Analysis of k-ary n-cubes with dimension-ordered routing

K -ary n -cubes have been one of the most popular interconnection networks for practical multicomputers due to their ease of implementation and ability to exploit communication locality found in many parallel applications. This paper describes an analytical model for k -ary n -cubes with dimension-ordered routing. The main feature of the model is its ability to captures network performance when an arbitrary number of virtual channels are used to reduce message blocking. Simulation experiments reveal that the latency results predicted by the analytical model are in good agreement with those provided by the simulation model.

[1]  W.-J. Guan,et al.  An analytical model for wormhole routing in multicomputer interconnection networks , 1993, [1993] Proceedings Seventh International Parallel Processing Symposium.

[2]  William J. Dally,et al.  Performance Analysis of k-Ary n-Cube Interconnection Networks , 1987, IEEE Trans. Computers.

[3]  Bruno Ciciani,et al.  Performance evaluation of deterministic wormhole routing in k-ary n-cubes , 1998, Parallel Comput..

[4]  Seth Abraham,et al.  Performance-Based Constraints for Multidimensional Networks , 2000, IEEE Trans. Parallel Distributed Syst..

[5]  Joydeep Ghosh,et al.  A Comprehensive Analytical Model for Wormhole Routng in Multicomputer Systems , 1994, J. Parallel Distributed Comput..

[6]  R. E. Kessler,et al.  Cray T3D: a new dimension for Cray Research , 1993, Digest of Papers. Compcon Spring.

[7]  E. Anderson,et al.  Performance of the CRAY T3E Multiprocessor , 1997, ACM/IEEE SC 1997 Conference (SC'97).

[8]  A. A. Chein,et al.  A cost and speed model for k-ary n-cube wormhole routers , 1998 .

[9]  Krishnan Padmanabhan,et al.  Performance of Multicomputer Networks under Pin-out Constraints , 1991, J. Parallel Distributed Comput..

[10]  Sudhakar Yalamanchili,et al.  Interconnection Networks: An Engineering Approach , 2002 .

[11]  William J. Dally,et al.  Deadlock-Free Message Routing in Multiprocessor Interconnection Networks , 1987, IEEE Transactions on Computers.

[12]  Chita R. Das,et al.  Hypercube Communication Delay with Wormhole Routing , 1994, IEEE Trans. Computers.

[13]  William J. Dally,et al.  Virtual-channel flow control , 1990, [1990] Proceedings. The 17th Annual International Symposium on Computer Architecture.

[14]  Ronald I. Greenberg,et al.  Modeling and Comparison of Wormhole Routed Mesh and Torus Networks , 1997 .

[15]  Erol Gelenbe,et al.  Multiprocessor Performance , 1990, SIGMETRICS Perform. Evaluation Rev..

[16]  Anant Agarwal,et al.  Limits on Interconnection Network Performance , 1991, IEEE Trans. Parallel Distributed Syst..

[17]  Leonard Kleinrock,et al.  Theory, Volume 1, Queueing Systems , 1975 .

[18]  Mary K. Vernon,et al.  Performance Analysis of Mesh Interconnection Networks with Deterministic Routing , 1994, IEEE Trans. Parallel Distributed Syst..