Delay analysis of the N-cube network
In this paper, we analyze the delay of an average message going through an arbitrary link of the N-cube. We view each link as an M/M/1 queue and find analytic recursive relations for the arrival rate of messages at an arbitrary link. Then, we calculate the delay per link as a function of the message generation rate at the processor. We investigate two model of communication. The first, uniform communication where each processor communicate with any other processor with the same probability. The second is clustered communication, where neighboring processors communicate more than distant processors do. Finally, we investigate the effect of adding one more link at each node of the cube (Folded Hypercube) on the delay and the maximum number of hops.
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- [All78]A. O. Allen, Probability, Statistics, and Queueing Theory, Academic Press, 1978.Google Scholar
- [Bat80]K. E. Batcher, “Design of a Massively Parallel Processor,” Trans. on Computers, Vol. C-29,N9, Sept. 1980, pp. 836–840.Google Scholar
- [Fox85]G. Fox, The Performance of the Caltech Hypercube in Scientific Calculations, Caltech Report CALT-68-1298, Caltech, 1985.Google Scholar
- [HwB84]K. Hwang and F. A. Briggs, Computer Architecture and Parallel Processing, McGraw-Hill, 1984.Google Scholar
- [Kle76a]L. Kleinrock, Queueing Systems, Volume 1: Theory, John Wiley and Sons, 1976.Google Scholar
- [Kle76b]L. Kleinrock, Queueing Systems, Volume 2: Computer Applications, John Wiley and Sons, 1976.Google Scholar
- [KuS82]D. J. Kuck and R. A. Stokes, “The Burroughs Scientific Processor (BSP),” IEEE Transactions on Computers, Vol. C-31, May 1982, pp. 363–376.Google Scholar
- [LaE89]S. Latif and A. El-Amawy, “On Folded Hypercubes,” Proc. of International Conference on Parallel Processing, 1989.Google Scholar
- [Ncu86]NCUBE Corp., NCUBE Handbook, version 1.0, NCUBE Corp., Beaverton, Oregon, 1986.Google Scholar