Abstract

This paper investigates the lightpath establishment problem in the optical layer, which arises in multilayer traffic engineering. The static version of the problem is considered, in which the set of requested lightpaths is known initially, and the objective is to set up as many of these lightpaths as possible by assigning the physical layer resources efficiently. In establishing the lightpaths, physical layer impairments are also considered, such that the bit error rates of all established lightpaths should remain within acceptable limits. A heuristic algorithm, called ROLE, is proposed for the solution of this problem. An integer linear programming (ILP) formulation for the static lightpath establishment with physical layer impairments is also developed, which considers the aggregated effect of physical layer impairments. This formulation is used as a performance benchmark for ROLE on smaller-size networks. It also provides upper bounds even when the ILP model cannot be solved to optimality. The performance of ROLE is close to the optimum solutions for all studied problem sets, for which the optimum solution can be obtained. ROLE significantly outperforms previously proposed algorithms in terms of the number of lightpaths established. The effect of switch cross-talk ratio on the problem solution is also investigated.

© 2010 Optical Society of America

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References

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2009 (4)

B. Chen, S. Bose, W. Zhong, H. Wang, “A new lightpath establishing method for dynamic traffic grooming under the overlay model,” Photonic Network Commun., vol. 17, no. 1, pp. 11–20, 2009.
[CrossRef]

K. Christodoulopoulos, K. Manousakis, E. Varvarigos, “Considering physical layer impairments in offline RWA,” IEEE Network, vol. 23, no. 3, pp. 26–33, 2009.
[CrossRef]

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. Pareta, I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, no. 7, pp. 926–944, 2009.
[CrossRef]

2007 (1)

N. Sengezer, E. Karasan, “An efficient virtual topology design and traffic engineering scheme for IP/WDM networks,” Lect. Notes Comput. Sci., vol. 4534, pp. 319–328, 2007.
[CrossRef]

2005 (2)

2004 (1)

I. Tomkos, D. Vogiatzis, C. Mas, I. Zacharopoulos, A. Tzanakaki, E. Varvarigos, “Performance engineering of metropolitan area optical networks through impairment constraint routing,” IEEE Commun. Mag., vol. 42, no. 8, pp. S40–S47, 2004.
[CrossRef]

2003 (2)

R. Sabella, H. Zang, E. Labonatory, “Guest editorial: Traffic engineering in optical networks,” IEEE Network, vol. 17, no. 2, pp. 6–7, 2003.
[CrossRef]

Y. Huang, W. Wen, J. Heritage, B. Mukherjee, “Signal-quality consideration for dynamic connection provisioning in all-optical wavelength-routed networks,” Proc. SPIE, vol. 5285, pp. 163–173, 2003.
[CrossRef]

2000 (2)

X. Xiao, A. Hannan, B. Bailey, L. Ni, “Traffic engineering with MPLS in the Internet,” IEEE Network, vol. 14, no. 2, pp. 28–33, 2000.
[CrossRef]

H. Zang, J. Jue, B. Mukherjee, “A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,” Opt. Networks Mag., vol. 1, no. 1, pp. 47–60, 2000.

1999 (1)

1995 (1)

R. Ramaswami, K. Sivarajan, “Routing and wavelength assignment in all-optical networks,” IEEE/ACM Trans. Netw., vol. 3, no. 5, pp. 489–500, 1995.
[CrossRef]

Aggelou, M.

D. Monoyios, K. Vlachos, M. Aggelou, I. Tomkos, “On the use of multi-objective optimization algorithms for solving the impairment aware-RWA problem,” in IEEE Int. Conf. on Communications, 2009.

Agogbua, J.

D. Awduche, J. Malcolm, J. Agogbua, M. O’Dell, J. McManus, “Requirements for traffic engineering over MPLS,” IETF RFC 2702, 1999.

Agrawal, G.

G. Agrawal, Lightwave Technology: Communication Systems. New Jersey, USA: Wiley, 2005.
[CrossRef]

G. Agrawal, Fiber-Optic Communication Systems. Wiley-Interscience, 2002.
[CrossRef]

Al Zahr, S.

M. Ezzahdi, S. Al Zahr, M. Koubàa, N. Puech, M. Gagnaire, “LERP: a quality of transmission dependent heuristic for routing and wavelength assignment in hybrid WDM networks,” École Nationle Superieure des Telecommunications, Technical Report 2006D003, 2006.

Angelou, M.

S. Azodolmolky, Y. Pointurier, M. Klinkowski, E. Marin, D. Careglio, J. Sole-Pareta, M. Angelou, I. Tomkos, “On the offline physical layer impairment aware RWA algorithms in transparent optical networks: state-of-the-art and beyond,” in Int. Conf. on Optical Network Design and Modeling, 2009.

Araujo, A.

