Abstract

Feature Issue on High Availability in Optical Networks

We study the optimal survivability design problem under a scheduled traffic model in wavelength-convertible WDM optical mesh networks. In this model, a set of demands is given, and the setup and tear-down time of a demand are known in advance. We formulate the joint routing and wavelength assignment problems as integer linear problems that maximally exploit network resource reuse in both space and time. Moreover, we propose efficient heuristic algorithms with different demand-ordering policies to solve large survivable routing and wavelength assignment problems under the scheduled traffic model. Our simulation results indicate that the optimization of resource sharing in space and time enabled by our connection-holding-time-aware protection schemes can achieve significantly better resource utilization than schemes that are holding-time unaware. In addition, the proposed heuristic algorithms are shown to be indeed very effective.

© 2006 Optical Society of America

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  1. W. D. Grover, Mesh-Based Survivable Networks: Options and Strategies for Optical, MPLS, SONET, and ATM Networking (Prentice-Hall, 2003).
  2. T.-H. Wu, ''Emerging technologies for fiber network survivability,'' IEEE Commun. Mag. 33(2), 58-59, 62-74 (1995).
  3. H. Zang, WDM Mesh Networks: Management and Survivability (Kluwer, 2003).
  4. H. T. Mouftah and P.-H. Ho, Optical Networks: Architecture and Survivability (Kluwer, 2003).
  5. H. Zang, C. Ou, and B. Mukherjee, ''Path-protection routing and wavelength-assignment in WDM mesh networks under shared-risk-group constraints,'' in Proc. SPIE 4585, 49-60 (2001).
  6. H. Zang, C. Ou, and B. Mukherjee, ''Path-protection routing and wavelength assignment (RWA) in WDM mesh networks under duct-layer constraints,'' IEEE/ACM Trans. Netw. 11, 248-258 (2003).
  7. Y. Miyao and H. Saito, ''Optimal design and evaluation of survivable WDM transport networks,'' IEEE J. Sel. Areas Commun. 16, 1190-1198 (1998).
  8. M. Clouqueur and W. D. Grover, ''Mesh-restorable networks with complete dual failure restorability and with selectively enhanced dual-failure restorability properties,'' in Proceedings of OPTICOMM (SPIE, 2002), pp. 1-12.
  9. J. Doucette and W. D. Grover, ''Capacity design studies of span-restorable mesh transport networks with shared-risk link group (SRLG) effects,'' in Proceedings of OPTICOMM (SPIE, 2002), pp. 25-38.
  10. T. Li and B. Wang, ''Cost-effective shared path protection in WDM optical mesh networks with partial wavelength conversion,'' Photon. Network Commun. 8, 251-266 (2004).
  11. H. Zang and B. Mukherjee, ''Connection management for survivable wavelength-routed WDM mesh networks,'' Opt. Networks Mag. Special Issue on Protection and Survivability in Optical Networks 2(4), 17-28 (2001).
  12. S. Yuan and J. P. Jue, ''Shared protection routing algorithm for optical network,'' Opt. Networks Mag. 3, 32-39 (2002).
  13. A. Todimala and B. Ramamurthy, ''A dynamic partitioning sub-path protection routing technique in WDM mesh networks,'' in International Conference on Computer Communications (ICCC'02) (ICCC Press, 2002), 327-340.
  14. T. Li and B. Wang, ''Efficient online algorithms for dynamic shared path protection in optical WDM networks,'' Photon. Network Commun. 9, 207-222 (2005).
  15. J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, ''Routing and wavelength assignments of scheduled light-path demands,'' IEEE J. Sel. Areas Commun. 21, 1231-1240 (2003).
  16. J. Kuri, ''Optimization problems in WDM optical transport networks with scheduled light-path demands,'' Ph.D. thesis (ENST Paris, 2003).
  17. J. Kuri, N. Puech, and M. Gagnaire, ''Diverse routing of scheduled light path demands in an optical transport network,'' in Proceedings of Fourth International Workshop on the Design of Reliable Communication Networks (DRCN 2003) (IEEE, 2003), pp. 69-76.
  18. M. Tornatore, A. Pattavina, J. Zhang, B. Mukherjee, and C. Ou, ''Efficient shared-path protection exploiting the knowledge of connection-holding time,'' in Optical Fiber Communications Conference (OFC'05) (Optical Society of America, 2005), paper OThk2.
  19. C. V. Saradhi, L. K. Wei, and M. Gurusamy, ''Provisioning fault-tolerant scheduled light-path demands in WDM mesh networks,'' in Proceedings of the First International Conference on Broadband Networks (BroadNets 2004) (IEEE Computer Society, 2004), pp. 150-159.
  20. B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, ''Routing and wavelength assignment under a scheduled traffic model in reconfigurable WDM optical networks,'' in Proceedings of Broadnets'05 (IEEE, 2005), pp. 15-24.
  21. T. Li and B. Wang, ''On survivable service provisioning in WDM optical networks under a scheduled traffic model,'' in Proceedings of IEEE Globecom'05 (IEEE, 2005), pp. 1900-1904.
  22. T. Li and B. Wang, ''On optimal survivability design in WDM optical networks under a scheduled traffic model,'' in Proceedings of the 5th IEEE International Workshop on Design of Reliable Communication Networks (DRCN) (IEEE, 2005), pp. 23-30.
  23. The problems can easily be shown to be NP-complete.
  24. Assume that demands in D′ are indexed from 1 to ∣D′∣.

