Abstract

The ever-increasing Internet Protocol (IP) traffic volume has finally brought to light the high inefficiency of current wavelength-routed over rigid-grid optical networks in matching the client layer requirements. Such an issue results in the deployment of large-size, expensive, and power-consuming IP/Multi-Protocol Label Switching (MPLS) layers to perform the required grooming/aggregation functionality. To deal with this problem, the emerging flexgrid technology, allowing for reduced-size frequency grids (usually referred to as frequency slots), has recently attracted much attention among network operators, component and equipment suppliers, and the research community. In this paper, we tackle the multilayer IP/MPLS-over-flexgrid optimization problem. To this end, an integer linear programing formulation and a greedy randomized adaptive search procedure (GRASP) metaheuristic are provided. Using GRASP, we analyze the cost implications that a set of frequency slot widths have on the capital expenditure investments required to deploy such a multilayer network. For the sake of a compelling analysis, exhaustive numerical experiments are carried out considering a set of realistic network topologies, network equipment costs, and traffic instances. Results show that investments in optical equipment capable of operating under slot widths of 12.5 GHz, or even 25 GHz, are more appropriate, given the expected traffic evolution.

© 2012 OSA

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  1. M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, 2009.
    [CrossRef]
  2. M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, “Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Commun. Mag., vol. 48, no. 8, pp. 138–145, 2010.
    [CrossRef]
  3. Finisar, “Programmable narrow-band filtering using the WaveShaper 1000E and WaveShaper 4000E,” White Paper, 2011[Online]. Available: http://www.finisar.com.
  4. ITU-T Recommendation G.694.1, “Spectral grids for WDM applications: DWDM frequency grid,” 2012 [Online]. Available: http://www.itu.int/rec/T-REC-G.694.1-201202-I/en.
  5. K. Christodoulopoulos, I. Tomkos, and E. Varvarigos, “Elastic bandwidth allocation in flexible OFDM based optical networks,” J. Lightwave Technol., vol. 29, no. 9, pp. 1354–1366, May2011.
    [CrossRef]
  6. Y. Wang, X. Cao, and Y. Pan, “A study of the routing and spectrum allocation in spectrum-sliced elastic optical path networks,” in IEEE Int. Conf. on Computer Communications (INFOCOM), Apr. 2011.
  7. L. Velasco, M. Klinkowski, M. Ruiz, and J. Comellas, “Modeling the routing and spectrum allocation problem for future elastic optical networks,” Photonic Network Commun., 2012 [Online]. Available: http://dx.doi.org/10.1007/s11107-012-0378-7.
  8. X. Wan, L. Wang, N. Hua, H. Zhang, and X. Zheng, “Dynamic routing and spectrum assignment in flexible optical path networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, JWA55.
  9. K. Christodoulopoulos, I. Tomkos, and E. Varvarigos, “Dynamic bandwidth allocation in flexible OFDM-based networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, OTuI5.
  10. M. Klinkowski and K. Walkowiak, “Routing and spectrum assignment in spectrum sliced elastic optical path network,” IEEE Commun. Lett., vol. 15, no. 8, pp. 884–886, Dec.2011.
    [CrossRef]
  11. J. Santamaría, O. Cordón, S. Damas, R. Martí, and R. Palma, “GRASP and path relinking hybridizations for the point matching-based image registration problem,” J. Heuristics, vol. 18, no. 1, pp. 169–192, 2012.
    [CrossRef]
  12. H. Höller, B. Melián, and S. Voß, “Applying the pilot method to improve VNS and GRASP metaheuristics for the design of SDH/WDM networks,” Eur. J. Oper. Res., vol. 191, no. 3, pp. 691–704, Dec.2008.
    [CrossRef]
  13. O. Pedrola, M. Ruiz, L. Velasco, D. Careglio, O. González de Dios, and J. Comellas, “A GRASP with path-relinking heuristic for the survivable IP/MPLS-over-WSON multi-layer network optimization problem,” Comput. Oper. Res., 2012 [Online]. Available: http://dx.doi.org/10.1016/j.cor.2011.10.026.
  14. M. G. C. Resende and C. C. Ribeiro, “Greedy randomized adaptive search procedures: Advances and applications,” in Handbook of Metaheuristics, M. Gendreau and J. Y. Potvin, Eds., 2nd ed.Springer Science+Business Mediapp, 2010, pp. 29–63.
  15. O. Ribal and A. Morea, “Cost-efficiency of mixed 10-40-100 Gb/s networks and elastic optical networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, OTuI4.
  16. M. Ruiz, O. Pedrola, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “Survivable IP/MPLS-over-WSON multi-layer network optimization,” J. Opt. Commun. Netw., vol. 3, no. 8, pp. 629–640, Aug.2011.
    [CrossRef]
  17. K. Zhu and B. Mukherjee, “Traffic grooming in an optical WDM mesh network,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 122–133, Jan.2002.
    [CrossRef]
  18. B. Chen, G. Rouskas, and R. Dutta, “Clustering methods for hierarchical traffic grooming in large-scale mesh WDM networks,” J. Opt. Commun. Netw., vol. 2, no. 8, pp. 502–514, Aug.2010.
    [CrossRef]
  19. S. Koo, G. Sahin, and S. Subramaniam, “Dynamic LSP routing in IP/MPLS-over-WDM networks,” IEEE J. Sel. Areas Commun., vol. 24, no. 12, pp. 45–55, Dec.2006.
    [CrossRef]
  20. H. Höller and S. Voß, “A heuristic approach for combined equipment-planning and routing in multi-layer SDH/WDM networks,” Eur. J. Oper. Res., vol. 171, no. 3, pp. 787–796, June2006.
    [CrossRef]
  21. M. Pióro and D. Medhi, Routing, Flow, and Capacity Design in Communication and Computer Networks. Morgan Kaufmann Publishers, 2004.
  22. X. Zhang, F. Shen, L. Wang, S. Wang, L. Li, and H. Luo, “Two-layer mesh network optimization based on inter-layer decomposition,” Photonic Network Commun., vol. 21, no. 3, pp. 310–320, 2011.
    [CrossRef]
  23. IBM ILOG CPLEX, 2012 [Online]. Available: http://www-01.ibm.com/software/integration/optimization/cplex/.
  24. P. Hansen and N. Mladenovic, “Variable neighborhood search: principles and applications,” Eur. J. Oper. Res., vol. 130, no. 3, pp. 449–467, May2001.
    [CrossRef]
  25. STRONGEST: Scalable, Tunable and Resilient Optical Networks Guaranteeing Extremely-high Speed Transport, 2012 [Online]. Available: http://www.ict-strongest.eu/.
  26. E. Martins and M. Pascoal, “A new implementation of Yen’s ranking loopless paths algorithm,” 4OR: Q. J. Oper. Res., vol. 1, no. 2, pp. 121–133, 2003.
    [CrossRef]
  27. P. Festa, J. F. Gonçalves, M. G. C. Resende, and R. M. A. Silva, “Automatic tuning of GRASP with path-relinking heuristics with a biased random-key genetic algorithm,” in Experimental Algorithms (Vol. 6049 of Lecture Notes in Computer Science). 2010, pp. 338–349.
  28. O. Pedrola, A. Castro, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “CAPEX study for grid dependent multi-layer IP/MPLS-over-EON using relative BV-WSS costs,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2012, NTu2J.7.