M. Lima, A. Cesar, A. Araujo, “Optical network optimization with transmission impairments based on genetic algorithm,” in Proc. of the 2003 SBMO/IEEE MTT-S Int. Microwave and Optoelectronics Conf., 2003, vol. 1, pp. 361–365.

Awduche, D.

D. Awduche, L. Berger, D. Gan, T. Li, V. Srinivasan, G. Swallow, “RSVP-TE: extensions to RSVP for LSP tunnels,” IETF RFC 3209, 2001.

B. Rajagopalan, J. Luciani, D. Awduche, “IP over optical networks: a framework,” IETF RFC 3717, 2004.

D. Awduche, J. Malcolm, J. Agogbua, M. O’Dell, J. McManus, “Requirements for traffic engineering over MPLS,” IETF RFC 2702, 1999.

Azodolmolky, S.

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. Pareta, I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, no. 7, pp. 926–944, 2009.
[CrossRef]

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

S. Azodolmolky, Y. Pointurier, M. Klinkowski, E. Marin, D. Careglio, J. Sole-Pareta, M. Angelou, I. Tomkos, “On the offline physical layer impairment aware RWA algorithms in transparent optical networks: state-of-the-art and beyond,” in Int. Conf. on Optical Network Design and Modeling, 2009.

Bailey, B.

X. Xiao, A. Hannan, B. Bailey, L. Ni, “Traffic engineering with MPLS in the Internet,” IEEE Network, vol. 14, no. 2, pp. 28–33, 2000.
[CrossRef]

Bayart, D.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Berger, L.

D. Awduche, L. Berger, D. Gan, T. Li, V. Srinivasan, G. Swallow, “RSVP-TE: extensions to RSVP for LSP tunnels,” IETF RFC 3209, 2001.

Bose, S.

B. Chen, S. Bose, W. Zhong, H. Wang, “A new lightpath establishing method for dynamic traffic grooming under the overlay model,” Photonic Network Commun., vol. 17, no. 1, pp. 11–20, 2009.
[CrossRef]

Brandt-Pearce, M.

J. He, M. Brandt-Pearce, Y. Pointurier, C. Brown, S. Subramaniam, “Adaptive wavelength assignment using wavelength spectrum separation for distributed optical networks,” in IEEE Int. Conf. on Communications, 2007, pp. 2406–2411.

Brown, C.

J. He, M. Brandt-Pearce, Y. Pointurier, C. Brown, S. Subramaniam, “Adaptive wavelength assignment using wavelength spectrum separation for distributed optical networks,” in IEEE Int. Conf. on Communications, 2007, pp. 2406–2411.

Cantrell, C.

C. Cantrell, “Transparent optical metropolitan-area networks,” in LEOS, 16th Annu. Meeting, 2003, vol. 2, pp. 608–609.

Careglio, D.

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. Pareta, I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, no. 7, pp. 926–944, 2009.
[CrossRef]

S. Azodolmolky, Y. Pointurier, M. Klinkowski, E. Marin, D. Careglio, J. Sole-Pareta, M. Angelou, I. Tomkos, “On the offline physical layer impairment aware RWA algorithms in transparent optical networks: state-of-the-art and beyond,” in Int. Conf. on Optical Network Design and Modeling, 2009.

Cesar, A.

M. Lima, A. Cesar, A. Araujo, “Optical network optimization with transmission impairments based on genetic algorithm,” in Proc. of the 2003 SBMO/IEEE MTT-S Int. Microwave and Optoelectronics Conf., 2003, vol. 1, pp. 361–365.

Chen, B.

B. Chen, S. Bose, W. Zhong, H. Wang, “A new lightpath establishing method for dynamic traffic grooming under the overlay model,” Photonic Network Commun., vol. 17, no. 1, pp. 11–20, 2009.
[CrossRef]

Christodoulopoulos, K.

K. Christodoulopoulos, K. Manousakis, E. Varvarigos, “Considering physical layer impairments in offline RWA,” IEEE Network, vol. 23, no. 3, pp. 26–33, 2009.
[CrossRef]

K. Manousakis, K. Christodoulopoulos, E. Varvarigos, “Impairment-aware offline RWA for transparent optical networks,” in Proc. IEEE Conf. on Computer Communications (INFOCOM), 2009, pp. 1557–1565.

Cinkler, T.

S. Zsigmond, B. Megyer, T. Cinkler, A. Tzanakaki, I. Tomkos, “A new method for considering physical impairments in multilayer routing,” in COST291/GBOU ONNA Workshop on Design of Next Generation Optical Networks, 2006.

Colle, D.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Comellas, J.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Datta, D.

Eiselt, M.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Ezzahdi, M.

