Abstract

A new interconnection network for massively parallel computing is introduced. This network is called a hierarchal optical ring interconnection (HORN). The HORN consists of a single-hop, scalable, constant-degree, strictly nonblocking, fault-tolerant interconnection topology that uses wavelength-division multiple access to provide better utilization of the terahertz bandwidth offered by optics. The proposed optical network integrates the attractive features of hierarchical ring interconnections, e.g., a simple node interface, a constant node degree, better support for the locality of reference, and fault tolerance, with the advantages of optics. The HORN topology is presented, its architectural properties are analyzed, and an optical design methodology for it is described. Furthermore, a brief feasibility study of the HORN is conducted. The study shows that the topology is highly amenable to optical implementation with commercially available optical elements.

© 1997 Optical Society of America

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References

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  1. J. W. Goodman, F. J. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
    [CrossRef]
  2. S. P. Dandamudi, D. L. Eager, “Hierarchical interconnection networks for Multicomputer Systems,” IEEE Trans. Comput. 39, 786–797 (1990).
    [CrossRef]
  3. M. Holliday, M. Stumm, “Performance evaluation of hierarchical ring-based shared memory multiprocessors,” IEEE Trans. Comput. 43, 52–67 (1989).
    [CrossRef]
  4. Z. G. Vranesic, M. Stumm, D. M. Lewis, R. White, “Hector: a hierarchically structured shared-memory multiprocessor,” IEEE Comput. 28, 72–79 (1991).
    [CrossRef]
  5. B. E. A. Saleh, M. C. Teich, Fundamentals of photonics, (Wiley-Interscience, New York, 1991).
    [CrossRef]
  6. M. R. Feldman, C. C. Guest, T. J. Drabik, S. C. Esner, “Comparison between electrical and free-space optical interconnects for fine-grain processor arrays based on connection density capabilities,” Appl. Opt. 28, 3820–3829 (1989).
    [CrossRef] [PubMed]
  7. F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. C. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1665–1674 (1991).
    [CrossRef]
  8. A. Louri, H. Sung, “An optical multi-mesh hypercube: a scalable optical interconnection network for massively parallel computing,” J. Lightwave Technol. 12, 704–716 (1994).
    [CrossRef]
  9. A. D. McAulay, Optical Computer Architectures (Wiley Interscience, New York, 1991).
  10. A. Guha, J. Bristow, C. Sullivan, A. Husain, “Optical interconnections for massively parallel architectures,” Appl. Opt. 29, 1077–1093 (1990).
    [CrossRef] [PubMed]
  11. M. J. Murdocca, A Digital Design Methodology for Optical Computing (MIT Press, Cambridge, Mass., 1990).
  12. A. E. Willner, C. J. Chang-Hasnain, J. E. Leight “2-D WDM optical interconnections using multiple-wavelength VCSEL’s for simultaneous and reconfigurable communication among many planes,” IEEE Photon. Technol. Lett. 5, 838–841 (1993).
    [CrossRef]
  13. M. I. Irshid, M. Kavehrad, “A fully transparent fiber-optic ring architecture for WDM networks,” J. Lightwave Technol. 10, 101–108 (1992).
    [CrossRef]
  14. Y. Li, A. W. Lohmann, S. B. Rao, “Free-space optical mesh-connected bus networks using wavelength-division multiple access,” Appl. Opt. 32, 6425–6437 (1993).
    [CrossRef] [PubMed]
  15. P. W. Dowd, K. Bogineni, K. A. Aly, J. A. Perreult, “Hierarchical scalable photonic architectures for high-performance processor interconnection,” IEEE Trans. Comput. 42, 1105–1120 (1993).
    [CrossRef]
  16. L. G. Kazovsky, P. T. Poggiolini, “STARNET: a multi-gigabit-per-second optical LAN utilizing a passive WDM star,” J. Lightwave Technol. 11, 1009–1026 (1993).
    [CrossRef]
  17. J. Bannister, M. Gerla, M. Kovacevie, “An all-optical multifiber tree network,” J. Lightwave Technol. 11, 997–1008 (1993).
    [CrossRef]
  18. G. Bell, “Ultracomputers: a teraflop before its time,” Commun. ACM 35, 27–47 (1992).
    [CrossRef]
  19. D. A. Reed, H. D. Schwetman, “Cost-performance bounds for multicomputer networks,” IEEE Trans. Comput. 32, 83–95 (1983).
    [CrossRef]
  20. R. J. Berinato, “Acousto-optic tapped delay-line filter,” Appl. Opt. 32, 5797–5809 (1993).
    [CrossRef] [PubMed]
  21. R. B. Jenkins, B. D. Clymer, “Acousto-optic comparison switch for optical switching networks with analog addressing techniques,” Appl. Opt. 31, 5453–5463 (1992).
    [CrossRef] [PubMed]
  22. J. P. Powers, An Introduction to Fiber Optic Systems (Aksen, Homewood, Ill., 1993).
  23. G. M. Lundy, “Analyzing a CSMA/CD protocol through a systems of communicating machines specification,” IEEE Trans. Commun. 41, 447–450 (1993).
    [CrossRef]
  24. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley-Interscience, New York, 1992).
  25. “Electron components: optical semiconductor devices,” in A Data Sheet Pack for Optical Semiconductor Devices,” (NEC, May1995), pp. 1–200.
  26. V. Kumar, A. Grama, A. Gupta, G. Karypis, Introduction to Parallel Computing (Benjamin/Cummings, Redwood City, Calif., 1994).

