Skip to main content
SpringerLink
Log in

A Lagrangian-Relaxation Based Network Profit Optimization For Mesh SONET-Over-WDM Networks

  • Published:
Photonic Network Communications Aims and scope Submit manuscript

Abstract

In Wavelength Division Multiplexing (WDM) networks, the huge capacity of wavelength channels is generally much larger than the bandwidth requirement of individual traffic streams from network users. Traffic grooming techniques aggregate low-bandwidth traffic streams onto high-bandwidth wavelength channels. In this paper, we study the optimization problem of grooming the static traffic in mesh Synchronous Optical Network (SONET) over WDM networks. The problem is formulated as a constrained integer linear programming problem and an innovative optimization objective is developed as network profit optimization. The routing cost in the SONET and WDM layers as well as the revenue generated by accepting SONET traffic demands are modelled. Through the optimization process, SONET traffic demands will be selectively accepted based on the profit (i.e., the excess of revenue over network cost) they generate. Consiering the complexity of the network optimization problem, a decomposition approach using Lagrangian relaxation is proposed. The overall relaxed dual problem is decomposed into routing and wavelength assignment and SONET traffic routing sub-problems. The subgradient approach is used to optimize the derived dual function by updating the Lagrange multipliers. To generate a feasible network routing scheme, a heuristic algorithm is proposed based on the dual solution. A systematic approach to obtain theoretical performance bounds is presented for an arbitrary topology mesh network. This is the first time that such theoretical performance bounds are obtained for SONET traffic grooming in mesh topology networks. The optimization results of sample networks indicate that the roposed algorithm achieves good sub-optimal solutions. Finally, the influence of various network parameters is studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Ramaswami, K. Sivarajan, Optical Networks: A Practical Perspective 2nd ed., (Morgan Kaufmann Publishers, 2001).

  2. R. Dutta G. N. Rouskas (Jan. 2000) ArticleTitleA survey of virtual topology design algorithms for wavelength routed optical networks Optical Networks Magazine 1 IssueID1 73–89

    Google Scholar 

  3. E. Leonardi M. Mellia M. A. Marsan (Jan. 2000) ArticleTitleAlgorithms for the logical topology design in WDM all-optical networks Optical Networks Magazine 1 IssueID1 35–46

    Google Scholar 

  4. K. Zhu H. Zhu B. Mukherjee (March/April. 2003) ArticleTitleTraffic engineering in multigranularity heterogeneous optical WDM mesh networks through dynamic traffic grooming IEEE Network 17 IssueID2 8–15

    Google Scholar 

  5. K. Zhu H. Zang B. Mukherjee (Sept. 2003) ArticleTitleA comprehensive study on next-generation optical grooming switches IEEE Journal on Selected Areas in Communications 21 IssueID7 1173–1186 Occurrence Handle10.1109/JSAC.2003.815683

    Article  Google Scholar 

  6. T. Cinkler (March/April. 2003) ArticleTitleTraffic and λ grooming IEEE Network 17 IssueID2 16–21 Occurrence Handle10.1109/MNET.2003.1188282

    Article  Google Scholar 

  7. R. Dutta G. N. Rouskas (Nov./Dec. 2002) ArticleTitleTraffic grooming in WDM networks: Past and future IEEE Network 16 IssueID6 46–56 Occurrence Handle10.1109/MNET.2002.1081765

    Article  Google Scholar 

  8. E. Modiano P. J. Lin (July. 2001) ArticleTitleTraffic grooming in WDM networks IEEE Communications Magazine 39 IssueID7 124–129 Occurrence Handle10.1109/35.933446

    Article  Google Scholar 

  9. A. Chiu E. H. Modiano (Jan. 2000) ArticleTitleTraffic grooming algorithms for reducing electronic multiplexing costs in WDM ring networks IEEE/OSA Journal of Lightwave Technology 18 IssueID1 2–12 Occurrence Handle10.1109/50.818901

    Article  Google Scholar 

  10. H. Zhu H. Zang K. Zhu B. Mukherjee (April. 2003) ArticleTitleA novel generic graph model for traffic grooming in heterogeneous WDM mesh networks IEEE/ACM Transaction on Networking 11 IssueID2 285–299

