Abstract
The stretched hypercube has recently been introduced as an attractive alternative to the well-known hypercube. Previous research on this network topology has mainly focused on topological properties, VLSI and algorithmic aspects of this network. Several analytical models have been proposed in the literature for different interconnection networks, as the most cost-effective tools to evaluate the performance merits of such systems. This paper proposes an analytical performance model to predict message latency in wormhole-switched stretched hypercube interconnection networks with fully adaptive routing. The analysis focuses on a fully adaptive routing algorithm which has been shown to be the most effective for stretched hypercube networks. The results obtained from simulation experiments confirm that the proposed model exhibits a good accuracy under different operating conditions.
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References
Abraham, S., Padmanabhan, K.: Performance of the direct binary n-cube networks for multiprocessors. IEEE Trans. on Computers 37(7), 1000–1011 (1989)
Agarwal: Limits on interconnection network performance. IEEE Transactions on Parallel and Distributed Systems 2(4), 398–412 (1991)
Berthome, P., Ferreira, A., Perennes, S.: Optimal Information Dissemination in Star and Pancake Networks. IEEE Trans. on Parallel and Distributed Systems 7(12), 1292–1300 (1996)
Boppana, R.V., Chalasani, S.: A Comparison of Adaptive Wormhole Routing Algorithms. In: ISCA 1993. Proceedings of the 20th Annual International Symposium on Computer Architecture, pp. 351–360 (1993)
Boppana, R.V., Chalasani, S.: A Framework for Designing Deadlock-Free Wormhole Routing Algorithms. IEEE Transactions on Parallel and Distributed Systems 7(2), 169–183 (1996)
Boura, Y., Das, C.R., Jacob, T.M.: A performance model for adaptive routing in hypercubes. In: Proceedings of the International Workshop on Parallel Processing, pp. 11–16 (1994)
Chen, C., Chen, J.: Optimal Parallel Routing in Star Networks. IEEE Trans. Computers 46(12), 1293–1303 (1997)
Chen, C., Chen, J.: Nearly Optimal One-to-many Parallel Routing in Star Networks. IEEE Trans. on Parallel and Distributed Systems 8(12), 1196–1202 (1997)
Ciciani, B., Colajanni, M., Paolucci, C.: An accurate model for the performance analysis of deterministic wormhole routing. In: Proceedings of the 11th International Parallel Processing Symposium, pp. 353–359 (1997)
Dally, W.J.: Virtual channel flow control. IEEE Transactions on Parallel and Distributed Systems 3(2), 194–205 (1992)
Day, K., Tripathi, A.: A Comparative Study of Topological Properties of Hypercubes and Star Graphs. IEEE Transactions on Parallel and Distributed Systems 5(1), 31–38 (1994)
Draper, J.T., Ghosh, J.: A Comprehensive analytical model for wormhole routing in multicomputer systems. Jour. of Parallel and Distributed Computing 23(2), 202–214 (1994)
Duato, J., Yalamanchili, C., Ni, L.: Interconnection Networks: an engineering approach. IEEE computer society press, Los Alamitos (1997)
Fujita, S.: Neighborhood Information Dissemination in the Star Graph. IEEE Trans. on Computers 49(12), 1366–1370 (2000)
Graham, S.W., Seidel, S.R.: The Cost of Broadcasting on Star Graphs and k-ary hypercubes. IEEE Trans. Computers 42(6), 756–759 (1993)
Greenberg, R., Guan, L.: Modelling and comparison of wormhole routed mesh and torus networks. In: Proceedings of the 9th IASTED International Conference on Parallel and Distributed Computing and Systems, pp. 501–506 (1997)
Jwo, J.S., Lakshmivarahan, S., Dhall, S.K.: Embedding of Cycles and Grids in Star Graphs. Journal of Circuits, Systems and Computers 1(1), 43–74 (1991)
Lee, J.I., Chang, H.: Embedding Complete Binary Trees in Star Graphs. Journal of the Korea Information Science Society 21(2), 407–415 (1994)
Kessler, R.E., Schwarzmeier, J.L.: CRAY: T3D: A new dimension for Cray Research. CompCon, 176–182 (1993)
Kim, J., Das, C.R.: Hypercube communication delay with wormhole routing. IEEE Transactions on Computers 43(7), 806–814 (1994)
Kleinrock, L.: Queueing Systems, vol. 1. John Wiley, New York (1975)
Meraji, S., Sarbazi-Azad, A.: Deterministic routing in stretched hypercubes, Technical Report, School of Computer Science, IPM, Tehran, Iran (2006)
Shareghi, P., Sarbazi-Azad, H.: Topological Properties of Stretched Graphs. In: Proc. of the 4th ACS/IEEE International Conference on Computer Systems and Applications, Dubai/Sharjah, UAE, March 18-20, pp. 123–126 (2006)
Najafabadi, H.H., Sarbazi-Azad, H., Rajabzadeh, P.: Performance Modeling of Fully Adaptive Wormhole Routing in 2-D Mesh-Connected Multiprocessors. In: MASCOTS 2004. 12th Proc. of the IEEE ACM International Symp. on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems, pp. 528–534 (2004)
Nayebi, S.M., shamaei, A.: Using listener-based integration to develop a simulation platform for interconnection networks - Xmulator, Sharif university of Technology, http://www.xmulator.com
Nigam, M., Sahni, S., Krishnamurthy, B.: Embedding Hamiltonians and Hypercubes in Star Interconnection Graphs. In: Proc. Intl. Conf. Parallel Processing, vol. 3, pp. 340–343 (1990)
Patel, A., Kusalik, A., McCrosky, C.: Area-Efficient VLSI Layout for Binary Hypercubes. IEEE Trans. on Computers 49(2) (2000)
Rezazad, M., Sarbazi-Azad, H.: A Constraint-Based Performance Comparison of Hypercube and Star Multicomputers with Failures. In: AINA 2005. 19th International Conference on Advanced Information Networking and Applications, pp. 841–846 (2005)
Sheu, J.P., Liaw, W., Chen, T.: A Broadcasting Algorithm in Star Graph Interconnection Networks. Information Processing Letters 48(5), 237–241 (1993)
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Meraji, S., Sarbazi-Azad, H. (2007). Mathematical Performance Modelling of Stretched Hypercubes. In: Rao, S., Chatterjee, M., Jayanti, P., Murthy, C.S.R., Saha, S.K. (eds) Distributed Computing and Networking. ICDCN 2008. Lecture Notes in Computer Science, vol 4904. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77444-0_39
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DOI: https://doi.org/10.1007/978-3-540-77444-0_39
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