2012 (3)

L. Velasco, M. Klinkowski, M. Ruiz, and J. Comellas, “Modeling the routing and spectrum allocation problem for future elastic optical networks,” Photonic Network Commun., 2012 [Online]. Available: http://dx.doi.org/10.1007/s11107-012-0378-7.

J. Santamaría, O. Cordón, S. Damas, R. Martí, and R. Palma, “GRASP and path relinking hybridizations for the point matching-based image registration problem,” J. Heuristics, vol. 18, no. 1, pp. 169–192, 2012.
[CrossRef]

O. Pedrola, M. Ruiz, L. Velasco, D. Careglio, O. González de Dios, and J. Comellas, “A GRASP with path-relinking heuristic for the survivable IP/MPLS-over-WSON multi-layer network optimization problem,” Comput. Oper. Res., 2012 [Online]. Available: http://dx.doi.org/10.1016/j.cor.2011.10.026.

2011 (4)

M. Klinkowski and K. Walkowiak, “Routing and spectrum assignment in spectrum sliced elastic optical path network,” IEEE Commun. Lett., vol. 15, no. 8, pp. 884–886, Dec.2011.
[CrossRef]

X. Zhang, F. Shen, L. Wang, S. Wang, L. Li, and H. Luo, “Two-layer mesh network optimization based on inter-layer decomposition,” Photonic Network Commun., vol. 21, no. 3, pp. 310–320, 2011.
[CrossRef]

K. Christodoulopoulos, I. Tomkos, and E. Varvarigos, “Elastic bandwidth allocation in flexible OFDM based optical networks,” J. Lightwave Technol., vol. 29, no. 9, pp. 1354–1366, May2011.
[CrossRef]

M. Ruiz, O. Pedrola, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “Survivable IP/MPLS-over-WSON multi-layer network optimization,” J. Opt. Commun. Netw., vol. 3, no. 8, pp. 629–640, Aug.2011.
[CrossRef]

2010 (2)

B. Chen, G. Rouskas, and R. Dutta, “Clustering methods for hierarchical traffic grooming in large-scale mesh WDM networks,” J. Opt. Commun. Netw., vol. 2, no. 8, pp. 502–514, Aug.2010.
[CrossRef]

M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, “Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Commun. Mag., vol. 48, no. 8, pp. 138–145, 2010.
[CrossRef]

2009 (1)

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, 2009.
[CrossRef]

2008 (1)

H. Höller, B. Melián, and S. Voß, “Applying the pilot method to improve VNS and GRASP metaheuristics for the design of SDH/WDM networks,” Eur. J. Oper. Res., vol. 191, no. 3, pp. 691–704, Dec.2008.
[CrossRef]

2006 (2)

S. Koo, G. Sahin, and S. Subramaniam, “Dynamic LSP routing in IP/MPLS-over-WDM networks,” IEEE J. Sel. Areas Commun., vol. 24, no. 12, pp. 45–55, Dec.2006.
[CrossRef]