1994 (1)

A. Louri, H. Sung, “An optical multi-mesh hypercube: a scalable optical interconnection network for massively parallel computing,” J. Lightwave Technol. 12, 704–716 (1994).
[CrossRef]

1993 (7)

Y. Li, A. W. Lohmann, S. B. Rao, “Free-space optical mesh-connected bus networks using wavelength-division multiple access,” Appl. Opt. 32, 6425–6437 (1993).
[CrossRef] [PubMed]

P. W. Dowd, K. Bogineni, K. A. Aly, J. A. Perreult, “Hierarchical scalable photonic architectures for high-performance processor interconnection,” IEEE Trans. Comput. 42, 1105–1120 (1993).
[CrossRef]

L. G. Kazovsky, P. T. Poggiolini, “STARNET: a multi-gigabit-per-second optical LAN utilizing a passive WDM star,” J. Lightwave Technol. 11, 1009–1026 (1993).
[CrossRef]

J. Bannister, M. Gerla, M. Kovacevie, “An all-optical multifiber tree network,” J. Lightwave Technol. 11, 997–1008 (1993).
[CrossRef]

A. E. Willner, C. J. Chang-Hasnain, J. E. Leight “2-D WDM optical interconnections using multiple-wavelength VCSEL’s for simultaneous and reconfigurable communication among many planes,” IEEE Photon. Technol. Lett. 5, 838–841 (1993).
[CrossRef]

R. J. Berinato, “Acousto-optic tapped delay-line filter,” Appl. Opt. 32, 5797–5809 (1993).
[CrossRef] [PubMed]

G. M. Lundy, “Analyzing a CSMA/CD protocol through a systems of communicating machines specification,” IEEE Trans. Commun. 41, 447–450 (1993).
[CrossRef]

1992 (3)

R. B. Jenkins, B. D. Clymer, “Acousto-optic comparison switch for optical switching networks with analog addressing techniques,” Appl. Opt. 31, 5453–5463 (1992).
[CrossRef] [PubMed]

M. I. Irshid, M. Kavehrad, “A fully transparent fiber-optic ring architecture for WDM networks,” J. Lightwave Technol. 10, 101–108 (1992).
[CrossRef]

G. Bell, “Ultracomputers: a teraflop before its time,” Commun. ACM 35, 27–47 (1992).
[CrossRef]

1991 (2)

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. C. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1665–1674 (1991).
[CrossRef]

Z. G. Vranesic, M. Stumm, D. M. Lewis, R. White, “Hector: a hierarchically structured shared-memory multiprocessor,” IEEE Comput. 28, 72–79 (1991).
[CrossRef]

1990 (2)

S. P. Dandamudi, D. L. Eager, “Hierarchical interconnection networks for Multicomputer Systems,” IEEE Trans. Comput. 39, 786–797 (1990).
[CrossRef]

A. Guha, J. Bristow, C. Sullivan, A. Husain, “Optical interconnections for massively parallel architectures,” Appl. Opt. 29, 1077–1093 (1990).
[CrossRef] [PubMed]

1989 (2)

1984 (1)

J. W. Goodman, F. J. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

1983 (1)

D. A. Reed, H. D. Schwetman, “Cost-performance bounds for multicomputer networks,” IEEE Trans. Comput. 32, 83–95 (1983).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley-Interscience, New York, 1992).

