Bubbles can make self-timed pipelines fast

  • Mark R. Greenstreet
  • Kenneth Steiglitz
Article

Abstract

We explore the practical limits on throughput imposed by timing in a long, self-timed, circulating pipeline (ring). We consider models with both fixed and random delays and derive exact results for pipelines where these delays are fixed or exponentially distributed random variables. We also give relationships that provide upper and lower bounds on throughput for any pipeline where the delays are independent random variables. In each of these cases, we show that the asymptotic processor utilization is independent of the length of the pipeline; thus, linear speedup is achieved. We present conditions under which this utilization approaches 100%.

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References

  1. 1.
    H.T. Kung, L.M. Ruane and D.W.L. Yen, “A Two-Level Pipelined Systolic Array for Convolution,”Proc. of the CMU Conf. on VLSI Systems and Computation, Pittsburgh, PA, 1981.Google Scholar
  2. 2.
    R.J. Lipton and D. Lopresti, “A Systolic Array for Rapid String Comparison,”Proc. of the 1985 Chapel Hill conf. on VLSI, Chapel Hill, NC, 1985.Google Scholar
  3. 3.
    S.D. Kugelmass and K. Steiglitz, “A Scalable Architecture for Lattice-Gas Simulations,”J. Computational Physics, vol. 84, 1989, pp. 311–325.CrossRefMATHGoogle Scholar
  4. 4.
    U. Frisch, B. Hasslacher and Y. Pomeau, “A Lattice Gas Automaton for the Navier-Stokes Equation,”Phys. Rev. Lett., vol. 56, 1986, pp. 1505–1508.CrossRefGoogle Scholar
  5. 5.
    C.L. Seitz, “System Timing,” inIntroduction to VLSI Systems, C.A. Mead and L.A. Conway, Reading, MA: Addison-Wesley, 1980, pp. 245–258.Google Scholar
  6. 6.
    I.E. Sutherland, “Micropipelines,”Communications of the ACM, vol. 32, June 1989.Google Scholar
  7. 7.
    D.L. Dill, S.M. Nowick and R.F. Sproull,Specification and Automatic Verification of Self-timed Queues, Technical Report CSL-TR-89-387, Computer Systems Laboratory, Stanford University, Stanford, CA, 1989.Google Scholar
  8. 8.
    R.E. Miller,Switching Theory, New York: Wiley, 1965.Google Scholar
  9. 9.
    M.R. Greenstreet, T.E. Williams and J. Staunstrup, “Self-Timed Iteration,”VLSI '87: Proc. of the Int. Conf. on VLSI, Vancouver, 1987.Google Scholar
  10. 10.
    W. Feller,An Introduction to Probability Theory and Its Applications, Vol. 1, New York: Wiley, 1968.Google Scholar
  11. 11.
    J. Kao, personal communication.Google Scholar
  12. 12.
    A.O. Allen,Probability, Statistics, and Queuing Theory, with Computer Science Applications, New York: Academic Press, 1978.Google Scholar
  13. 13.
    A.L. Fisher and H.T. Kung, “Synchronizing Large VLSI Processor Arrays,”IEEE Trans. on Computers, vol. C-34, 1985, pp. 734–740.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Mark R. Greenstreet
    • 1
  • Kenneth Steiglitz
    • 1
  1. 1.Department of Computer SciencePrinceton UniversityPrinceton

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