M. Ezzahdi, S. Al Zahr, M. Koubàa, N. Puech, M. Gagnaire, “LERP: a quality of transmission dependent heuristic for routing and wavelength assignment in hybrid WDM networks,” École Nationle Superieure des Telecommunications, Technical Report 2006D003, 2006.

Feng, H.

Gagnaire, M.

M. Ezzahdi, S. Al Zahr, M. Koubàa, N. Puech, M. Gagnaire, “LERP: a quality of transmission dependent heuristic for routing and wavelength assignment in hybrid WDM networks,” École Nationle Superieure des Telecommunications, Technical Report 2006D003, 2006.

Gan, D.

D. Awduche, L. Berger, D. Gan, T. Li, V. Srinivasan, G. Swallow, “RSVP-TE: extensions to RSVP for LSP tunnels,” IETF RFC 3209, 2001.

Gunkel, M.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Hannan, A.

X. Xiao, A. Hannan, B. Bailey, L. Ni, “Traffic engineering with MPLS in the Internet,” IEEE Network, vol. 14, no. 2, pp. 28–33, 2000.
[CrossRef]

He, J.

J. He, M. Brandt-Pearce, Y. Pointurier, C. Brown, S. Subramaniam, “Adaptive wavelength assignment using wavelength spectrum separation for distributed optical networks,” in IEEE Int. Conf. on Communications, 2007, pp. 2406–2411.

Heritage, J.

Huang, Y.

Y. Huang, J. Heritage, B. Mukherjee, “Connection provisioning with transmission impairment consideration in optical WDM networks with high-speed channels,” J. Lightwave Technol., vol. 23, no. 3, pp. 982–993, 2005.
[CrossRef]

Y. Huang, W. Wen, J. Heritage, B. Mukherjee, “Signal-quality consideration for dynamic connection provisioning in all-optical wavelength-routed networks,” Proc. SPIE, vol. 5285, pp. 163–173, 2003.
[CrossRef]

Jue, J.

H. Zang, J. Jue, B. Mukherjee, “A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,” Opt. Networks Mag., vol. 1, no. 1, pp. 47–60, 2000.

Karasan, E.

N. Sengezer, E. Karasan, “An efficient virtual topology design and traffic engineering scheme for IP/WDM networks,” Lect. Notes Comput. Sci., vol. 4534, pp. 319–328, 2007.
[CrossRef]

Klinkowski, M.

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. Pareta, I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, no. 7, pp. 926–944, 2009.
[CrossRef]

S. Azodolmolky, Y. Pointurier, M. Klinkowski, E. Marin, D. Careglio, J. Sole-Pareta, M. Angelou, I. Tomkos, “On the offline physical layer impairment aware RWA algorithms in transparent optical networks: state-of-the-art and beyond,” in Int. Conf. on Optical Network Design and Modeling, 2009.

Klonidis, D.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Koubàa, M.

M. Ezzahdi, S. Al Zahr, M. Koubàa, N. Puech, M. Gagnaire, “LERP: a quality of transmission dependent heuristic for routing and wavelength assignment in hybrid WDM networks,” École Nationle Superieure des Telecommunications, Technical Report 2006D003, 2006.

Labonatory, E.

R. Sabella, H. Zang, E. Labonatory, “Guest editorial: Traffic engineering in optical networks,” IEEE Network, vol. 17, no. 2, pp. 6–7, 2003.
[CrossRef]

Li, T.

D. Awduche, L. Berger, D. Gan, T. Li, V. Srinivasan, G. Swallow, “RSVP-TE: extensions to RSVP for LSP tunnels,” IETF RFC 3209, 2001.

Lima, M.

M. Lima, A. Cesar, A. Araujo, “Optical network optimization with transmission impairments based on genetic algorithm,” in Proc. of the 2003 SBMO/IEEE MTT-S Int. Microwave and Optoelectronics Conf., 2003, vol. 1, pp. 361–365.

Luciani, J.

B. Rajagopalan, J. Luciani, D. Awduche, “IP over optical networks: a framework,” IETF RFC 3717, 2004.

Malcolm, J.

D. Awduche, J. Malcolm, J. Agogbua, M. O’Dell, J. McManus, “Requirements for traffic engineering over MPLS,” IETF RFC 2702, 1999.

Manousakis, K.

K. Christodoulopoulos, K. Manousakis, E. Varvarigos, “Considering physical layer impairments in offline RWA,” IEEE Network, vol. 23, no. 3, pp. 26–33, 2009.
[CrossRef]

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

K. Manousakis, K. Christodoulopoulos, E. Varvarigos, “Impairment-aware offline RWA for transparent optical networks,” in Proc. IEEE Conf. on Computer Communications (INFOCOM), 2009, pp. 1557–1565.

Marin, E.

