, C. Scott S.:Performance of the Cray T3E multiprocessor.Proc. Supercomputing Conference (1997).

    Google Scholar 

  3. Boura, Y. Das, C.R.T.M.Jacob:A performance model for adaptive routing in hypercubes.Proc. Int. Workshop Parallel Processing (1994)11–16.

    Google Scholar 

  4. Chien A.:A cost and performance model for k-ary n-cube wormhole routers.IEEE TPDS 9 (2 )(1998)150–162.

    Google Scholar 

  5. Ciciani B. Colajanni M. Paolucci C.:An accurate model for the performance analysis of deterministic wormhole routing.Proc.11 th IPPS (1997)353–359.

    Google Scholar 

  6. Dally W.J.:Performance analysis of k-ary n-cubes interconnection networks.IEEE TC C — 39 (6)(1990)775–785.

    Google Scholar 

  7. Dally W.J.:Virtual channel flow control.IEEE TPDS 3 (2 )(1992)194–205.

    Google Scholar 

  8. Draper, J.T. Ghosh, J.:A Comprehensive analytical model for wormhole routing in multicomputer systems.J. Parallel & Distributed Computing 32 (1994)202–214.

    Google Scholar 

  9. Duato, J.:A new theory of deadlock-free routing in wormhole networks.IEEE TPDS 4 (12 )(1993)1320–1331.

    Google Scholar 

  10. Duato, J. Yalamanchili, S., Ni L.:Interconnection network:An engineering approach. IEEE Computer Society Press (1997).

    Google Scholar 

  11. Glass, C.J. Ni L.M.:The turn model for adaptive routing.Proc.19 th Annual Symp. Computer Architecture (1992)268–277.

    Google Scholar 

  12. Grammatikakis, M. Hsu, D.F. Kratzel M. Sibeyn, J.:Packet routing in fixed-connection networks:A survey.J. Parallel & Distributed Computing 54 (1998)77–132.

    Google Scholar 

  13. Hwang, K.:Advanced Computer Architecture:Parallelism Scalability Programmability. McGraw-Hill Computer Science Series (1993).

    Google Scholar 

  14. Kessler, R.E. Schwarzmeier, J.L.:Cray T3D:A new dimension for Cray Research.in CompCon (1993)176–182.

    Google Scholar 

  15. Kleinrock, L.:Queueing Systems. Vol.1,John Wiley, New York (1975).

    Google Scholar 

  16. Lin, X. Mckinley P.K. Lin, L.M.:The message flow model for routing in wormhole-routed networks.Proc.ICPP (1993)294–297.

    Google Scholar 

  17. Ni L., McKinley P.K.:A survey of wormhole routing techniques in direct networks. IEEE Computer 25 (2 )(1993)62–76.

    Google Scholar 

  18. Ould-Khaoua M.:A performance model for Duato’s adaptive routing algorithm in k-ary n-cubes.IEEE TC 48 (12 )(1999)1–8.

    Google Scholar 

  19. Pfister, G.J., Norton, V.A.:Hotspot contention and combining in multistage interconnection networks.IEEE TC 34 (10)(1985)943–948.

    Google Scholar 

  20. Sarbazi-Azad H. Ould-Khaoua M. Mackenzie, L.M.:Performance Analysis of k-ary n-cubes with Fully Adaptive Routing.Proc. ICPADS’2000 (2000),Iwate Japan.

    Google Scholar 

  21. Sarbazi-Azad H. Ould-Khaoua, M. Mackenzie, L.M.:An analytical model of fullyadaptive wormhole-routed k-ary n-cubes in the presence of hot-spot traffic.Proc IPDPS’2000 (2000)605–610.

    Google Scholar 

  22. Sarbazi-Azad H. Ould-Khaoua M. Mackenzie, L.M.:Modelling adaptive routing in wormhole-routed k-ary n-cubes in the presence of digit-reversal traffic.Technical report, Department of Computing Science, Glasgow University U.K.(2000).

    Google Scholar 

  23. Seigel H.J.:Interconnection networks for large-scale parallel Processing. McGraw-Hill (1990).

    Google Scholar 

  24. Su C., Shin K.G.:Adaptive deadlock-free routing in multicomputers using one extra channel.Proc. ICPP (1993)175–182.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computing Science, University of Glasgow, G12 8QQ, Glasgow, UK

    H. Sarbazi-Azad & L.M. Mackenzie

  2. Department of Computer Science, University of Strathclyde, G1 1XH, Glasgow, UK

    M. Ould-Khaoua

Authors
  1. H. Sarbazi-Azad
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  2. L.M. Mackenzie
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  3. M. Ould-Khaoua
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Editor information

Editors and Affiliations

  1. Departamento de Arquitectura de Computadores, Universidad Politecnica de Catalunya, Spain

    Mateo Valero

  2. Department of Information and Computer Sciences, Nara Women’s University, Japan

    Kazuki Joe

  3. Institute of Industrial Science Center for Conceptual Information Processing Research, University of Tokyo, Japan

    Masaru Kitsuregawa

  4. Graduate School of Engineering Electrical Engineering Department, University of Tokyo, Japan

    Hidehiko Tanaka

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© 2000 Springer-Verlag Berlin Heidelberg

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Sarbazi-Azad, H., Mackenzie, L., Ould-Khaoua, M. (2000). An Analytic Model or Communication Latency in Wormhole-Switched k -Ary n -Cube Interconnection Networks with Digit-Reversal Traffic. In: Valero, M., Joe, K., Kitsuregawa, M., Tanaka, H. (eds) High Performance Computing. ISHPC 2000. Lecture Notes in Computer Science, vol 1940. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39999-2_19

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  • DOI: https://doi.org/10.1007/3-540-39999-2_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41128-4

  • Online ISBN: 978-3-540-39999-5

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