A General Performance Model for Multistage Interconnection Networks

In this paper we analyze the general case of Multistage Interconnection Networks (MINs), made of k × k switches with finite, infinite or zero length buffers (unbuffered). The exact solution of the steady state distribution of the first stage is derived for all cases. We use this to get an approximation for the steady state distributions in the second stage and beyond. In the case of unbuffered switches we reach the known exact solution for all the stages of the MIN. Our results are validated by extensive simulations.

[1]  Daniel M. Dias,et al.  Analysis and Simulation of Buffered Delta Networks , 1981, IEEE Transactions on Computers.

[2]  Reinhard Lüling,et al.  On the communication throughput of buffered multistage interconnection networks , 1996, SPAA '96.

[3]  Marc Snir,et al.  The Performance of Multistage Interconnection Networks for Multiprocessors , 1983, IEEE Transactions on Computers.

[4]  Janak H. Patel.  Performance of Processor-Memory Interconnections for Multiprocessors , 1981, IEEE Transactions on Computers.

[5]  Paul G. Spirakis,et al.  Queueing delays in buffered multistage interconnection networks , 2018, SIGMETRICS '87.

[6]  Alan Weiss,et al.  The Distribution of Waiting Times in Clocked Multistage Interconnection Networks , 1988, IEEE Trans. Computers.

[7]  Ralph Grishman,et al.  The NYU Ultracomputer—Designing an MIMD Shared Memory Parallel Computer , 1983, IEEE Transactions on Computers.

[8]  Paul G. Spirakis,et al.  The performance of multistage interconnection networks with finite buffers , 1990, SIGMETRICS '90.

[9]  G. Jack Lipovski,et al.  Banyan networks for partitioning multiprocessor systems , 1973, ISCA '73.

[10]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[11]  Kevin P. McAuliffe,et al.  The IBM Research Parallel Processor Prototype (RP3): Introduction and Architecture , 1985, ICPP.

[12]  R.R. Kock.  Increasing the size of a network by a constant factor can increase performance by more than a constant factor , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[13]  Arif Merchant,et al.  A Markov chain approximation for the analysis of banyan networks , 1991, SIGMETRICS '91.

[14]  Thomas G. Robertazzi,et al.  The Performance of Multistage Interconnection Networks for Multiprocessors , 1993 .