    Google Scholar 

  11. C. Ou K. Zhu J. Zhang H. Zhu B. Mukherjee H. Zang L. H. Sahasrabuddhe (Jan. 2004) ArticleTitleTraffic grooming for survivable WDM networks: Dedicated protection Journal of Optical Networking 3 IssueID1 50–74 Occurrence Handle10.1364/JON.3.000050

    Article  Google Scholar 

  12. C. Ou K. Zhu H. Zang L. H. Sahasrabuddhe B. Mukherjee (Nov. 2003) ArticleTitleTraffic grooming for survivable WDM networks: Shared protection IEEE Journal on Selected Areas in Communications 21 IssueID9 1367–1383

    Google Scholar 

  13. C. Xin, C. Qiao, Performance analysis of multi-hop traffic grooming in mesh WDM optical networks, Proceedings. of ICCCN’03 (Dallas, TX, USA, Oct. 2003), pp.237–242.

  14. C. Xin, C. Qiao, S. Dixit, Traffic grooming in mesh WDM optical networks: Performance analysis, Proceedings. of Globecom’03 (San Francisco, CA, USA, Dec. 2003), vol. 7, pp. 3732–3736.

  15. E. Oki, K. Shiomoto, M. Katayama, W. Imajuku, N. Yamanaka, Performance of dynamic multi-layer routing schemes in IP + optical networks, Proceedings. of 2003 Workshop on High Performance Switching and Routing (HPSR’03) (Torino, Italy, June 2003), pp. 233–238.

  16. H. Zhu H. Zang K. Zhu B. Mukherjee (May/June. 2003) ArticleTitleDynamic traffic grooming in WDM mesh networks using a Novel Graph Model Optical Networks Magazine 4 IssueID3 65–75

    Google Scholar 

  17. R. Srinivasan A. K. Somani (Oct. 2004) ArticleTitleAnalysis of optical networks with heterogeneous grooming architectures IEEE/ACM Transaction on Networking 12 IssueID5 931–943

    Google Scholar 

  18. R. Srinivasan A. K. Somani (March. 2003) ArticleTitleDynamic routing in WDM grooming architectures Photonic Network Communications 5 IssueID2 123–135 Occurrence Handle10.1023/A:1022108108724

    Article  Google Scholar 

  19. S. Thiagarajan A. K. Somani (May/June. 2001) ArticleTitleCapacity fairness of WDM networks with grooming capabilities Optical Networks Magazine 2 IssueID2 24–32

    Google Scholar 

  20. S. Zhang, B. Ramamurthy, Dynamic traffic grooming algorithms for reconfigurable SONET over WDM networks, IEEE Journal on Selected Areas in Communications, 21(7) Sept. 2003), pp. 1165–1172.

    Google Scholar 

  21. R. Dutta G. N. Rouskas (Jan. 2002) ArticleTitleOn optimal traffic grooming in WDM rings IEEE Journal on Selected Areas in Communications 20 IssueID1 110–121 Occurrence Handle10.1109/49.974666

    Article  Google Scholar 

  22. T. Song H. Zhang Y. Guo X. Zheng (March. 2004) ArticleTitleOptimal design of WDM ring networks to minimize SDH ADMs Journal of Optical Communications 24 IssueID3 144–148

    Google Scholar 

  23. X. Zhang C. Qiao (Oct. 2000) ArticleTitleAn effective and comprehensive approach for traffic grooming and wavelength assignment in SONET/WDM rings IEEE/ACM Transaction on Networking 8 IssueID5 608–617 Occurrence Handle10.1109/90.879347

    Article  Google Scholar 

  24. O. Gerstel R. Ramaswami G. H. Sasaki (Oct. 2000) ArticleTitleCost-effective traffic grooming in WDM rings IEEE/ACM Transaction on Networking 8 IssueID5 618–630 Occurrence Handle10.1109/90.879348

    Article  Google Scholar 

  25. J. Hu (Jan. 2002) ArticleTitleOptical traffic grooming in wavelength-division-multiplexing rings with all-to-all uniform traffic Journal of Optical Networking 1 IssueID1 32–42

    Google Scholar 

  26. W. Cho J. Wang B. Mukherjee (July. 2001) ArticleTitleImproved approaches for cost-effective traffic grooming in WDM ring networks: Uniform-traffic case Photonic Network Communications 3 IssueID3 245–254 Occurrence Handle10.1023/A:1011451314905