Aly, K. A.

P. W. Dowd, K. Bogineni, K. A. Aly, J. A. Perreult, “Hierarchical scalable photonic architectures for high-performance processor interconnection,” IEEE Trans. Comput. 42, 1105–1120 (1993).
[CrossRef]

Athale, R. A.

J. W. Goodman, F. J. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Bannister, J.

J. Bannister, M. Gerla, M. Kovacevie, “An all-optical multifiber tree network,” J. Lightwave Technol. 11, 997–1008 (1993).
[CrossRef]

Bell, G.

G. Bell, “Ultracomputers: a teraflop before its time,” Commun. ACM 35, 27–47 (1992).
[CrossRef]

Berinato, R. J.

Bogineni, K.

P. W. Dowd, K. Bogineni, K. A. Aly, J. A. Perreult, “Hierarchical scalable photonic architectures for high-performance processor interconnection,” IEEE Trans. Comput. 42, 1105–1120 (1993).
[CrossRef]

Bristow, J.

Chang-Hasnain, C. J.

A. E. Willner, C. J. Chang-Hasnain, J. E. Leight “2-D WDM optical interconnections using multiple-wavelength VCSEL’s for simultaneous and reconfigurable communication among many planes,” IEEE Photon. Technol. Lett. 5, 838–841 (1993).
[CrossRef]

Clymer, B. D.

Dandamudi, S. P.

S. P. Dandamudi, D. L. Eager, “Hierarchical interconnection networks for Multicomputer Systems,” IEEE Trans. Comput. 39, 786–797 (1990).
[CrossRef]

Dowd, P. W.

P. W. Dowd, K. Bogineni, K. A. Aly, J. A. Perreult, “Hierarchical scalable photonic architectures for high-performance processor interconnection,” IEEE Trans. Comput. 42, 1105–1120 (1993).
[CrossRef]

Drabik, T. J.

Eager, D. L.

S. P. Dandamudi, D. L. Eager, “Hierarchical interconnection networks for Multicomputer Systems,” IEEE Trans. Comput. 39, 786–797 (1990).
[CrossRef]

Esener, S. C.

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. C. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1665–1674 (1991).
[CrossRef]

Esner, S. C.

Feldman, M. R.

Gerla, M.

J. Bannister, M. Gerla, M. Kovacevie, “An all-optical multifiber tree network,” J. Lightwave Technol. 11, 997–1008 (1993).
[CrossRef]

Goodman, J. W.

J. W. Goodman, F. J. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Grama, A.

V. Kumar, A. Grama, A. Gupta, G. Karypis, Introduction to Parallel Computing (Benjamin/Cummings, Redwood City, Calif., 1994).

Guest, C. C.

Guha, A.

Gupta, A.

V. Kumar, A. Grama, A. Gupta, G. Karypis, Introduction to Parallel Computing (Benjamin/Cummings, Redwood City, Calif., 1994).

Holliday, M.

M. Holliday, M. Stumm, “Performance evaluation of hierarchical ring-based shared memory multiprocessors,” IEEE Trans. Comput. 43, 52–67 (1989).
[CrossRef]

Husain, A.

Irshid, M. I.

M. I. Irshid, M. Kavehrad, “A fully transparent fiber-optic ring architecture for WDM networks,” J. Lightwave Technol. 10, 101–108 (1992).
[CrossRef]

Jenkins, R. B.

Karypis, G.

V. Kumar, A. Grama, A. Gupta, G. Karypis, Introduction to Parallel Computing (Benjamin/Cummings, Redwood City, Calif., 1994).

Kavehrad, M.

