Wavelength Assignment Optimization in SDH over WDM Rings

  • Chung, Jibok (Electronics and Telecommunications Research Institute) ;
  • Lee, Heesang (Department of Industrial Engineering, Hankuk University of Foreign Studies) ;
  • Han, ChiMoon (Department of Electronic Engineering, Hankuk University of Foreign Studies)
  • Published : 2003.05.01

Abstract

In this study, we propose a mathematical model based on the graph theory for the wavelength assignment problem arising in the design of SDH (Synchronous Digital Hierarchy) over WDM (Wavelength Division Multiplexing) ring networks. We propose a branch- and -price algorithm to solve the suggested models effectively within reasonable time in realistic SDH over WDM ring networks. By exploiting the structure of ring networks, we developed a polynomial time algorithm for efficient column generation and a branching rule that conserves the structure of column generation. In a computer simulation study, the suggested approach can find the optimal solutions within reasonable time and show better performance than the existing heuristics.

Keywords

References

  1. R. K. Ahuja, T. L. Magnanti and J. B. Orlin, Network flows: theory, algorithms and applications, Prentice Hall Inc, 1992
  2. J. Birge and K. Murty eds., Mathematical Programming: State of the Art 1994, University of Michigan, 1994
  3. G. Ellinas et al., A Novel Wavelength Assignment Algorithm for 4-fiber WDM Self-Healing Rings, IEEE ICC '98, 1998 https://doi.org/10.1109/ICC.1998.682662
  4. O. Gerstel et al., 'Wavelength Assignment in a WDM Ring to Minimize Cost of Embedded SONET Rings, IEEE Infocom '98, 1998
  5. O. Gerstel et al., Combined WDM and SONET Network Design, IEEE Infocom '99, 1999 https://doi.org/10.1109/INFCOM.1999.751460
  6. M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, 1980
  7. J. Y. Hsiao et al., 'An Efficient Algorithms for Finding a Maximum Weighted 2-independent Set on Interval Graph, Information Processing Letters, No.43, 1992, 229-235 https://doi.org/10.1016/0020-0190(92)90216-I
  8. H. Lee and J. Chung, 'Wavelength Assignment Optimization in Uni-Directional WDM ring,' IE interface, Vol.13, No.4, 2000
  9. T. Lee et al., 'Optimal Routing and Wavelength Assignment in WDM Ring Networks,' IEEE JSAC, Vol.18, No.10, 2000, 2146-2154 https://doi.org/10.1109/49.887934
  10. Liu et al., Wavelength Assignment in WDM Rings to Minimize SONET ADMs, IEEE Infocom '00, 2000
  11. A. Mehrotra and M. A. Trick, 'A Column Generation Approach for Graph Coloring,' INFORMS Journal on Computing, 8, 1996, 344-354 https://doi.org/10.1287/ijoc.8.4.344
  12. H. Shiraz et al., 'Effective Wavelength Assignment Algorithms for Optimizing Design Cost in SONET/WDM Rings,' J. of Lightwave Technology, Vol.19, No.10, 2001, 1427-1439 https://doi.org/10.1109/50.956130
  13. T. E. Stern and K. Bala, Multiwavelength Optical Networks: A layered approach, Addison-Wesley, 1999
  14. A. Tucker, 'Matrix Characterization of Circular-Arc Graph,' Pacific J. of Mathematics, Vol.39, No.2, 1971, 535-545 https://doi.org/10.2140/pjm.1971.39.535
  15. A. Tucker, 'Coloring a Family of Circular Arcs,' SIAM J. Applied Math, 29(3), 1975, 493-502 https://doi.org/10.1137/0129040
  16. X. Yuan and A. Fulay, Wavelength Assignment to Minimize the Number of SONET ADMs in WDM Rings, IEEE ICC'02, 2002