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
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.
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.
S.D. Kugelmass and K. Steiglitz, “A Scalable Architecture for Lattice-Gas Simulations,”J. Computational Physics, vol. 84, 1989, pp. 311–325.
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.
C.L. Seitz, “System Timing,” inIntroduction to VLSI Systems, C.A. Mead and L.A. Conway, Reading, MA: Addison-Wesley, 1980, pp. 245–258.
I.E. Sutherland, “Micropipelines,”Communications of the ACM, vol. 32, June 1989.
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.
R.E. Miller,Switching Theory, New York: Wiley, 1965.
M.R. Greenstreet, T.E. Williams and J. Staunstrup, “Self-Timed Iteration,”VLSI '87: Proc. of the Int. Conf. on VLSI, Vancouver, 1987.
W. Feller,An Introduction to Probability Theory and Its Applications, Vol. 1, New York: Wiley, 1968.
J. Kao, personal communication.
A.O. Allen,Probability, Statistics, and Queuing Theory, with Computer Science Applications, New York: Academic Press, 1978.
A.L. Fisher and H.T. Kung, “Synchronizing Large VLSI Processor Arrays,”IEEE Trans. on Computers, vol. C-34, 1985, pp. 734–740.
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This work was supported in part by NSF Grant MIP-8705454, U.S. Army Research Office—Durham Contract DAAG29-85-K-0191, and DARPA Contract N00014-82-K-0549.
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Greenstreet, M.R., Steiglitz, K. Bubbles can make self-timed pipelines fast. J VLSI Sign Process Syst Sign Image Video Technol 2, 139–148 (1990). https://doi.org/10.1007/BF00935211
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DOI: https://doi.org/10.1007/BF00935211