H. Höller and S. Voß, “A heuristic approach for combined equipment-planning and routing in multi-layer SDH/WDM networks,” Eur. J. Oper. Res., vol. 171, no. 3, pp. 787–796, June2006.
[CrossRef]

2003 (1)

E. Martins and M. Pascoal, “A new implementation of Yen’s ranking loopless paths algorithm,” 4OR: Q. J. Oper. Res., vol. 1, no. 2, pp. 121–133, 2003.
[CrossRef]

2002 (1)

K. Zhu and B. Mukherjee, “Traffic grooming in an optical WDM mesh network,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 122–133, Jan.2002.
[CrossRef]

2001 (1)

P. Hansen and N. Mladenovic, “Variable neighborhood search: principles and applications,” Eur. J. Oper. Res., vol. 130, no. 3, pp. 449–467, May2001.
[CrossRef]

Cao, X.

Y. Wang, X. Cao, and Y. Pan, “A study of the routing and spectrum allocation in spectrum-sliced elastic optical path networks,” in IEEE Int. Conf. on Computer Communications (INFOCOM), Apr. 2011.

Careglio, D.

O. Pedrola, M. Ruiz, L. Velasco, D. Careglio, O. González de Dios, and J. Comellas, “A GRASP with path-relinking heuristic for the survivable IP/MPLS-over-WSON multi-layer network optimization problem,” Comput. Oper. Res., 2012 [Online]. Available: http://dx.doi.org/10.1016/j.cor.2011.10.026.

M. Ruiz, O. Pedrola, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “Survivable IP/MPLS-over-WSON multi-layer network optimization,” J. Opt. Commun. Netw., vol. 3, no. 8, pp. 629–640, Aug.2011.
[CrossRef]

O. Pedrola, A. Castro, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “CAPEX study for grid dependent multi-layer IP/MPLS-over-EON using relative BV-WSS costs,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2012, NTu2J.7.

Castro, A.

O. Pedrola, A. Castro, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “CAPEX study for grid dependent multi-layer IP/MPLS-over-EON using relative BV-WSS costs,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2012, NTu2J.7.

Chen, B.

Christodoulopoulos, K.

K. Christodoulopoulos, I. Tomkos, and E. Varvarigos, “Elastic bandwidth allocation in flexible OFDM based optical networks,” J. Lightwave Technol., vol. 29, no. 9, pp. 1354–1366, May2011.
[CrossRef]

K. Christodoulopoulos, I. Tomkos, and E. Varvarigos, “Dynamic bandwidth allocation in flexible OFDM-based networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, OTuI5.

Comellas, J.

L. Velasco, M. Klinkowski, M. Ruiz, and J. Comellas, “Modeling the routing and spectrum allocation problem for future elastic optical networks,” Photonic Network Commun., 2012 [Online]. Available: http://dx.doi.org/10.1007/s11107-012-0378-7.

O. Pedrola, M. Ruiz, L. Velasco, D. Careglio, O. González de Dios, and J. Comellas, “A GRASP with path-relinking heuristic for the survivable IP/MPLS-over-WSON multi-layer network optimization problem,” Comput. Oper. Res., 2012 [Online]. Available: http://dx.doi.org/10.1016/j.cor.2011.10.026.

Cordón, O.

J. Santamaría, O. Cordón, S. Damas, R. Martí, and R. Palma, “GRASP and path relinking hybridizations for the point matching-based image registration problem,” J. Heuristics, vol. 18, no. 1, pp. 169–192, 2012.
[CrossRef]

Damas, S.

J. Santamaría, O. Cordón, S. Damas, R. Martí, and R. Palma, “GRASP and path relinking hybridizations for the point matching-based image registration problem,” J. Heuristics, vol. 18, no. 1, pp. 169–192, 2012.
[CrossRef]

Dutta, R.

Fernández-Palacios, J. P.

M. Ruiz, O. Pedrola, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “Survivable IP/MPLS-over-WSON multi-layer network optimization,” J. Opt. Commun. Netw., vol. 3, no. 8, pp. 629–640, Aug.2011.
[CrossRef]

O. Pedrola, A. Castro, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “CAPEX study for grid dependent multi-layer IP/MPLS-over-EON using relative BV-WSS costs,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2012, NTu2J.7.

Festa, P.

P. Festa, J. F. Gonçalves, M. G. C. Resende, and R. M. A. Silva, “Automatic tuning of GRASP with path-relinking heuristics with a biased random-key genetic algorithm,” in Experimental Algorithms (Vol. 6049 of Lecture Notes in Computer Science). 2010, pp. 338–349.

Finisar,

Finisar, “Programmable narrow-band filtering using the WaveShaper 1000E and WaveShaper 4000E,” White Paper, 2011[Online]. Available: http://www.finisar.com.

Gonçalves, J. F.

P. Festa, J. F. Gonçalves, M. G. C. Resende, and R. M. A. Silva, “Automatic tuning of GRASP with path-relinking heuristics with a biased random-key genetic algorithm,” in Experimental Algorithms (Vol. 6049 of Lecture Notes in Computer Science). 2010, pp. 338–349.

González de Dios, O.