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. Pareta, I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, no. 7, pp. 926–944, 2009.
[CrossRef]

S. Azodolmolky, Y. Pointurier, M. Klinkowski, E. Marin, D. Careglio, J. Sole-Pareta, M. Angelou, I. Tomkos, “On the offline physical layer impairment aware RWA algorithms in transparent optical networks: state-of-the-art and beyond,” in Int. Conf. on Optical Network Design and Modeling, 2009.

Mas, C.

I. Tomkos, D. Vogiatzis, C. Mas, I. Zacharopoulos, A. Tzanakaki, E. Varvarigos, “Performance engineering of metropolitan area optical networks through impairment constraint routing,” IEEE Commun. Mag., vol. 42, no. 8, pp. S40–S47, 2004.
[CrossRef]

McManus, J.

D. Awduche, J. Malcolm, J. Agogbua, M. O’Dell, J. McManus, “Requirements for traffic engineering over MPLS,” IETF RFC 2702, 1999.

Megyer, B.

S. Zsigmond, B. Megyer, T. Cinkler, A. Tzanakaki, I. Tomkos, “A new method for considering physical impairments in multilayer routing,” in COST291/GBOU ONNA Workshop on Design of Next Generation Optical Networks, 2006.

Monoyios, D.

D. Monoyios, K. Vlachos, M. Aggelou, I. Tomkos, “On the use of multi-objective optimization algorithms for solving the impairment aware-RWA problem,” in IEEE Int. Conf. on Communications, 2009.

Mukherjee, B.

Y. Huang, J. Heritage, B. Mukherjee, “Connection provisioning with transmission impairment consideration in optical WDM networks with high-speed channels,” J. Lightwave Technol., vol. 23, no. 3, pp. 982–993, 2005.
[CrossRef]

Y. Huang, W. Wen, J. Heritage, B. Mukherjee, “Signal-quality consideration for dynamic connection provisioning in all-optical wavelength-routed networks,” Proc. SPIE, vol. 5285, pp. 163–173, 2003.
[CrossRef]

H. Zang, J. Jue, B. Mukherjee, “A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,” Opt. Networks Mag., vol. 1, no. 1, pp. 47–60, 2000.

B. Ramamurthy, D. Datta, H. Feng, J. Heritage, B. Mukherjee, “Impact of transmission impairments on the teletraffic performance of wavelength-routed optical networks,” J. Lightwave Technol., vol. 17, no. 10, pp. 1713–1723, 1999.
[CrossRef]

Nejabati, R.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Ni, L.

X. Xiao, A. Hannan, B. Bailey, L. Ni, “Traffic engineering with MPLS in the Internet,” IEEE Network, vol. 14, no. 2, pp. 28–33, 2000.
[CrossRef]

O’Dell, M.

D. Awduche, J. Malcolm, J. Agogbua, M. O’Dell, J. McManus, “Requirements for traffic engineering over MPLS,” IETF RFC 2702, 1999.

Pareta, J.

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. Pareta, I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, no. 7, pp. 926–944, 2009.
[CrossRef]

Pickavet, M.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Pointurier, Y.

S. Azodolmolky, Y. Pointurier, M. Klinkowski, E. Marin, D. Careglio, J. Sole-Pareta, M. Angelou, I. Tomkos, “On the offline physical layer impairment aware RWA algorithms in transparent optical networks: state-of-the-art and beyond,” in Int. Conf. on Optical Network Design and Modeling, 2009.

J. He, M. Brandt-Pearce, Y. Pointurier, C. Brown, S. Subramaniam, “Adaptive wavelength assignment using wavelength spectrum separation for distributed optical networks,” in IEEE Int. Conf. on Communications, 2007, pp. 2406–2411.

Puech, N.

M. Ezzahdi, S. Al Zahr, M. Koubàa, N. Puech, M. Gagnaire, “LERP: a quality of transmission dependent heuristic for routing and wavelength assignment in hybrid WDM networks,” École Nationle Superieure des Telecommunications, Technical Report 2006D003, 2006.

Rajagopalan, B.

B. Rajagopalan, J. Luciani, D. Awduche, “IP over optical networks: a framework,” IETF RFC 3717, 2004.

Ramamurthy, B.

Ramaswami, R.

R. Ramaswami, K. Sivarajan, “Routing and wavelength assignment in all-optical networks,” IEEE/ACM Trans. Netw., vol. 3, no. 5, pp. 489–500, 1995.
[CrossRef]

Sabella, R.

R. Sabella, H. Zang, E. Labonatory, “Guest editorial: Traffic engineering in optical networks,” IEEE Network, vol. 17, no. 2, pp. 6–7, 2003.
[CrossRef]

Salvadori, E.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Saradhi, C.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Sengezer, N.