M. I. Irshid, M. Kavehrad, “A fully transparent fiber-optic ring architecture for WDM networks,” J. Lightwave Technol. 10, 101–108 (1992).
[CrossRef]

Kazovsky, L. G.

L. G. Kazovsky, P. T. Poggiolini, “STARNET: a multi-gigabit-per-second optical LAN utilizing a passive WDM star,” J. Lightwave Technol. 11, 1009–1026 (1993).
[CrossRef]

Kiamilev, F.

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. C. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1665–1674 (1991).
[CrossRef]

Kovacevie, M.

J. Bannister, M. Gerla, M. Kovacevie, “An all-optical multifiber tree network,” J. Lightwave Technol. 11, 997–1008 (1993).
[CrossRef]

Krishnamoorthy, A. V.

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. C. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1665–1674 (1991).
[CrossRef]

Kumar, V.

V. Kumar, A. Grama, A. Gupta, G. Karypis, Introduction to Parallel Computing (Benjamin/Cummings, Redwood City, Calif., 1994).

Kung, S. Y.

J. W. Goodman, F. J. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Lee, S. H.

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. C. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1665–1674 (1991).
[CrossRef]

Leight, J. E.

A. E. Willner, C. J. Chang-Hasnain, J. E. Leight “2-D WDM optical interconnections using multiple-wavelength VCSEL’s for simultaneous and reconfigurable communication among many planes,” IEEE Photon. Technol. Lett. 5, 838–841 (1993).
[CrossRef]

Leonberger, F. J.

J. W. Goodman, F. J. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Lewis, D. M.

Z. G. Vranesic, M. Stumm, D. M. Lewis, R. White, “Hector: a hierarchically structured shared-memory multiprocessor,” IEEE Comput. 28, 72–79 (1991).
[CrossRef]

Li, Y.

Lohmann, A. W.

Louri, A.

A. Louri, H. Sung, “An optical multi-mesh hypercube: a scalable optical interconnection network for massively parallel computing,” J. Lightwave Technol. 12, 704–716 (1994).
[CrossRef]

Lundy, G. M.

G. M. Lundy, “Analyzing a CSMA/CD protocol through a systems of communicating machines specification,” IEEE Trans. Commun. 41, 447–450 (1993).
[CrossRef]

Marchand, P.

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. C. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1665–1674 (1991).
[CrossRef]

McAulay, A. D.

A. D. McAulay, Optical Computer Architectures (Wiley Interscience, New York, 1991).

Murdocca, M. J.

M. J. Murdocca, A Digital Design Methodology for Optical Computing (MIT Press, Cambridge, Mass., 1990).

Perreult, J. A.

P. W. Dowd, K. Bogineni, K. A. Aly, J. A. Perreult, “Hierarchical scalable photonic architectures for high-performance processor interconnection,” IEEE Trans. Comput. 42, 1105–1120 (1993).
[CrossRef]

Poggiolini, P. T.

L. G. Kazovsky, P. T. Poggiolini, “STARNET: a multi-gigabit-per-second optical LAN utilizing a passive WDM star,” J. Lightwave Technol. 11, 1009–1026 (1993).
[CrossRef]

Powers, J. P.

J. P. Powers, An Introduction to Fiber Optic Systems (Aksen, Homewood, Ill., 1993).

Rao, S. B.

Reed, D. A.

D. A. Reed, H. D. Schwetman, “Cost-performance bounds for multicomputer networks,” IEEE Trans. Comput. 32, 83–95 (1983).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of photonics, (Wiley-Interscience, New York, 1991).
[CrossRef]

Schwetman, H. D.

D. A. Reed, H. D. Schwetman, “Cost-performance bounds for multicomputer networks,” IEEE Trans. Comput. 32, 83–95 (1983).
[CrossRef]

Stumm, M.

Z. G. Vranesic, M. Stumm, D. M. Lewis, R. White, “Hector: a hierarchically structured shared-memory multiprocessor,” IEEE Comput. 28, 72–79 (1991).
[CrossRef]

M. Holliday, M. Stumm, “Performance evaluation of hierarchical ring-based shared memory multiprocessors,” IEEE Trans. Comput. 43, 52–67 (1989).
[CrossRef]

Sullivan, C.