O. Pedrola, M. Ruiz, L. Velasco, D. Careglio, O. González de Dios, and J. Comellas, “A GRASP with path-relinking heuristic for the survivable IP/MPLS-over-WSON multi-layer network optimization problem,” Comput. Oper. Res., 2012 [Online]. Available: http://dx.doi.org/10.1016/j.cor.2011.10.026.

Hansen, P.

P. Hansen and N. Mladenovic, “Variable neighborhood search: principles and applications,” Eur. J. Oper. Res., vol. 130, no. 3, pp. 449–467, May2001.
[CrossRef]

Hirano, A.

M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, “Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Commun. Mag., vol. 48, no. 8, pp. 138–145, 2010.
[CrossRef]

Höller, H.

H. Höller, B. Melián, and S. Voß, “Applying the pilot method to improve VNS and GRASP metaheuristics for the design of SDH/WDM networks,” Eur. J. Oper. Res., vol. 191, no. 3, pp. 691–704, Dec.2008.
[CrossRef]

H. Höller and S. Voß, “A heuristic approach for combined equipment-planning and routing in multi-layer SDH/WDM networks,” Eur. J. Oper. Res., vol. 171, no. 3, pp. 787–796, June2006.
[CrossRef]

Hua, N.

X. Wan, L. Wang, N. Hua, H. Zhang, and X. Zheng, “Dynamic routing and spectrum assignment in flexible optical path networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, JWA55.

Jinno, M.

M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, “Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Commun. Mag., vol. 48, no. 8, pp. 138–145, 2010.
[CrossRef]

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, 2009.
[CrossRef]

Junyent, G.

M. Ruiz, O. Pedrola, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “Survivable IP/MPLS-over-WSON multi-layer network optimization,” J. Opt. Commun. Netw., vol. 3, no. 8, pp. 629–640, Aug.2011.
[CrossRef]

O. Pedrola, A. Castro, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “CAPEX study for grid dependent multi-layer IP/MPLS-over-EON using relative BV-WSS costs,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2012, NTu2J.7.

Klinkowski, M.

L. Velasco, M. Klinkowski, M. Ruiz, and J. Comellas, “Modeling the routing and spectrum allocation problem for future elastic optical networks,” Photonic Network Commun., 2012 [Online]. Available: http://dx.doi.org/10.1007/s11107-012-0378-7.

M. Klinkowski and K. Walkowiak, “Routing and spectrum assignment in spectrum sliced elastic optical path network,” IEEE Commun. Lett., vol. 15, no. 8, pp. 884–886, Dec.2011.
[CrossRef]

Koo, S.

S. Koo, G. Sahin, and S. Subramaniam, “Dynamic LSP routing in IP/MPLS-over-WDM networks,” IEEE J. Sel. Areas Commun., vol. 24, no. 12, pp. 45–55, Dec.2006.
[CrossRef]

Kozicki, B.

M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, “Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Commun. Mag., vol. 48, no. 8, pp. 138–145, 2010.
[CrossRef]

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, 2009.
[CrossRef]

Li, L.

X. Zhang, F. Shen, L. Wang, S. Wang, L. Li, and H. Luo, “Two-layer mesh network optimization based on inter-layer decomposition,” Photonic Network Commun., vol. 21, no. 3, pp. 310–320, 2011.
[CrossRef]

Luo, H.

X. Zhang, F. Shen, L. Wang, S. Wang, L. Li, and H. Luo, “Two-layer mesh network optimization based on inter-layer decomposition,” Photonic Network Commun., vol. 21, no. 3, pp. 310–320, 2011.
[CrossRef]

Martí, R.

J. Santamaría, O. Cordón, S. Damas, R. Martí, and R. Palma, “GRASP and path relinking hybridizations for the point matching-based image registration problem,” J. Heuristics, vol. 18, no. 1, pp. 169–192, 2012.
[CrossRef]

Martins, E.

E. Martins and M. Pascoal, “A new implementation of Yen’s ranking loopless paths algorithm,” 4OR: Q. J. Oper. Res., vol. 1, no. 2, pp. 121–133, 2003.
[CrossRef]

Matsuoka, S.

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, 2009.
[CrossRef]

Medhi, D.

M. Pióro and D. Medhi, Routing, Flow, and Capacity Design in Communication and Computer Networks. Morgan Kaufmann Publishers, 2004.

Melián, B.

H. Höller, B. Melián, and S. Voß, “Applying the pilot method to improve VNS and GRASP metaheuristics for the design of SDH/WDM networks,” Eur. J. Oper. Res., vol. 191, no. 3, pp. 691–704, Dec.2008.
[CrossRef]

Mladenovic, N.

P. Hansen and N. Mladenovic, “Variable neighborhood search: principles and applications,” Eur. J. Oper. Res., vol. 130, no. 3, pp. 449–467, May2001.
[CrossRef]

Morea, A.

O. Ribal and A. Morea, “Cost-efficiency of mixed 10-40-100 Gb/s networks and elastic optical networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, OTuI4.

Mukherjee, B.

K. Zhu and B. Mukherjee, “Traffic grooming in an optical WDM mesh network,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 122–133, Jan.2002.
[CrossRef]

Palma, R.

J. Santamaría, O. Cordón, S. Damas, R. Martí, and R. Palma, “GRASP and path relinking hybridizations for the point matching-based image registration problem,” J. Heuristics, vol. 18, no. 1, pp. 169–192, 2012.
[CrossRef]

Pan, Y.