    Article  Google Scholar 

  27. J. Wang W. Cho V. R. Vemuri B. Mukherjee (Nov. 2001) ArticleTitleImproved approaches for cost-effective traffic grooming in WDM ring networks: ILP formulations and single-hop and multihop connections IEEE/OSA Journal of Lightwave Technology 19 IssueID1 1645–1653 Occurrence Handle10.1109/50.964064

    Article  Google Scholar 

  28. B. Chen, G. N. Rouskas, R. Dutta, Traffic grooming in WDM ring networks with the min–max objective, Proceedings. of the Third International IFIP-TC6 Networking Conference (Networking’04), Lecture Notes in Computer Science, vol. 3042 (Athens, Greece, May 2004), pp. 174–185.

  29. A. R. B. Billah B. Wang A. A. S. Awwal (Sept. 2003) ArticleTitleEffective traffic grooming algorithms in SONET/WDM ring networks Photonic Network Communications 6 IssueID2 119–138 Occurrence Handle10.1023/A:1024779029796

    Article  Google Scholar 

  30. J. Bermond, D. Coudert, Traffic grooming in unidirectional WDM ring networks using design theory, Proceedings. of ICC ’03 (Anchorage, AL, USA, May 2003), vol. 2, pp. 1402–1406.

  31. R. Dutta, S. Huang, G. N. Rouskas, On optimal traffic grooming in elemental network topologies, Proceedings. of 4th Annual Optical Networking and Communications Conference (OptiComm’03) (Dallas, TX, USA, Oct. 2003), pp. 13–24.

  32. R. Dutta, S. Huang, G. N. Rouskas, Traffic grooming in path, star and tree networks: complexity, bounds and algorithms, Proceedings. of SIGMETRICS’03 (San Diego, CA, USA, June 2003), pp. 298–299.

  33. L. A. Cox SuffixJr. J. Sanchez (May/June. 2001) ArticleTitleCost savings from optimized packing and grooming of optical circuits: mesh versus ring comparisons Optical Networks Magazine 2 IssueID2 72–90

    Google Scholar 

  34. K. Zhu B. Mukherjee (Jan. 2002) ArticleTitleTraffic grooming in an optical WDM mesh network IEEE Journal on Selected Areas in Communications 20 IssueID1 122–133 Occurrence Handle10.1109/49.974667

    Article  Google Scholar 

  35. D. Zhemin M. Hamdi (Nov./Dec. 2003) ArticleTitleTraffic grooming in optical WDM mesh networks using the blocking island paradigm Optical Networks Magazine 4 IssueID6 7–15

    Google Scholar 

  36. Billah A.R.B., Wang B., Awwal A.A.S. () Multicast traffic grooming in WDM optical mesh networks, Proceedings. of Globecom’03 (San Francisco, CA, USA, Dec. 2003), vol. 5, pp. 2755–2760.

  37. H. Wen R. He L. Li S. Wang (April. 2003) ArticleTitleDynamic traffic-grooming algorithms in wavelength-division-multiplexing mesh networks Journal of Optical Networking 2 IssueID4 100–111

    Google Scholar 

  38. M. Ali, D. Elie-Dit-Cosaque, Routing of 40Gb/s traffic in heterogeneous optical networks, Proceedings. of ICC’03 (Anchorage, AL, USA, May 2003), vol. 2, pp. 1391–1396.

  39. I. Widjaja, I. Saniee, L. Qian, A. Elwalid, J. Ellson, L. Cheng, A new approach for automatic grooming of SONET circuits to optical express links, Proceedings. of ICC’03, (Anchorage, AL, USA, May 2003), vol. 2, pp. 1407–1411.

  40. K. Zhu B. Mukherjee (March/April. 2003) ArticleTitleA review of traffic grooming in WDM optical networks: architectures and challenges optical networks magazine 4 IssueID2 55–64

    Google Scholar 

  41. A. Gencata B. Mukherjee (April. 2003) ArticleTitleVirtual-topology adaptation for WDM mesh networks under dynamic traffic IEEE/ACM Transaction on Networking 11 IssueID2 236–247 Occurrence Handle10.1109/TNET.2003.810319

    Article  Google Scholar 

  42. K. Zhu H. Zhu B. Mukherjee (March/April. 2003) ArticleTitleTraffic engineering in multigranularity heterogeneous optical WDM mesh networks through dynamic traffic grooming IEEE Network 17 IssueID2 8–15

    Google Scholar 

  43. V. R. Konda, T. Y. Chow, Algorithm for traffic grooming in optical networks to minimize the number of transceivers, Proceedings. of 2001 IEEE Workshop on High Performance Switching and Routing (HPSR’01) (Dallas, TX, USA, May 2001),pp. 218–221.