Sung, H.

A. Louri, H. Sung, “An optical multi-mesh hypercube: a scalable optical interconnection network for massively parallel computing,” J. Lightwave Technol. 12, 704–716 (1994).
[CrossRef]

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of photonics, (Wiley-Interscience, New York, 1991).
[CrossRef]

Vranesic, Z. G.

Z. G. Vranesic, M. Stumm, D. M. Lewis, R. White, “Hector: a hierarchically structured shared-memory multiprocessor,” IEEE Comput. 28, 72–79 (1991).
[CrossRef]

White, R.

Z. G. Vranesic, M. Stumm, D. M. Lewis, R. White, “Hector: a hierarchically structured shared-memory multiprocessor,” IEEE Comput. 28, 72–79 (1991).
[CrossRef]

Willner, A. E.

A. E. Willner, C. J. Chang-Hasnain, J. E. Leight “2-D WDM optical interconnections using multiple-wavelength VCSEL’s for simultaneous and reconfigurable communication among many planes,” IEEE Photon. Technol. Lett. 5, 838–841 (1993).
[CrossRef]

Appl. Opt. (5)

Commun. ACM (1)

G. Bell, “Ultracomputers: a teraflop before its time,” Commun. ACM 35, 27–47 (1992).
[CrossRef]

IEEE Comput. (1)

Z. G. Vranesic, M. Stumm, D. M. Lewis, R. White, “Hector: a hierarchically structured shared-memory multiprocessor,” IEEE Comput. 28, 72–79 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. E. Willner, C. J. Chang-Hasnain, J. E. Leight “2-D WDM optical interconnections using multiple-wavelength VCSEL’s for simultaneous and reconfigurable communication among many planes,” IEEE Photon. Technol. Lett. 5, 838–841 (1993).
[CrossRef]

IEEE Trans. Commun. (1)

G. M. Lundy, “Analyzing a CSMA/CD protocol through a systems of communicating machines specification,” IEEE Trans. Commun. 41, 447–450 (1993).
[CrossRef]

IEEE Trans. Comput. (4)

D. A. Reed, H. D. Schwetman, “Cost-performance bounds for multicomputer networks,” IEEE Trans. Comput. 32, 83–95 (1983).
[CrossRef]

P. W. Dowd, K. Bogineni, K. A. Aly, J. A. Perreult, “Hierarchical scalable photonic architectures for high-performance processor interconnection,” IEEE Trans. Comput. 42, 1105–1120 (1993).
[CrossRef]

S. P. Dandamudi, D. L. Eager, “Hierarchical interconnection networks for Multicomputer Systems,” IEEE Trans. Comput. 39, 786–797 (1990).
[CrossRef]

M. Holliday, M. Stumm, “Performance evaluation of hierarchical ring-based shared memory multiprocessors,” IEEE Trans. Comput. 43, 52–67 (1989).
[CrossRef]

J. Lightwave Technol. (5)

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. C. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1665–1674 (1991).
[CrossRef]

A. Louri, H. Sung, “An optical multi-mesh hypercube: a scalable optical interconnection network for massively parallel computing,” J. Lightwave Technol. 12, 704–716 (1994).
[CrossRef]

L. G. Kazovsky, P. T. Poggiolini, “STARNET: a multi-gigabit-per-second optical LAN utilizing a passive WDM star,” J. Lightwave Technol. 11, 1009–1026 (1993).
[CrossRef]

J. Bannister, M. Gerla, M. Kovacevie, “An all-optical multifiber tree network,” J. Lightwave Technol. 11, 997–1008 (1993).
[CrossRef]

M. I. Irshid, M. Kavehrad, “A fully transparent fiber-optic ring architecture for WDM networks,” J. Lightwave Technol. 10, 101–108 (1992).
[CrossRef]

Proc. IEEE (1)

J. W. Goodman, F. J. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Other (7)

J. P. Powers, An Introduction to Fiber Optic Systems (Aksen, Homewood, Ill., 1993).

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley-Interscience, New York, 1992).

“Electron components: optical semiconductor devices,” in A Data Sheet Pack for Optical Semiconductor Devices,” (NEC, May1995), pp. 1–200.