N. Sengezer, E. Karasan, “An efficient virtual topology design and traffic engineering scheme for IP/WDM networks,” Lect. Notes Comput. Sci., vol. 4534, pp. 319–328, 2007.
[CrossRef]

Shen, L.

Simeonidou, D.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Simonneau, C.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Sivarajan, K.

R. Ramaswami, K. Sivarajan, “Routing and wavelength assignment in all-optical networks,” IEEE/ACM Trans. Netw., vol. 3, no. 5, pp. 489–500, 1995.
[CrossRef]

Sole-Pareta, J.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

S. Azodolmolky, Y. Pointurier, M. Klinkowski, E. Marin, D. Careglio, J. Sole-Pareta, M. Angelou, I. Tomkos, “On the offline physical layer impairment aware RWA algorithms in transparent optical networks: state-of-the-art and beyond,” in Int. Conf. on Optical Network Design and Modeling, 2009.

Srinivasan, V.

D. Awduche, L. Berger, D. Gan, T. Li, V. Srinivasan, G. Swallow, “RSVP-TE: extensions to RSVP for LSP tunnels,” IETF RFC 3209, 2001.

Staessens, D.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Subramaniam, S.

J. He, M. Brandt-Pearce, Y. Pointurier, C. Brown, S. Subramaniam, “Adaptive wavelength assignment using wavelength spectrum separation for distributed optical networks,” in IEEE Int. Conf. on Communications, 2007, pp. 2406–2411.

Swallow, G.

D. Awduche, L. Berger, D. Gan, T. Li, V. Srinivasan, G. Swallow, “RSVP-TE: extensions to RSVP for LSP tunnels,” IETF RFC 3209, 2001.

Tomkos, I.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. Pareta, I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, no. 7, pp. 926–944, 2009.
[CrossRef]

I. Tomkos, D. Vogiatzis, C. Mas, I. Zacharopoulos, A. Tzanakaki, E. Varvarigos, “Performance engineering of metropolitan area optical networks through impairment constraint routing,” IEEE Commun. Mag., vol. 42, no. 8, pp. S40–S47, 2004.
[CrossRef]

D. Monoyios, K. Vlachos, M. Aggelou, I. Tomkos, “On the use of multi-objective optimization algorithms for solving the impairment aware-RWA problem,” in IEEE Int. Conf. on Communications, 2009.

S. Azodolmolky, Y. Pointurier, M. Klinkowski, E. Marin, D. Careglio, J. Sole-Pareta, M. Angelou, I. Tomkos, “On the offline physical layer impairment aware RWA algorithms in transparent optical networks: state-of-the-art and beyond,” in Int. Conf. on Optical Network Design and Modeling, 2009.

S. Zsigmond, B. Megyer, T. Cinkler, A. Tzanakaki, I. Tomkos, “A new method for considering physical impairments in multilayer routing,” in COST291/GBOU ONNA Workshop on Design of Next Generation Optical Networks, 2006.

Tzanakaki, A.

I. Tomkos, D. Vogiatzis, C. Mas, I. Zacharopoulos, A. Tzanakaki, E. Varvarigos, “Performance engineering of metropolitan area optical networks through impairment constraint routing,” IEEE Commun. Mag., vol. 42, no. 8, pp. S40–S47, 2004.
[CrossRef]

S. Zsigmond, B. Megyer, T. Cinkler, A. Tzanakaki, I. Tomkos, “A new method for considering physical impairments in multilayer routing,” in COST291/GBOU ONNA Workshop on Design of Next Generation Optical Networks, 2006.

Varvarigos, E.

K. Christodoulopoulos, K. Manousakis, E. Varvarigos, “Considering physical layer impairments in offline RWA,” IEEE Network, vol. 23, no. 3, pp. 26–33, 2009.
[CrossRef]

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

I. Tomkos, D. Vogiatzis, C. Mas, I. Zacharopoulos, A. Tzanakaki, E. Varvarigos, “Performance engineering of metropolitan area optical networks through impairment constraint routing,” IEEE Commun. Mag., vol. 42, no. 8, pp. S40–S47, 2004.
[CrossRef]

K. Manousakis, K. Christodoulopoulos, E. Varvarigos, “Impairment-aware offline RWA for transparent optical networks,” in Proc. IEEE Conf. on Computer Communications (INFOCOM), 2009, pp. 1557–1565.

Vlachos, K.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

D. Monoyios, K. Vlachos, M. Aggelou, I. Tomkos, “On the use of multi-objective optimization algorithms for solving the impairment aware-RWA problem,” in IEEE Int. Conf. on Communications, 2009.

Vogiatzis, D.

I. Tomkos, D. Vogiatzis, C. Mas, I. Zacharopoulos, A. Tzanakaki, E. Varvarigos, “Performance engineering of metropolitan area optical networks through impairment constraint routing,” IEEE Commun. Mag., vol. 42, no. 8, pp. S40–S47, 2004.
[CrossRef]

Wang, H.

