This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Performance Model for Duato's Fully Adaptive Routing Algorithm in k$k$-Ary n$n$-Cubes
December 1999 (vol. 48 no. 12)
pp. 1297-1304

Abstract—Analytical models of deterministic routing in wormhole-routed $k$-ary $n$-cubes have widely been reported in the literature. Although many fully adaptive routing algorithms have been proposed to overcome the performance limitations of deterministic routing, there have been hardly any studies that describe analytical models for these algorithms. This paper proposes a new analytical model for obtaining latency measures in high-radix $k$-ary $n$-cubes with fully adaptive routing, based on Duato's algorithm [10]. The validity of the model is demonstrated by comparing analytical results with those obtained through simulation experiments.

[1] A. Agarwal, "Limits on Interconnection Network Performance," IEEE Trans. Parallel and Distributed Systems, vol. 2, no. 4, pp. 398-412, Oct. 1991.
[2] Y. Boura, C.R. Das, and T.M. Jacob, “A Performance Model for Adaptive Routing in Hypercubes,” Proc. Int'l Workshop Parallel Processing, pp. 11-16, Dec. 1994.
[3] A.A. Chien, “A Cost and Performance Model for$k$-ary$n$-cubes Wormhole Routers,” IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 2, pp. 150-162, Feb. 1998.
[4] B. Ciciani, M. Colajanni, and C. Paolucci, “An Accurate Model for the Performance Analysis of Deterministic Wormhole Routing,” Proc. 11th Int'l Parallel Processing Symp., pp. 353-359, 1997.
[5] Cray Research Inc., “The Cray T3E Scalable Parallel Processing System,” on Cray's web page athttp://www.cray.com/PUBLIC/product-infoT3E .
[6] W.J. Dally and C.L. Seitz, “Deadlock-Free Message Routing in Multiprocessor Interconnection Networks,” IEEE Trans. Computers, Vol. C-36, No. 5, May 1987, pp. 547-553.
[7] W.J. Dally, "Performance Analysis of k-ary n-Cube Interconnection Networks," IEEE Trans. Computers, vol. 39, no. 6, pp. 775-785, June 1992.
[8] W.J. Dally, "Virtual-Channel Flow Control," IEEE Trans. Parallel and Distributed Systems, vol. 3, no. 2, pp. 194-205, Mar. 1992.
[9] W.J. Dally, L.R. Dennison, D. Harris, K. Kan, and T. Xanthopoulus, “The Reliable Router: A Reliable and High-Performance Communication Substrate for Parallel Computers,” Proc. Workshop Parallel Computer Routing and Comm., pp. 241–255, May 1994.
[10] J. Duato, "A New Theory of Deadlock-Free Adaptive Routing in Wormhole Networks," IEEE Trans. Parallel and Distributed Systems, vol. 4, no. 12, pp. 1,320-1,331, Dec. 1993.
[11] J. Duato and P. López, "Performance Evaluation of Adaptive Routing Algorithms for k-ary n-cubes," Proc. Workshop Parallel Computer Routing and Communication, May. 1994.
[12] J.T. Draper and J. Ghosh, "A Comprehensive Analytical Model for Wormhole Routing in Multicomputer Systems," J. Parallel and Distributed Computing, vol. 23, pp. 202-214, Nov. 1994.
[13] R. Greenberg and L. Guan, “Modelling and Comparison of Wormhole Routed Mesh and Torus Networks,” Proc. Ninth IASTED Int'l Conf. Parallel and Distributed Computing and Systems, 1997.
[14] D. Bäumer et al., "Framework Development for Large Systems," Comm. ACM, vol. 40, no. 10, Oct. 1997, pp. 52-59.
[15] R.E. Kessler and J.L. Schwarzmeier, "CRAY T3D: A New Dimension for Cray Research," Proc. COMPCON, pp. 176-182, Feb. 1993.
[16] L. Kleinrock, Queueing Systems, vol. 1.New York: John Wiley, 1975.
[17] J. Kim and C.R. Das, “Hypercube Communication Delay with Wormhole Routing,” IEEE Trans. Computers, vol. 43, no. 7, pp. 806-814, July 1994.
[18] D.H. Linder and J.C. Harden, "An Adaptive and Fault Tolerant Wormhole Routing Strategy for k-Ary n-Cubes," IEEE Trans. Computers, vol. 40, no. 1, pp. 2-12, Jan. 1991.
[19] X. Lin, P.K. Mckinley, and L.M. Lin, “The Message Flow Model for Routing in Wormhole-Routed Networks,” Proc. Int'l Conf. Parallel Processing, pp. 294-297, 1993.
[20] M. Noakes and W.J. Dally, “System Design of the J-Machine,” Proc. Advanced Research in VLSI, pp. 179-192, 1990.
[21] S. Nugent, "The iPSC/2 Direct-Connect Communications Technology," Proc. Third Conf. Hypercube Concurrent Computers and Applications, pp. 51-60, Jan. 1998.
[22] J. Riorda, An Introduction to Combinatorial Analysis, chapter 5, pp. 104-105. John Wiley&Sons, 1958.
[23] C. L. Seitz,“The cosmic cube,”CACM, vol. 28, pp. 22–33, Jan. 1985.
[24] C.L. Seitz, “The Hypercube Communication Chip,” Display File 5182:DF:85, Dept. of Computer Science, California Inst. of Tech nology, Mar. 1985.
[25] C. Su and K.G. Shin, “Adaptive Deadlock-Free Routing in Multicomputers Using One Extra Channel,” Proc. Int'l Conf. Parallel Processing, pp. 175-182, 1993.
[26] W.A. Whiteworth, Choice and Chance, p. 91. Cambridge Univ. Press, 1901.

Index Terms:
Multicomputers, interconnection networks, adaptive routing, deterministic routing, virtual channels, message latency, performance modeling.
Citation:
Mohamed Ould-Khaoua, "A Performance Model for Duato's Fully Adaptive Routing Algorithm in k$k$-Ary n$n$-Cubes," IEEE Transactions on Computers, vol. 48, no. 12, pp. 1297-1304, Dec. 1999, doi:10.1109/12.817384
Usage of this product signifies your acceptance of the Terms of Use.