Performance Modelling of Torus Interconnection Networks with Deep Buffers

Abstract Analytical models of deterministic routing in wormhole-switched networks have been widely reported in the literature. However, all of these models have assumed no, or neglectable, buffers at each switching element of the network. This paper proposes a new analytical model for wormhole-switched torus with finite buffers and multiple virtual channels. The validity of the model has been demonstrated by comparing analytical results with those obtained from simulation experiments.

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

[2]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[3]  Randolph Nelson,et al.  Probability, Stochastic Processes, and Queueing Theory , 1995 .

[4]  William J. Dally,et al.  The Reliable Router: A Reliable and High-Performance Communication Substrate for Parallel Computers , 1994, PCRCW.

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

[6]  Demetres D. Kouvatsos,et al.  Performance modelling and evaluation of heterogeneous networks , 2005, Perform. Evaluation.

[7]  Philip Heidelberger,et al.  Blue Gene/L torus interconnection network , 2005, IBM J. Res. Dev..

[9]  Gaetano Zanghirati,et al.  A Cray T3E implementation of a parallel stochastic dynamic assets and liabilities management model , 2000, Parallel Comput..

[10]  Hamid Sarbazi-Azad,et al.  Performance modeling and evaluation of high-performance parallel and distributed systems , 2005, Perform. Evaluation.

[11]  William J. Dally,et al.  Principles and Practices of Interconnection Networks , 2004 .

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

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

[14]  Hamid Sarbazi-Azad,et al.  Design and performance of networks for super-, cluster-, and grid-computing: Part I , 2005, J. Parallel Distributed Comput..

[15]  Hamid Sarbazi-Azad Performance analysis of wormhole routing in multicomputer interconnection networks , 2001 .

[16]  José E. Moreira,et al.  Blue Gene/L programming and operating environment , 2005, IBM J. Res. Dev..

[17]  Chita R. Das,et al.  Performance Analysis of Finite-Buffered Asynchronous Multistage Interconnection Networks , 1996, IEEE Trans. Parallel Distributed Syst..

[18]  Leonard Kleinrock,et al.  An analytical model for wormhole routing with finite size input buffers , 1997 .

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

[20]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[21]  Randolph D. Nelson,et al.  Probability, stochastic processes, and queueing theory - the mathematics of computer performance modeling , 1995 .

[22]  Hamid Sarbazi-Azad,et al.  Analysis of k-ary n-cubes with dimension-ordered routing , 2003, Future Gener. Comput. Syst..

[23]  Mohamed Ould-Khaoua,et al.  Prediction of communication delay in torus networks under multiple time-scale correlated traffic , 2005, Perform. Evaluation.

[24]  Hamid Sarbazi-Azad,et al.  A Performance Model of Software-based Deadlock Recovery Routing Algorithm in Hypercubes , 2005, Parallel Process. Lett..