The Limitations of Interconnections in Providing Communication Between an Array of Points

  • Haldun M. Ozaktas
  • Joseph W. Goodman
Part of the Frontiers of Computing Systems Research book series (FCSR, volume 2)


We present a comparative analysis of optical, normally conducting, re-peatered and superconducting interconnection performance in a very large scale digital computing environment. We derive tradeoff relations between delay, bandwidth and system size for each technology based on communication (wiring) volume and heat removal considerations and discuss their numerical and asymptotic properties. We show that the bisection-bandwidth and bisection-inverse delay products—which are appropriate measures of performance for communication limited applications—are bounded from above for normally conducting layouts, whereas they may be arbitrarily increased for repeatered, optical and superconducting layouts. The latter two are shown to suffer slower growth rate of signal delay with increasing system size in 3 dimensions than repeatered interconnections and thus offer the best performance. Based on the considerations of this paper, the comparison between optical and superconducting interconnections for same dimensional layouts reduces to a comparison of their respective communication energies.


Heat Removal Normal Conductor Optical Interconnection Connection Graph Increase System Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols


system radius in grid units


cross sectional area associated with each physical line


bit repetition rate along each edge of connection graph


vacuum velocity of light


capacitance per unit length


linear extent of a unit cell


linear extent of an element


linear extent of a transducer


Euclidean dimension of layout space


energy associated with each transmitted bit of information


functional form of connection flux distribution


functional form of line length distribution


height of dielectric




volume critical current density


surface critical current density


number of graph edges per element


number of wiring tracks per cell


length of a line in real units


inductance per unit length


order of moment of line length distribution


number of wiring layers


fractal dimension of layout


number of elements


interConnectivity (Rent exponent) of layout


maximum amount of power we can remove per cross section


length of a line in grid units


average connection length in grid units


mth moment of line length distribution


resistance per unit length


drive impedance


intrinsic delay of repeating devices


inverse of worst case signal delay


inverse of average signal delay


height of conductor


minimum temporal pulse width associated with each transmitted bit of information


device imposed component of T


line imposed component of T


propagation delay along a line


minimum pulse repetition interval along a line


nominal logic voltage level


width of conductor


transverse linear extent associated with each physical line


characteristic impedance


attenuation constant


number of parallel physical lines used to establish each graph edge


classical skin depth


permittivity of dielectric


coefficient for average connection length


optical wavelength


superconducting penetration depth


permeability of dielectric


resistivity of conductor


worst case signal delay


average signal delay


velocity of propagation


fundamental frequency component


optimal number of repeater stages

ζm, ζ’m, ζ”m

coefficients for the moments of line length distribution


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Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Haldun M. Ozaktas
    • 1
  • Joseph W. Goodman
    • 1
  1. 1.Information Systems Laboratory, Durand Building, Department of Electrical EngineeringStanford UniversityStanfordUSA

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