Y. Wang, X. Cao, and Y. Pan, “A study of the routing and spectrum allocation in spectrum-sliced elastic optical path networks,” in IEEE Int. Conf. on Computer Communications (INFOCOM), Apr. 2011.

Pascoal, M.

E. Martins and M. Pascoal, “A new implementation of Yen’s ranking loopless paths algorithm,” 4OR: Q. J. Oper. Res., vol. 1, no. 2, pp. 121–133, 2003.
[CrossRef]

Pedrola, O.

O. Pedrola, M. Ruiz, L. Velasco, D. Careglio, O. González de Dios, and J. Comellas, “A GRASP with path-relinking heuristic for the survivable IP/MPLS-over-WSON multi-layer network optimization problem,” Comput. Oper. Res., 2012 [Online]. Available: http://dx.doi.org/10.1016/j.cor.2011.10.026.

M. Ruiz, O. Pedrola, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “Survivable IP/MPLS-over-WSON multi-layer network optimization,” J. Opt. Commun. Netw., vol. 3, no. 8, pp. 629–640, Aug.2011.
[CrossRef]

O. Pedrola, A. Castro, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “CAPEX study for grid dependent multi-layer IP/MPLS-over-EON using relative BV-WSS costs,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2012, NTu2J.7.

Pióro, M.

M. Pióro and D. Medhi, Routing, Flow, and Capacity Design in Communication and Computer Networks. Morgan Kaufmann Publishers, 2004.

Resende, M. G. C.

P. Festa, J. F. Gonçalves, M. G. C. Resende, and R. M. A. Silva, “Automatic tuning of GRASP with path-relinking heuristics with a biased random-key genetic algorithm,” in Experimental Algorithms (Vol. 6049 of Lecture Notes in Computer Science). 2010, pp. 338–349.

M. G. C. Resende and C. C. Ribeiro, “Greedy randomized adaptive search procedures: Advances and applications,” in Handbook of Metaheuristics, M. Gendreau and J. Y. Potvin, Eds., 2nd ed.Springer Science+Business Mediapp, 2010, pp. 29–63.

Ribal, O.

O. Ribal and A. Morea, “Cost-efficiency of mixed 10-40-100 Gb/s networks and elastic optical networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, OTuI4.

Ribeiro, C. C.

M. G. C. Resende and C. C. Ribeiro, “Greedy randomized adaptive search procedures: Advances and applications,” in Handbook of Metaheuristics, M. Gendreau and J. Y. Potvin, Eds., 2nd ed.Springer Science+Business Mediapp, 2010, pp. 29–63.

Rouskas, G.

Ruiz, M.

O. Pedrola, M. Ruiz, L. Velasco, D. Careglio, O. González de Dios, and J. Comellas, “A GRASP with path-relinking heuristic for the survivable IP/MPLS-over-WSON multi-layer network optimization problem,” Comput. Oper. Res., 2012 [Online]. Available: http://dx.doi.org/10.1016/j.cor.2011.10.026.

L. Velasco, M. Klinkowski, M. Ruiz, and J. Comellas, “Modeling the routing and spectrum allocation problem for future elastic optical networks,” Photonic Network Commun., 2012 [Online]. Available: http://dx.doi.org/10.1007/s11107-012-0378-7.

M. Ruiz, O. Pedrola, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “Survivable IP/MPLS-over-WSON multi-layer network optimization,” J. Opt. Commun. Netw., vol. 3, no. 8, pp. 629–640, Aug.2011.
[CrossRef]

Sahin, G.

S. Koo, G. Sahin, and S. Subramaniam, “Dynamic LSP routing in IP/MPLS-over-WDM networks,” IEEE J. Sel. Areas Commun., vol. 24, no. 12, pp. 45–55, Dec.2006.
[CrossRef]

Santamaría, J.

J. Santamaría, O. Cordón, S. Damas, R. Martí, and R. Palma, “GRASP and path relinking hybridizations for the point matching-based image registration problem,” J. Heuristics, vol. 18, no. 1, pp. 169–192, 2012.
[CrossRef]

Shen, F.

X. Zhang, F. Shen, L. Wang, S. Wang, L. Li, and H. Luo, “Two-layer mesh network optimization based on inter-layer decomposition,” Photonic Network Commun., vol. 21, no. 3, pp. 310–320, 2011.
[CrossRef]

Silva, R. M. A.

P. Festa, J. F. Gonçalves, M. G. C. Resende, and R. M. A. Silva, “Automatic tuning of GRASP with path-relinking heuristics with a biased random-key genetic algorithm,” in Experimental Algorithms (Vol. 6049 of Lecture Notes in Computer Science). 2010, pp. 338–349.

Sone, Y.

M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, “Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Commun. Mag., vol. 48, no. 8, pp. 138–145, 2010.
[CrossRef]

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, 2009.
[CrossRef]

Subramaniam, S.

S. Koo, G. Sahin, and S. Subramaniam, “Dynamic LSP routing in IP/MPLS-over-WDM networks,” IEEE J. Sel. Areas Commun., vol. 24, no. 12, pp. 45–55, Dec.2006.
[CrossRef]

Takara, H.