V. Kumar, A. Grama, A. Gupta, G. Karypis, Introduction to Parallel Computing (Benjamin/Cummings, Redwood City, Calif., 1994).

M. J. Murdocca, A Digital Design Methodology for Optical Computing (MIT Press, Cambridge, Mass., 1990).

A. D. McAulay, Optical Computer Architectures (Wiley Interscience, New York, 1991).

B. E. A. Saleh, M. C. Teich, Fundamentals of photonics, (Wiley-Interscience, New York, 1991).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Diagram of a HORN (4, 3). PE’s are indicated by the black-filled circles and switching nodes are indicated by the gray-filled circles. All hierarchical groups are labeled with the notation H (n, g), where n identifies the hierarchy and g identifies a unique group at hierarchy n.

Fig. 2
Fig. 2

Wavelength assignment in which there are 22 wavelengths available for remote communications. All rings of all hierarchies are assigned a unique wavelength. The local wavelength assignment for the H (1, 11) ring is shown with all other H (1) rings assigned in the same manner.

Fig. 3
Fig. 3

Steps employed to route a packet from the source PE to the destination PE. Packets always travel in a counterclockwise direction.

Fig. 4
Fig. 4

Fault-tolerance aspects shown for the rings of the upper hierarchies of the HORN: (a) Normal operation of the ring during which only the primary ring is being utilized. (b) Operation when a link in a ring breaks. The ring wraps in on itself, with the primary and remote rings now both utilized. (c) Operation when two links in a ring breaks such that two separate rings are produced.

Fig. 5
Fig. 5

Time-slot allocation for local communication. The vertical axis shows the wavelengths and the horizontal axis shows the time slots. One time cycle is shown. During one cycle each PE can send on all wavelengths. TS, time slot; P, PE.

Fig. 6
Fig. 6

Time-slot allocation for remote communication. The vertical axis shows the wavelengths and the horizontal axis shows the time slots. One time cycle is shown. During one cycle each PE can send on all wavelengths.

Fig. 7
Fig. 7

Graph of the minimum power budget required for different numbers of processing nodes in a ring.

Fig. 8
Fig. 8

Graph of the dynamic range plotted versus the processing nodes for different values of the power-coupling loss from the bus to a node (x).

Fig. 9
Fig. 9

Graphs for one-to-all broadcasting, all-to-all broadcasting, single-node accumulation, and one-to-all personalized communication. (a) Graph of the communication delay plotted versus N (number of processing nodes) for a variety of Δ s (the time duration of a single time slot) in a one-to-all broadcast for the HORN TDMA. (b) Graph of the communication delay plotted versus N for a variety of Δ s in an all-to-all broadcast, a single-node accumulation, and a one-to-all personalized communication for the HORN TDMA.

Fig. 10
Fig. 10

Electro-optical components of the HORN: (a) Composition of a PE. The label Rx’s represents an array of fixed, tuned receivers, and the label Tx represents a single tunable transmitter. EDFA’s are shown within dotted lines because they need to be used only if the power budget calculations of a single ring are not met. (b) Composition of a switching node.

Tables (2)

Tables Icon

Table 1 Routing Table for the Example AOTF Configuration Shown in Fig. 1

Tables Icon

Table 2 Cost Scalability Expressions for Components of the HORNa

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

N1=MaxH1, i  i.
Λ=N.
S=N1H1, 1+1H1, 1H2, 1++1N.
10 log10PinPout=αN,
ηring=x21-xN-210-αN/10=10N-2 log101-x+20 log10 x-αNdecibels.
xoptimum2N.
ηring,optimum1e22N210-αN/10=-2.6+6 log2 N+αNdecibels.
Power Budget=Ptxdecibels-Pmindecibels>2.6+6 log2N+αNdecibles=ηring,optimum,
Pmax=P0x210-2α/10,
Pmin=P0x21-xN-210-Nα/10.
DR=10N-2α/101-xN-2=N-2-10 log101-x+αdecibels.
Tone-to-allTDMATC,
TC=N*Δs.
Tone-to-allTDMA=TC2.
TTDMA=TC.

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