Abstract

We consider the problem of traffic grooming in wavelength-division-multiplexing rings with all-to-all uniform traffic. Our objective is to minimize the total number of electronic add-drop multiplexers (ADMs) required. We derive explicit optimal solutions for two special cases: one with a traffic granularity of 4 and the other with 16. When the traffic granularity is equal to 4, we also show that the minimum number of ADMs can be achieved either with the minimum number of wavelengths, a result that was conjectured in earlier research [J. Lightwave Technol. <b>18,</b> 2 (2000)], or with ADMs uniformly placed among nodes. Our results here are among the few in which analytically tractable optimal solutions are obtained for the traffic grooming problem. Our solutions provide insight as well as valuable tools for evaluating other approximate and heuristic algorithms.

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  1. R. Ramaswami and K. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, Los Altos, Calif., 1998).
  2. R. Berry and E. Modiano, "Reducing electronic multiplexing costs in SONET/WDM rings with dynamic changing traffic," IEEE J. Sel. Areas Commun. 18, 1961-1971 (2000).
  3. A. Chiu and E. Modiano, "Reducing electronic multiplexing costs in unidirectional SONET/WDM ring networks via efficient traffic grooming," in Proceedings of Globecom (Institute of Electrical and Electronics Engineers, New York, 1998), Vol. 1, pp. 322-327.
  4. A. Chiu and E. Modiano, "Traffic grooming algorithms for reducing electronic multiplexing costs in WDM ring networks," J. Lightwave Technol. 18, 2-12 (2000).
  5. O. Gerstel, P. Lin, and G. Sasaki, "Wavelength assignment in a WDM ring to minimize the cost of embedded SONET rings," in Proceedings of Infocom (Institute of Electrical and Electronics Engineers, New York, 1998), Vol. 1, pp. 94-101.
  6. O. Gerstel, P. Lin, and G. Sasaki, "Combined WDM and SONET network design," in Proceedings of Infocom (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2, pp. 734-743.
  7. O. Gerstel, R. Ramaswami, and G. Sasaki, "Cost effective traffic grooming in WDM rings," in Proceedings of Infocom (Institute of Electrical and Electronics Engineers, New York, 1998), Vol. 1, pp. 69-77.
  8. J. Q. Hu, "Traffic grooming in WDM ring networks: a linear programming solution," White Paper (Sycamore Networks, Inc., Chelmsford, Mass., 2001).
  9. C. Qiao, X. Zhang, and L. Zhou, "Scheduling all-to-all connections in WDM rings," in All-Optical Communication Systems: Architecture, Control, and Network Issues II, R. A. Cryan and J. M. Senior, eds., Proc. SPIE 2919, 218-229 (1996).
  10. G. Sasaki, O. Gerstel, and R. Ramaswami, "A WDM ring network for incremental traffic," presented at the Thirty-Sixth Annual Allerton Conference on Communication, Control, and Computing, Monticello, Ill., 23-25 Sept. 1998.
  11. J. Simmons, E. Goldstein, and A. Saleh, "On the value of wavelength add-drop in WDM rings with uniform traffic," in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 361-362.
  12. J. Simmons, E. Goldstein, and A. Saleh, "Quantifying the benefits of wavelength add-drop WDM rings with distance independent and dependent traffic," J. Lightwave Technol. 17, 48-57 (1999).
  13. X. Zhang and C. Qiao, "Scheduling in unidirectional WDM rings and its extensions," in All-Optical Communication Systems: Architecture, Control, and Network Issues III, J. M. Senior, R. A. Cryan, and C. M. Qiao, eds., Proc. SPIE 3230, 208-219 (1997).
  14. X. Zhang and C. Qiao, "An effective and comprehensive solution to traffic grooming and wavelength assignment in WDM rings," in All-Optical Networking: Architecture, Control, and Management Issues, J. M. Senior and C. M. Qiao, eds., Proc. SPIE 3531, 221-232 (1998).
  15. J. Q. Hu, "Optimal traffic grooming for WDM rings with all-to-all uniform traffic," White Paper (Sycamore Networks, Inc., Chelmsford, Mass., 2001).

IEEE J. Sel. Areas Commun.

R. Berry and E. Modiano, "Reducing electronic multiplexing costs in SONET/WDM rings with dynamic changing traffic," IEEE J. Sel. Areas Commun. 18, 1961-1971 (2000).

J. Lightwave Technol.

A. Chiu and E. Modiano, "Traffic grooming algorithms for reducing electronic multiplexing costs in WDM ring networks," J. Lightwave Technol. 18, 2-12 (2000).

J. Simmons, E. Goldstein, and A. Saleh, "Quantifying the benefits of wavelength add-drop WDM rings with distance independent and dependent traffic," J. Lightwave Technol. 17, 48-57 (1999).

Proceedings of Globecom

A. Chiu and E. Modiano, "Reducing electronic multiplexing costs in unidirectional SONET/WDM ring networks via efficient traffic grooming," in Proceedings of Globecom (Institute of Electrical and Electronics Engineers, New York, 1998), Vol. 1, pp. 322-327.

Proceedings of Infocom

O. Gerstel, P. Lin, and G. Sasaki, "Combined WDM and SONET network design," in Proceedings of Infocom (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2, pp. 734-743.

O. Gerstel, R. Ramaswami, and G. Sasaki, "Cost effective traffic grooming in WDM rings," in Proceedings of Infocom (Institute of Electrical and Electronics Engineers, New York, 1998), Vol. 1, pp. 69-77.

Other

J. Q. Hu, "Traffic grooming in WDM ring networks: a linear programming solution," White Paper (Sycamore Networks, Inc., Chelmsford, Mass., 2001).

C. Qiao, X. Zhang, and L. Zhou, "Scheduling all-to-all connections in WDM rings," in All-Optical Communication Systems: Architecture, Control, and Network Issues II, R. A. Cryan and J. M. Senior, eds., Proc. SPIE 2919, 218-229 (1996).

G. Sasaki, O. Gerstel, and R. Ramaswami, "A WDM ring network for incremental traffic," presented at the Thirty-Sixth Annual Allerton Conference on Communication, Control, and Computing, Monticello, Ill., 23-25 Sept. 1998.

J. Simmons, E. Goldstein, and A. Saleh, "On the value of wavelength add-drop in WDM rings with uniform traffic," in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 361-362.

O. Gerstel, P. Lin, and G. Sasaki, "Wavelength assignment in a WDM ring to minimize the cost of embedded SONET rings," in Proceedings of Infocom (Institute of Electrical and Electronics Engineers, New York, 1998), Vol. 1, pp. 94-101.

X. Zhang and C. Qiao, "Scheduling in unidirectional WDM rings and its extensions," in All-Optical Communication Systems: Architecture, Control, and Network Issues III, J. M. Senior, R. A. Cryan, and C. M. Qiao, eds., Proc. SPIE 3230, 208-219 (1997).

X. Zhang and C. Qiao, "An effective and comprehensive solution to traffic grooming and wavelength assignment in WDM rings," in All-Optical Networking: Architecture, Control, and Management Issues, J. M. Senior and C. M. Qiao, eds., Proc. SPIE 3531, 221-232 (1998).

J. Q. Hu, "Optimal traffic grooming for WDM rings with all-to-all uniform traffic," White Paper (Sycamore Networks, Inc., Chelmsford, Mass., 2001).

R. Ramaswami and K. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, Los Altos, Calif., 1998).

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