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Explanation of Performance Degradation in Turn Model

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Abstract

The Turn model routing algorithms for mesh interconnection network achieve partial adaptivity without any virtual channels. However, the routing performance measured by simulations is worse than with the simple deterministic routing algorithm. Authors have explained these results simply by uneven dynamic load through the network. However, this phenomenon has not been studied further.

This paper investigates performance degradation with Turn model and drawbacks of partially adaptive routing in comparison with the deterministic routing, and it introduces some new concepts. Our simulations deal with individual channels and results are presented by 3D graphs, rather than by commonly used averages. An additional parameter—channel occupation, which is consistent with queuing theory commonly used in many proposed analytical models, is introduced. We also propose a new structure, the Channel Directions Dependency Graph (CDDG). It provides a new approach in analysis, helps in understanding of dynamic routing behaviour, and it can be generalized in other routing algorithms.

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References

  1. V. S. Adve and M. K. Veron. Performance analysis of Mesh interconnection networks with deterministic routing. IEEE Transactions on Parallel and Distributed Systems, 5(3):225–246, 1994.

    Article  Google Scholar 

  2. A. Agarwal. Limits on Interconnection network performance. IEEE Transactions on Parallel and Distributed Systems, 2(4):398–412, 1991.

    Article  Google Scholar 

  3. R. V. Boppana and S. Chalasani. A comparison of adaptive wormhole routing algorithms. In Proceedings of the 20th International Symposium on Computer Architecture, pp. 351–360, ACM Press, New York, NY, 1993.

    Chapter  Google Scholar 

  4. B. Ciciani, M. Colajanni, and C. Paolucci. Performance evaluation of deterministic wormhole routing in k-ary n-cubes. Parallel Computing, 24:2053–2075, 1998.

    Article  MATH  Google Scholar 

  5. G. M. Chiu. The odd-even turn model for adaptive routing. IEEE Transactions on Parallel and Distributed Systems, 11(7):729–738, 2000.

    Article  Google Scholar 

  6. R. Cypher and L. Gravano. Storage-efficient, deadlock-free packet routing algorithms for Torus networks. IEEE Transactions on Computers, 43(12):1376–1385, 1994.

    Article  Google Scholar 

  7. W. J. Dally and C. L. Seitz. Deadlock-free packet routing in multiprocessor interconnection networks. IEEE Transactions on Computers, 36(5):547–553, 1987.

    MATH  Google Scholar 

  8. W. J. Dally. Virtual-channel flow control. IEEE Transactions on Parallel and Distributed Systems, 3(2):194–205, 1992.

    Article  Google Scholar 

  9. J. Duato. A new theory of deadlock-free adaptive routing in wormhole networks. IEEE Transactions on Parallel and Distributed Systems, 4(12):1320–1331, 1993.

    Article  Google Scholar 

  10. W. C. Feng and K. G. Shin. Impact of selection functions on routing algorithms performances in multicomputer networks. In Proceedings of the 11th International Conference on Supercomputing, pp. 132–139, ACM Press, New York, NY, 1997.

    Chapter  Google Scholar 

  11. S. Gajin. Adaptivity Analysis of the Turn Model in Multicomputers. Master thesis, Faculty of Electrical Engineering, University of Belgrade, 1999.

  12. C. J. Glass and L. M. Ni. The Turn Model for adaptive routing. In Proceedings of the 19th International Symposium on Computer Architecture, pp. 278–287, ACM Press, New York, NY, 1992.

    Chapter  Google Scholar 

  13. L. Gravano, G. D. Pifarré, P. E. Berman, and J. L. C. Sanz. Adaptive deadlock- and livelock-free routing with all minimal paths in Torus networks. IEEE Transactions on Parallel and Distributed Systems, 5(12):1233–1251, 1994.

    Article  Google Scholar 

  14. J. D. Shih, Fault-tolerant wormhole routing for hypercube networks. Information Processing Letters, 86:93–100, 2003.

    Article  MathSciNet  Google Scholar 

  15. A. Khonsari, H. Sarbazi-Azad, and M. Ould-Khaoua. An analytical model of adaptive wormhole routing with time-out. Future Generation Computer Systems, 19:1–12, 2003.

    Article  MATH  Google Scholar 

  16. L. Kleinrock. Queuing Systems: Theory, Vol. 1, Wiley, New York, 1975.

    Google Scholar 

  17. Y. Lan. An adaptive fault-tolerant routing algorithm for hypercube multicomputers. IEEE Transactions on Parallel and Distributed Systems, 6(11):1147–1152, 1995.

    Article  Google Scholar 

  18. S. S. Lam and M. Reiser. Congestion Control of store-and-forward networks by input buffer limits—an analysis. IEEE Transactions on Communications, 27(1):127–133, 1979.

    Article  Google Scholar 

  19. M. Ould-Khaoua. Message latency in the 2-dimensional mesh with wormhole routing. Microprocessors and Microsystems, 22:509–514, 1999.

    Article  Google Scholar 

  20. G. D. Pifarré, L. Gravano, S. A. Felperin, and J. L.C. Sanz. Fully adaptive minimal deadlock-free packet routing in hypercubes, Meshes, and other Networks: Algorithms and simulations. IEEE Transactions on Parallel and Distributed Systems, 5(3):247–263, 1994.

    Article  Google Scholar 

  21. H. Sarbazi-Azad. A mathematical model of deterministic wormhole routing in hypercube multicomputers using virtual channels. Applied Mathematical Modelling, 27:943–953, 2003.

    Article  MATH  Google Scholar 

  22. H. Sarbazi-Azad, M. Ould-Khaoua, and L. M. Mackenzie. Analytical modelling of wormhole-routed k-ary n-cubes in the presence of matrix-transpose traffic. Journal of Parallel and Distributed Computing, 63:396–409, 2003.

    Article  MATH  Google Scholar 

  23. L. Schwiebert. A performance evaluation of fully adaptive wormhole routing including selection function choice. In 19th IEEE International Performance, Computing, and Communications Conference, pp. 117–123, 2000.

  24. A. Shahrabi, L. M. Mackenzie, and M. Ould-Khaoua. An analytical model of wormhole-routed hypercubes under broadcast traffic. Performance Evaluation, 53:23–42, 2003.

    Article  Google Scholar 

  25. J. Upadhyay, V. Varavithya, and P. Mohapatra. A traffic-balanced adaptive wormhole routing scheme for two-dimensional meshes. IEEE Transactions on Computers, 46(2):190–197, 1997.

    Article  Google Scholar 

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Authors and Affiliations

  1. Belgrade University Computer Centre, University of Belgrade, Serbia and Montenegro

    Slavko Gajin & Zoran Jovanović

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  1. Slavko Gajin
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  2. Zoran Jovanović
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Correspondence to Slavko Gajin.

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Gajin, S., Jovanović, Z. Explanation of Performance Degradation in Turn Model. J Supercomput 37, 271–295 (2006). https://doi.org/10.1007/s11227-006-6454-y

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  • DOI: https://doi.org/10.1007/s11227-006-6454-y

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