M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, “Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Commun. Mag., vol. 48, no. 8, pp. 138–145, 2010.
[CrossRef]

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, 2009.
[CrossRef]

Tanaka, T.

M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, “Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Commun. Mag., vol. 48, no. 8, pp. 138–145, 2010.
[CrossRef]

Tomkos, I.

K. Christodoulopoulos, I. Tomkos, and E. Varvarigos, “Elastic bandwidth allocation in flexible OFDM based optical networks,” J. Lightwave Technol., vol. 29, no. 9, pp. 1354–1366, May2011.
[CrossRef]

K. Christodoulopoulos, I. Tomkos, and E. Varvarigos, “Dynamic bandwidth allocation in flexible OFDM-based networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, OTuI5.

Tsukishima, Y.

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, 2009.
[CrossRef]

Varvarigos, E.

K. Christodoulopoulos, I. Tomkos, and E. Varvarigos, “Elastic bandwidth allocation in flexible OFDM based optical networks,” J. Lightwave Technol., vol. 29, no. 9, pp. 1354–1366, May2011.
[CrossRef]

K. Christodoulopoulos, I. Tomkos, and E. Varvarigos, “Dynamic bandwidth allocation in flexible OFDM-based networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, OTuI5.

Velasco, L.

L. Velasco, M. Klinkowski, M. Ruiz, and J. Comellas, “Modeling the routing and spectrum allocation problem for future elastic optical networks,” Photonic Network Commun., 2012 [Online]. Available: http://dx.doi.org/10.1007/s11107-012-0378-7.

O. Pedrola, M. Ruiz, L. Velasco, D. Careglio, O. González de Dios, and J. Comellas, “A GRASP with path-relinking heuristic for the survivable IP/MPLS-over-WSON multi-layer network optimization problem,” Comput. Oper. Res., 2012 [Online]. Available: http://dx.doi.org/10.1016/j.cor.2011.10.026.

M. Ruiz, O. Pedrola, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “Survivable IP/MPLS-over-WSON multi-layer network optimization,” J. Opt. Commun. Netw., vol. 3, no. 8, pp. 629–640, Aug.2011.
[CrossRef]

O. Pedrola, A. Castro, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “CAPEX study for grid dependent multi-layer IP/MPLS-over-EON using relative BV-WSS costs,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2012, NTu2J.7.

Voß, S.

H. Höller, B. Melián, and S. Voß, “Applying the pilot method to improve VNS and GRASP metaheuristics for the design of SDH/WDM networks,” Eur. J. Oper. Res., vol. 191, no. 3, pp. 691–704, Dec.2008.
[CrossRef]

H. Höller and S. Voß, “A heuristic approach for combined equipment-planning and routing in multi-layer SDH/WDM networks,” Eur. J. Oper. Res., vol. 171, no. 3, pp. 787–796, June2006.
[CrossRef]

Walkowiak, K.

M. Klinkowski and K. Walkowiak, “Routing and spectrum assignment in spectrum sliced elastic optical path network,” IEEE Commun. Lett., vol. 15, no. 8, pp. 884–886, Dec.2011.
[CrossRef]

Wan, X.

X. Wan, L. Wang, N. Hua, H. Zhang, and X. Zheng, “Dynamic routing and spectrum assignment in flexible optical path networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, JWA55.

Wang, L.

X. Zhang, F. Shen, L. Wang, S. Wang, L. Li, and H. Luo, “Two-layer mesh network optimization based on inter-layer decomposition,” Photonic Network Commun., vol. 21, no. 3, pp. 310–320, 2011.
[CrossRef]

X. Wan, L. Wang, N. Hua, H. Zhang, and X. Zheng, “Dynamic routing and spectrum assignment in flexible optical path networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, JWA55.

Wang, S.

X. Zhang, F. Shen, L. Wang, S. Wang, L. Li, and H. Luo, “Two-layer mesh network optimization based on inter-layer decomposition,” Photonic Network Commun., vol. 21, no. 3, pp. 310–320, 2011.
[CrossRef]

Wang, Y.

Y. Wang, X. Cao, and Y. Pan, “A study of the routing and spectrum allocation in spectrum-sliced elastic optical path networks,” in IEEE Int. Conf. on Computer Communications (INFOCOM), Apr. 2011.

Watanabe, A.

M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, “Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Commun. Mag., vol. 48, no. 8, pp. 138–145, 2010.
[CrossRef]

Zhang, H.

X. Wan, L. Wang, N. Hua, H. Zhang, and X. Zheng, “Dynamic routing and spectrum assignment in flexible optical path networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, JWA55.

Zhang, X.

X. Zhang, F. Shen, L. Wang, S. Wang, L. Li, and H. Luo, “Two-layer mesh network optimization based on inter-layer decomposition,” Photonic Network Commun., vol. 21, no. 3, pp. 310–320, 2011.
[CrossRef]

Zheng, X.

X. Wan, L. Wang, N. Hua, H. Zhang, and X. Zheng, “Dynamic routing and spectrum assignment in flexible optical path networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, JWA55.

Zhu, K.