B. Chen, S. Bose, W. Zhong, H. Wang, “A new lightpath establishing method for dynamic traffic grooming under the overlay model,” Photonic Network Commun., vol. 17, no. 1, pp. 11–20, 2009.
[CrossRef]

Wen, W.

Y. Huang, W. Wen, J. Heritage, B. Mukherjee, “Signal-quality consideration for dynamic connection provisioning in all-optical wavelength-routed networks,” Proc. SPIE, vol. 5285, pp. 163–173, 2003.
[CrossRef]

Winston, W. L.

W. L. Winston, Operations Research: Applications and Algorithms, 4th ed., Thomson, 2004.

Xiao, X.

X. Xiao, A. Hannan, B. Bailey, L. Ni, “Traffic engineering with MPLS in the Internet,” IEEE Network, vol. 14, no. 2, pp. 28–33, 2000.
[CrossRef]

Yang, X.

X. Yang, L. Shen, B. Ramamurthy, “Survivable lightpath provisioning in WDM mesh networks under shared path protection and signal quality constraints,” J. Lightwave Technol., vol. 23, no. 4, pp. 1556–1567, 2005.
[CrossRef]

X. Yang, B. Ramamurthy, “Dynamic routing in translucent WDM optical networks,” in IEEE Int. Conf. on Communications, 2002, vol. 5, pp. 2796–2802.

Ye, Y.

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

Zacharopoulos, I.

I. Tomkos, D. Vogiatzis, C. Mas, I. Zacharopoulos, A. Tzanakaki, E. Varvarigos, “Performance engineering of metropolitan area optical networks through impairment constraint routing,” IEEE Commun. Mag., vol. 42, no. 8, pp. S40–S47, 2004.
[CrossRef]

Zang, H.

R. Sabella, H. Zang, E. Labonatory, “Guest editorial: Traffic engineering in optical networks,” IEEE Network, vol. 17, no. 2, pp. 6–7, 2003.
[CrossRef]

H. Zang, J. Jue, B. Mukherjee, “A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,” Opt. Networks Mag., vol. 1, no. 1, pp. 47–60, 2000.

Zhong, W.

B. Chen, S. Bose, W. Zhong, H. Wang, “A new lightpath establishing method for dynamic traffic grooming under the overlay model,” Photonic Network Commun., vol. 17, no. 1, pp. 11–20, 2009.
[CrossRef]

Zsigmond, S.

S. Zsigmond, B. Megyer, T. Cinkler, A. Tzanakaki, I. Tomkos, “A new method for considering physical impairments in multilayer routing,” in COST291/GBOU ONNA Workshop on Design of Next Generation Optical Networks, 2006.

Comput. Netw. (1)

S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. Pareta, I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Comput. Netw., vol. 53, no. 7, pp. 926–944, 2009.
[CrossRef]

IEEE Commun. Mag. (2)

I. Tomkos, D. Vogiatzis, C. Mas, I. Zacharopoulos, A. Tzanakaki, E. Varvarigos, “Performance engineering of metropolitan area optical networks through impairment constraint routing,” IEEE Commun. Mag., vol. 42, no. 8, pp. S40–S47, 2004.
[CrossRef]

S. Azodolmolky, D. Klonidis, I. Tomkos, Y. Ye, C. Saradhi, E. Salvadori, M. Gunkel, K. Manousakis, K. Vlachos, E. Varvarigos, R. Nejabati, D. Simeonidou, M. Eiselt, J. Comellas, J. Sole-Pareta, C. Simonneau, D. Bayart, D. Staessens, D. Colle, M. Pickavet, “A dynamic impairment aware networking solution for transparent mesh optical networks,” IEEE Commun. Mag., vol. 47, no. 5, pp. S38–S47, 2009.
[CrossRef]

IEEE Network (3)

K. Christodoulopoulos, K. Manousakis, E. Varvarigos, “Considering physical layer impairments in offline RWA,” IEEE Network, vol. 23, no. 3, pp. 26–33, 2009.
[CrossRef]

R. Sabella, H. Zang, E. Labonatory, “Guest editorial: Traffic engineering in optical networks,” IEEE Network, vol. 17, no. 2, pp. 6–7, 2003.
[CrossRef]

X. Xiao, A. Hannan, B. Bailey, L. Ni, “Traffic engineering with MPLS in the Internet,” IEEE Network, vol. 14, no. 2, pp. 28–33, 2000.
[CrossRef]

IEEE/ACM Trans. Netw. (1)

R. Ramaswami, K. Sivarajan, “Routing and wavelength assignment in all-optical networks,” IEEE/ACM Trans. Netw., vol. 3, no. 5, pp. 489–500, 1995.
[CrossRef]

J. Lightwave Technol. (3)

Lect. Notes Comput. Sci. (1)

N. Sengezer, E. Karasan, “An efficient virtual topology design and traffic engineering scheme for IP/WDM networks,” Lect. Notes Comput. Sci., vol. 4534, pp. 319–328, 2007.
[CrossRef]

Opt. Networks Mag. (1)

H. Zang, J. Jue, B. Mukherjee, “A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,” Opt. Networks Mag., vol. 1, no. 1, pp. 47–60, 2000.

