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Analytical Modeling of Multistage, Multipath Networks
October 1996 (vol. 7 no. 10)
pp. 1059-1064

Abstract—Because of their ability to tolerate faults, multipath, multistage networks provide useful interconnection schemes for large-scale parallel computers. However, the analytical models that have been used to analyze the performance Banyan networks cannot be used to evaluate the performance of multipath networks. We present here what we believe to be the first analytical model that allows calculation of the bandwidth of the general class of unbuffered, packet-switched, multipath, multistage networks. The equations yielded by the model can be solved either exactly or by Monte Carlo approximation. The model agrees well with the results of a more complex simulation and provides a first step towards solution of the open problem of modeling of buffered, packet-switched, multipath, multistage networks.

[1] F. Chong, E. Egozy, and A. DeHon, "Fault Tolerance and Performance of Multipath Multistage Interconnection Networks," Advanced Research in VLSI: MIT/Brown Conference 1992, T.F. Knight, Jr. and John Savage (eds.). MIT Press, March 1992.
[2] L. R. Goke and G. J. Lipovski,“Banyan networks for partitioning multiprocessor systems,”inFirst Ann. Symp. Comput. Archit., 1973, pp. 21–28.
[3] J.Y. Hui, Switching and Traffic Theory for Integrated Broadband Networks.Boston, Mass.: Kluwer Academic Publishers, pp. 246-270, 1990.
[4] C.P. Kruskal and M. Snir, "The Performance of Multistage Interconnection Networks for Multiprocessors," IEEE Trans. Computers, vol. 32, no. 12, Dec. 1983.
[5] V.P. Kumar and S.M. Reddy, "Design and Analysis of Fault-tolerant Multistage Networks With Low Link Complexity," Proc. 12th Int'l Symp. Computer Architecture, pp. 376-386, June, 1985.
[6] T. Leighton and B. Maggs, "Expanders Might be Practical: Fast Algorithms for Routing Around Faults in Multibutterflies," 30th Ann. Symp. Foundations of Computer Science.Los Alamitos, Calif.: IEEE Computer Society Press, Nov., 1989.
[7] T. Liu and L Kleinrock,“Performance analysis of finite-buffered multistage interconnection networks with a general traffic pattern,”in1991 ACM SIGMETRICS Conf.,San Diego, CA, May 1991, pp. 68–78.
[8] A. Merchant, "Analytical Models of the Performance Analysis of Banyan Networks," PhD Thesis, Stanford Univ. Department of Computer Science Report No. STAN-CS-90-1347, Dec. 1990.
[9] D.S. Parker and C.S. Raghavendra, "The Gamma Network," IEEE Trans. Computers, vol. 33, no. 4, Apr. 1984.
[10] J.H. Patel, "Performance of Processor-Memory Interconnections for Multiprocessors," IEEE Trans. Computers, vol. 30, no. 10, Oct. 1981.
[11] P.G. Sobalvarro, "Probabilistic Analysis of Multistage Interconnection Network Performance," Artificial Intelligence Laboratory Technical Report AITR-1364, MIT, Apr. 1992.
[12] T.H. Theimer, E.P. Rathgeb, and M.N. Huber, "Performance Analysis of Buffered Banyan Networks," IEEE Trans. Communications, vol. 39, no. 2, Feb. 1991.
[13] N.-F. Tzeng, P.-C. Yew, and C.-Q. Zhu, "The Performance of a Fault-Tolerant Multistage Interconnection Network," Proc. 1985 Int'l Conf. Parallel Processing, Aug. 1985, pp. 458-465.
[14] A. Varma and C.S. Raghavendra, "Performance Analysis of a Redundant-Path Interconnection Network," Proc. 1985 Int'l Conf. Parallel Processing, Aug. 1985, pp. 474-479.

Index Terms:
Network, analytical model, multistage network, multipath network, throughput, and performance.
Citation:
Patrick G. Sobalvarro, "Analytical Modeling of Multistage, Multipath Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 10, pp. 1059-1064, Oct. 1996, doi:10.1109/71.539737
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