K. Zhu and B. Mukherjee, “Traffic grooming in an optical WDM mesh network,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 122–133, Jan.2002.
[CrossRef]

4OR: Q. J. Oper. Res. (1)

E. Martins and M. Pascoal, “A new implementation of Yen’s ranking loopless paths algorithm,” 4OR: Q. J. Oper. Res., vol. 1, no. 2, pp. 121–133, 2003.
[CrossRef]

Comput. Oper. Res. (1)

O. Pedrola, M. Ruiz, L. Velasco, D. Careglio, O. González de Dios, and J. Comellas, “A GRASP with path-relinking heuristic for the survivable IP/MPLS-over-WSON multi-layer network optimization problem,” Comput. Oper. Res., 2012 [Online]. Available: http://dx.doi.org/10.1016/j.cor.2011.10.026.

Eur. J. Oper. Res. (3)

H. Höller, B. Melián, and S. Voß, “Applying the pilot method to improve VNS and GRASP metaheuristics for the design of SDH/WDM networks,” Eur. J. Oper. Res., vol. 191, no. 3, pp. 691–704, Dec.2008.
[CrossRef]

P. Hansen and N. Mladenovic, “Variable neighborhood search: principles and applications,” Eur. J. Oper. Res., vol. 130, no. 3, pp. 449–467, May2001.
[CrossRef]

H. Höller and S. Voß, “A heuristic approach for combined equipment-planning and routing in multi-layer SDH/WDM networks,” Eur. J. Oper. Res., vol. 171, no. 3, pp. 787–796, June2006.
[CrossRef]

IEEE Commun. Lett. (1)

M. Klinkowski and K. Walkowiak, “Routing and spectrum assignment in spectrum sliced elastic optical path network,” IEEE Commun. Lett., vol. 15, no. 8, pp. 884–886, Dec.2011.
[CrossRef]

IEEE Commun. Mag. (2)

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, 2009.
[CrossRef]

M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, “Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Commun. Mag., vol. 48, no. 8, pp. 138–145, 2010.
[CrossRef]

IEEE J. Sel. Areas Commun. (2)

K. Zhu and B. Mukherjee, “Traffic grooming in an optical WDM mesh network,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 122–133, Jan.2002.
[CrossRef]

S. Koo, G. Sahin, and S. Subramaniam, “Dynamic LSP routing in IP/MPLS-over-WDM networks,” IEEE J. Sel. Areas Commun., vol. 24, no. 12, pp. 45–55, Dec.2006.
[CrossRef]

J. Heuristics (1)

J. Santamaría, O. Cordón, S. Damas, R. Martí, and R. Palma, “GRASP and path relinking hybridizations for the point matching-based image registration problem,” J. Heuristics, vol. 18, no. 1, pp. 169–192, 2012.
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Commun. Netw. (2)

Photonic Network Commun. (2)

L. Velasco, M. Klinkowski, M. Ruiz, and J. Comellas, “Modeling the routing and spectrum allocation problem for future elastic optical networks,” Photonic Network Commun., 2012 [Online]. Available: http://dx.doi.org/10.1007/s11107-012-0378-7.

X. Zhang, F. Shen, L. Wang, S. Wang, L. Li, and H. Luo, “Two-layer mesh network optimization based on inter-layer decomposition,” Photonic Network Commun., vol. 21, no. 3, pp. 310–320, 2011.
[CrossRef]

Other (12)

IBM ILOG CPLEX, 2012 [Online]. Available: http://www-01.ibm.com/software/integration/optimization/cplex/.

M. Pióro and D. Medhi, Routing, Flow, and Capacity Design in Communication and Computer Networks. Morgan Kaufmann Publishers, 2004.

STRONGEST: Scalable, Tunable and Resilient Optical Networks Guaranteeing Extremely-high Speed Transport, 2012 [Online]. Available: http://www.ict-strongest.eu/.

P. Festa, J. F. Gonçalves, M. G. C. Resende, and R. M. A. Silva, “Automatic tuning of GRASP with path-relinking heuristics with a biased random-key genetic algorithm,” in Experimental Algorithms (Vol. 6049 of Lecture Notes in Computer Science). 2010, pp. 338–349.

O. Pedrola, A. Castro, L. Velasco, D. Careglio, J. P. Fernández-Palacios, and G. Junyent, “CAPEX study for grid dependent multi-layer IP/MPLS-over-EON using relative BV-WSS costs,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2012, NTu2J.7.

X. Wan, L. Wang, N. Hua, H. Zhang, and X. Zheng, “Dynamic routing and spectrum assignment in flexible optical path networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, JWA55.

K. Christodoulopoulos, I. Tomkos, and E. Varvarigos, “Dynamic bandwidth allocation in flexible OFDM-based networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, OTuI5.

Y. Wang, X. Cao, and Y. Pan, “A study of the routing and spectrum allocation in spectrum-sliced elastic optical path networks,” in IEEE Int. Conf. on Computer Communications (INFOCOM), Apr. 2011.

M. G. C. Resende and C. C. Ribeiro, “Greedy randomized adaptive search procedures: Advances and applications,” in Handbook of Metaheuristics, M. Gendreau and J. Y. Potvin, Eds., 2nd ed.Springer Science+Business Mediapp, 2010, pp. 29–63.