Photonic Network Commun. (1)

B. Chen, S. Bose, W. Zhong, H. Wang, “A new lightpath establishing method for dynamic traffic grooming under the overlay model,” Photonic Network Commun., vol. 17, no. 1, pp. 11–20, 2009.
[CrossRef]

Proc. SPIE (1)

Y. Huang, W. Wen, J. Heritage, B. Mukherjee, “Signal-quality consideration for dynamic connection provisioning in all-optical wavelength-routed networks,” Proc. SPIE, vol. 5285, pp. 163–173, 2003.
[CrossRef]

Other (16)

C. Cantrell, “Transparent optical metropolitan-area networks,” in LEOS, 16th Annu. Meeting, 2003, vol. 2, pp. 608–609.

W. L. Winston, Operations Research: Applications and Algorithms, 4th ed., Thomson, 2004.

“Dynamic Impairment Constraint Network for Transparent Mesh Optical Networks (DICONET) project,” http://www.diconet.eu.

M. Lima, A. Cesar, A. Araujo, “Optical network optimization with transmission impairments based on genetic algorithm,” in Proc. of the 2003 SBMO/IEEE MTT-S Int. Microwave and Optoelectronics Conf., 2003, vol. 1, pp. 361–365.

D. Monoyios, K. Vlachos, M. Aggelou, I. Tomkos, “On the use of multi-objective optimization algorithms for solving the impairment aware-RWA problem,” in IEEE Int. Conf. on Communications, 2009.

M. Ezzahdi, S. Al Zahr, M. Koubàa, N. Puech, M. Gagnaire, “LERP: a quality of transmission dependent heuristic for routing and wavelength assignment in hybrid WDM networks,” École Nationle Superieure des Telecommunications, Technical Report 2006D003, 2006.

S. Zsigmond, B. Megyer, T. Cinkler, A. Tzanakaki, I. Tomkos, “A new method for considering physical impairments in multilayer routing,” in COST291/GBOU ONNA Workshop on Design of Next Generation Optical Networks, 2006.

J. He, M. Brandt-Pearce, Y. Pointurier, C. Brown, S. Subramaniam, “Adaptive wavelength assignment using wavelength spectrum separation for distributed optical networks,” in IEEE Int. Conf. on Communications, 2007, pp. 2406–2411.

X. Yang, B. Ramamurthy, “Dynamic routing in translucent WDM optical networks,” in IEEE Int. Conf. on Communications, 2002, vol. 5, pp. 2796–2802.

S. Azodolmolky, Y. Pointurier, M. Klinkowski, E. Marin, D. Careglio, J. Sole-Pareta, M. Angelou, I. Tomkos, “On the offline physical layer impairment aware RWA algorithms in transparent optical networks: state-of-the-art and beyond,” in Int. Conf. on Optical Network Design and Modeling, 2009.

K. Manousakis, K. Christodoulopoulos, E. Varvarigos, “Impairment-aware offline RWA for transparent optical networks,” in Proc. IEEE Conf. on Computer Communications (INFOCOM), 2009, pp. 1557–1565.

G. Agrawal, Fiber-Optic Communication Systems. Wiley-Interscience, 2002.
[CrossRef]

G. Agrawal, Lightwave Technology: Communication Systems. New Jersey, USA: Wiley, 2005.
[CrossRef]

D. Awduche, J. Malcolm, J. Agogbua, M. O’Dell, J. McManus, “Requirements for traffic engineering over MPLS,” IETF RFC 2702, 1999.

D. Awduche, L. Berger, D. Gan, T. Li, V. Srinivasan, G. Swallow, “RSVP-TE: extensions to RSVP for LSP tunnels,” IETF RFC 3209, 2001.

B. Rajagopalan, J. Luciani, D. Awduche, “IP over optical networks: a framework,” IETF RFC 3717, 2004.

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Figures (21)

Fig. 1
Fig. 1

Flow chart of the ROLE algorithm.

Fig. 2
Fig. 2

Percentage of the routed demands by ROLE on topology 1.

Fig. 3
Fig. 3

Percentage of the routed demands by ROLE on topology 2.

Fig. 4
Fig. 4

Percentage of the routed demands by ROLE on topology 3.