  44. J. Hu (Nov. 2002) ArticleTitlegrooming in wavelength-division-multiplexing ring networks: A linear programming solution Journal of Optical Networking 1 IssueID11 397–408

    Google Scholar 

  45. A. Lardies R. Gupta R. A. Patterson (May/June. 2001) ArticleTitleTraffic grooming in a multi-layer network optical networks magazine 2 IssueID2 91–99

    Google Scholar 

  46. P. Prathombutr, J. Stach, E. K. Park, An algorithm for traffic grooming in WDM optical mesh networks with multiple objectives, Proceedings. of ICCCN’03 (Dallas, TX, USA, Oct. 2003), pp. 405–411.

  47. Y. Zhang, H. Liu, A lagrangian relaxation approach to the maximizing-number-of-connection problem in WDM networks, Proceedings. of Workshop on High Performance Switching and Routing (HPSR’03) (Turin, Italy, June 2003), pp. 23–28.

  48. Y. Zhang, Oliver Yang, An effective approach to the connection routing problem of all-optical wavelength routing DWDM networks with wavelength conversion capability, Proceedings. of ICC’03 (Anchorage, AL, USA, May 2003), vol. 2, pp. 1370–1374.

  49. M. E. M. Saad, Z. Luo, A lagrangian decomposition approach for the routing and wavelength assignment in multifibre WDM networks, Proceedings. of Globecom’02 (Taipei, Taiwan, Nov. 2002), vol. 3, pp. 2818–2822.

  50. D. P. Bertsekas, Nonlinear Programming (Athena Scientific, 1999).

  51. Z. Patrocinio Jr., G. R. Mateus, A lagrangian-based heuristic for traffic grooming in WDM optical networks, Proceedings. of Globecom’03 (San Francisco, CA, USA, Dec. 2003), vol. 5, pp. 2767–2771.

  52. M. Sridharan A. K. Somani M. V. Salapaka (April. 2001) ArticleTitleApproaches for capacity and revenue optimization in survivable WDM networks Journal of High Speed Networks 10 IssueID2 109–125

    Google Scholar 

  53. G. Xiao Y. W. Leung (Aug. 1999) ArticleTitleAlgorithms for allocating wavelength converters in all-optical networks IEEE/ACM Transaction on Networking 7 IssueID4 545–557 Occurrence Handle10.1109/90.793026

    Article  Google Scholar 

  54. I. Chlamtac A. Farago T. Zhang (June. 1996) ArticleTitleLightpath (Wavelength) routing in large WDM networks IEEE Journal on Selected Areas in Communications 14 IssueID5 909–913 Occurrence Handle10.1109/49.510914

    Article  Google Scholar 

  55. D. P. Bertsekas, Network Optimization Continuous and Discrete Models (Athena Scientific, 1998).

  56. Y. Zhang O. Yang H. Liu (Nov. 2004) ArticleTitleA lagrangian relaxation and subgradient approach for the routing and wavelength assignment problem in WDM networks IEEE Journal on Selected Areas in Communications 22 IssueID9 1752–1765 Occurrence Handle10.1109/JSAC.2004.833851

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CCNR (Computer Communication Network Research) Lab, School of Information Technology and Engineering, University of Ottawa, Ottawa, K1N 6N5, Ont, Canada

    Yiming Zhang & Oliver W. W. Yang

  2. Communications Research Centre Canada, Ottawa, K2H 8S2, Ont, Canada

    Jing Wu & Michel Savoie

Authors
  1. Yiming Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Oliver W. W. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Michel Savoie
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oliver W. W. Yang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Y., Wu, J., Yang, O.W.W. et al. A Lagrangian-Relaxation Based Network Profit Optimization For Mesh SONET-Over-WDM Networks. Photon Netw Commun 10, 155–178 (2005). https://doi.org/10.1007/s11107-005-2481-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11107-005-2481-5

Keywords

Search

Navigation