O. Ribal and A. Morea, “Cost-efficiency of mixed 10-40-100 Gb/s networks and elastic optical networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), Mar. 2011, OTuI4.

Finisar, “Programmable narrow-band filtering using the WaveShaper 1000E and WaveShaper 4000E,” White Paper, 2011[Online]. Available: http://www.finisar.com.

ITU-T Recommendation G.694.1, “Spectral grids for WDM applications: DWDM frequency grid,” 2012 [Online]. Available: http://www.itu.int/rec/T-REC-G.694.1-201202-I/en.

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Figures (3)

Fig. 1
Fig. 1

(Color online) (a) Geographical distribution for network topology locations. In blue, nodes that are the source/destination of IP/MPLS traffic demands. White circles represent candidate locations where network equipment can be installed if necessary. (b) A multilayer network illustrating a possible solution for the MIFO problem.

Fig. 2
Fig. 2

(Color online) Optical network topologies considered: the 21-node Spanish Telefónica (TEL), the 20-node British Telecom (BT), and the 21-node Deutsche Telecom (DT).

Fig. 3
Fig. 3

(Color online) Network CAPEX (IP/MPLS and optical equipment cost) as a function of the relative cost for one BV-WSS. The three network topologies are analyzed under the four different slot widths.

Tables (8)

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Table I FSs Required per Demand Under Each Frequency Grid

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Table II Traffic Profiles (TPs) Analyzed

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Table III Cost and Features of IP/MPLS Nodes

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Table IV Cost and Reach of BV-Ts

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Table V GRASP Automatically Tuned Parameters

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Table VI Average BV-T Number (#) and Bit-Rate (Gb/s)

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Table VII Average Reduction per Grid in Node Switching Capacity (SW) and Flow Switched (FS) (With Respect to the 50 GHz Grid)

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Table VIII Average BV-WSS Affordable Cost Increment per Frequency Grid (%)

Equations (37)

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

n d = b d s w B mod .
COST Equipment = v V ( α v + β v ) ,
COST FO = l L γ l len ( l ) a s 1 C OA + l L c C e E k K ( e ) λ e k l c n c s w len l C FO ,
minimize CAPEX = COST Equipment + COST FO
e E ( v ) k K ( e ) ω d e k = 1 , d D , v S D ( d ) ,
e E ( v ) k K ( e ) ω d e k 2 , d D , v S D ( d ) ¯ ,
e E ( v ) e e k K ( e ) ω d e k k K ( e ) ω d e k , d D , v S D ( d ) ¯ , e E ( v ) ,
l L ( v ) c C λ e k l c = c C δ e k c , e E , k K ( e ) , v V ( e ) ,
l L ( v ) c C λ e k l c 2 , e E , k K ( e ) , v V ( e ) ¯ ,
l L ( v ) l l c C λ e k l c c C λ e k l c , e E , k K ( e ) , v V ( e ) ¯ , l L ( v ) ,
c C δ e k c 1 , e E , k K ( e ) ,
c C s k n c δ e k c d D b d ω d e k , e E , k K ( e ) ,
l L λ e k l c M δ e k c , e E , k K ( e ) , c C ,
e E k K ( e ) c C h s c λ e k l c 1 , l L , s S ,
d D b d ω d e k r R b w ( r ) v e k r , e E , k K ( e ) ,
l L c C len ( l ) λ e k l c r R len ( r ) v e k r , e E , k K ( e ) ,
r R v e k r 1 , e E , k K ( e ) ,
e E k K ( e ) c C λ e k l c M γ l , l L ,
l L ( v ) γ l = φ v , v V ,
φ v M n NT μ n v , v V ,
n NT μ n v 1 , v V ,
φ v max φ + M μ n v , v V , n { Patch } ,
d D k K ( e ) ω d e k M μ n v , e E , v V ( e ) , n { MPLS } ,
n { WXC , MPLS } μ n v + l L ( v ) l l σ e k l e k 1 + M σ e k l e k 1 , e , e E , e e , k K ( e ) , k K ( e ) , v V , l L ( v ) ,
σ e k l e k c C λ e k l c , e , e E , e e , k K ( e ) , k K ( e ) , l L ,
σ e k l e k c C λ e k l c + c C λ e k l c 1 , e , e E , e e , k K ( e ) , k K ( e ) , l L ,
d D ω d e k M p P ( v ) Ψ e k v p , e E , k K ( e ) , v V ( e ) ,
p P ( v ) Ψ e k v p 1 , e E , k K ( e ) , v V ( e ) ,
e E k K ( e ) Ψ e k v p 1 , v V , p P ( v ) ,
d D b d ω d e k τ v p + M 1 Ψ e k v p , v V , p P ( v ) , e E , k K ( e ) ,
τ v p i PT p k i ρ i v p , v V , p P ( v ) ,
i PT ρ i v p 1 , v V , p P ( v ) ,
p P ( v ) τ v p j RT r k j π j v , v V ,
p P ( v ) i PT ρ i v p j RT r p k j π j v , v V ,
j RT π j v 1 , v V ,
α v + M 1 n { WXC , MPLS } μ n v C WXC + φ v C Trunk , v V ,
β v + M 1 n { MPLS } μ n v p P ( v ) i PT m p c i ρ i v p + j RT r c j π j v , v V .