Fig. 5
Fig. 5

Percentage of the routed demands by ROLE on topology 4.

Fig. 6
Fig. 6

Distribution of the blocked lightpath demands according to their lengths on topology 1.

Fig. 7
Fig. 7

Distribution of the blocked lightpath demands according to their lengths on topology 2.

Fig. 8
Fig. 8

Distribution of the blocked lightpath demands according to their lengths on topology 3.

Fig. 9
Fig. 9

Distribution of the blocked lightpath demands according to their lengths on topology 4.

Fig. 10
Fig. 10

Percentage of the routed demands by ROLE with different RWA algorithms on topology 1.

Fig. 11
Fig. 11

Percentage of the routed demands by ROLE with different RWA algorithms on topology 2.

Fig. 12
Fig. 12

Percentage of the routed demands by ROLE with different RWA algorithms on topology 3.

Fig. 13
Fig. 13

Percentage of the routed demands by ROLE with different RWA algorithms on topology 4.

Fig. 14
Fig. 14

Distribution of the blocked lightpath demands according to their lengths on topology 5.

Fig. 15
Fig. 15

Distribution of the blocked lightpath demands according to their lengths on topology 6.

Fig. 16
Fig. 16

Distribution of the blocked lightpath demands according to their lengths on topology 7.

Fig. 17
Fig. 17

Percentage of the routed demands by the heuristic algorithms on the DTAG topology.

Fig. 18
Fig. 18

Routed demand percentage versus switch cross-talk ratio for various numbers of lightpath demands for | W | = 16 .

Fig. 19
Fig. 19

Routed demand percentage versus switch cross-talk ratio for various numbers of lightpath demands for | W | = 128 .

Fig. 20
Fig. 20

Ratio of wavelength-blocked and BER-blocked lightpath demands versus switch cross-talk ratio.

Fig. 21
Fig. 21

Ratio of wavelength-blocked and BER-blocked lightpath demands versus number of offered lightpath demands per wavelength.

Tables (8)

Tables Icon

Table 1 Values of the Physical Model Parameters

Tables Icon

Table 2 Statistics on the Lengths of the Blocked Lightpaths for SDF and LDF Demand Sorting on Topologies 1–4

Tables Icon

Table 3 Percentage of the Established Lightpath Demands by ROLE With Different RWA Algorithms Averaged on Topologies 1–4

Tables Icon

Table 4 Average Values of the Maximum BERs Among the Lightpaths in the Established Virtual Topologies on Topologies 1–4

Tables Icon

Table 5 Number of Routed Demands With the ILP and Heuristic Solutions and Upper Bounds for Topology 5 a

Tables Icon

Table 6 Number of Routed Demands With the ILP and Heuristic Solutions and Upper Bounds for Topology 6 a

Tables Icon

Table 7 Number of Routed Demands With the ILP and Heuristic Solutions and Upper Bounds for Topology 7 a

Tables Icon

Table 8 Statistics on the Lengths of the Blocked Lightpaths for the ILP Solution and ROLE With SDF and LDF Demand Sorting on Topologies 5–7

Equations (16)

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

BER = 1 2 erfc ( Q 2 ) e Q 2 2 Q 2 π ,
Q = I 1 I 0 σ 1 + σ 0 .
Q end = I 1 , start I 0 , start σ 1 , start + σ 0 , start × σ 1 , start + σ 0 , start σ 1 , end + σ 0 , end × I 1 , end I 0 , end I 1 , start I 0 , start .
Q PMD = 10.2 B 2 D p 2 L ,
σ m 2 = σ s x m 2 + σ s s p m 2 + σ s h m 2 + σ th 2 ,
σ lim = Q start × ( σ 1 , start + σ 0 , start ) Q lim × Q PMD ,
σ 1 , end + σ 0 , end σ lim .
x w d p = { 1 , if demand d is routed on path p at w 0 , otherwise } ,
max d D p P d x w d p
w W p P d x w d p 1 , d D ,
d D p P d x w d p × T l d p C l , l L , w W .
T l d p = { 1 , if link l is on the p th path for demand d 0 , otherwise } .
σ 0 2 + σ 1 2 = m { 0 , 1 } ( 2 ξ pol R λ 2 b m P S ( w , d , p ) P X ( w , d , p ) + 2 q R λ B e ( b m P S ( w , d , p ) + P X ( w , d , p ) + P A ( w , d , p ) ) + 4 R λ 2 b m P S ( w , d , p ) P A ( w , d , p ) B e B o + n th B e ) .
K ( σ 0 2 + σ 1 2 ) ( σ 1 + σ 0 ) 2 .
M × ( 1 x w d p ) + σ lim 2 K ( σ 0 2 + σ 1 2 ) ,
w W , d D , p P .