2005 (4)

T. Li and B. Wang, ''Efficient online algorithms for dynamic shared path protection in optical WDM networks,'' Photon. Network Commun. 9, 207-222 (2005).

M. Tornatore, A. Pattavina, J. Zhang, B. Mukherjee, and C. Ou, ''Efficient shared-path protection exploiting the knowledge of connection-holding time,'' in Optical Fiber Communications Conference (OFC'05) (Optical Society of America, 2005), paper OThk2.

T. Li and B. Wang, ''On survivable service provisioning in WDM optical networks under a scheduled traffic model,'' in Proceedings of IEEE Globecom'05 (IEEE, 2005), pp. 1900-1904.

T. Li and B. Wang, ''On optimal survivability design in WDM optical networks under a scheduled traffic model,'' in Proceedings of the 5th IEEE International Workshop on Design of Reliable Communication Networks (DRCN) (IEEE, 2005), pp. 23-30.

2004 (2)

C. V. Saradhi, L. K. Wei, and M. Gurusamy, ''Provisioning fault-tolerant scheduled light-path demands in WDM mesh networks,'' in Proceedings of the First International Conference on Broadband Networks (BroadNets 2004) (IEEE Computer Society, 2004), pp. 150-159.

T. Li and B. Wang, ''Cost-effective shared path protection in WDM optical mesh networks with partial wavelength conversion,'' Photon. Network Commun. 8, 251-266 (2004).

2003 (7)

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, ''Routing and wavelength assignments of scheduled light-path demands,'' IEEE J. Sel. Areas Commun. 21, 1231-1240 (2003).

J. Kuri, ''Optimization problems in WDM optical transport networks with scheduled light-path demands,'' Ph.D. thesis (ENST Paris, 2003).

J. Kuri, N. Puech, and M. Gagnaire, ''Diverse routing of scheduled light path demands in an optical transport network,'' in Proceedings of Fourth International Workshop on the Design of Reliable Communication Networks (DRCN 2003) (IEEE, 2003), pp. 69-76.

W. D. Grover, Mesh-Based Survivable Networks: Options and Strategies for Optical, MPLS, SONET, and ATM Networking (Prentice-Hall, 2003).

H. Zang, WDM Mesh Networks: Management and Survivability (Kluwer, 2003).

H. T. Mouftah and P.-H. Ho, Optical Networks: Architecture and Survivability (Kluwer, 2003).

H. Zang, C. Ou, and B. Mukherjee, ''Path-protection routing and wavelength assignment (RWA) in WDM mesh networks under duct-layer constraints,'' IEEE/ACM Trans. Netw. 11, 248-258 (2003).

2002 (4)

M. Clouqueur and W. D. Grover, ''Mesh-restorable networks with complete dual failure restorability and with selectively enhanced dual-failure restorability properties,'' in Proceedings of OPTICOMM (SPIE, 2002), pp. 1-12.

J. Doucette and W. D. Grover, ''Capacity design studies of span-restorable mesh transport networks with shared-risk link group (SRLG) effects,'' in Proceedings of OPTICOMM (SPIE, 2002), pp. 25-38.

S. Yuan and J. P. Jue, ''Shared protection routing algorithm for optical network,'' Opt. Networks Mag. 3, 32-39 (2002).

A. Todimala and B. Ramamurthy, ''A dynamic partitioning sub-path protection routing technique in WDM mesh networks,'' in International Conference on Computer Communications (ICCC'02) (ICCC Press, 2002), 327-340.

2001 (2)

H. Zang and B. Mukherjee, ''Connection management for survivable wavelength-routed WDM mesh networks,'' Opt. Networks Mag. Special Issue on Protection and Survivability in Optical Networks 2(4), 17-28 (2001).

H. Zang, C. Ou, and B. Mukherjee, ''Path-protection routing and wavelength-assignment in WDM mesh networks under shared-risk-group constraints,'' in Proc. SPIE 4585, 49-60 (2001).

1998 (1)

Y. Miyao and H. Saito, ''Optimal design and evaluation of survivable WDM transport networks,'' IEEE J. Sel. Areas Commun. 16, 1190-1198 (1998).

1995 (1)

T.-H. Wu, ''Emerging technologies for fiber network survivability,'' IEEE Commun. Mag. 33(2), 58-59, 62-74 (1995).

Clouqueur, M.

M. Clouqueur and W. D. Grover, ''Mesh-restorable networks with complete dual failure restorability and with selectively enhanced dual-failure restorability properties,'' in Proceedings of OPTICOMM (SPIE, 2002), pp. 1-12.

Dotaro, E.

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, ''Routing and wavelength assignments of scheduled light-path demands,'' IEEE J. Sel. Areas Commun. 21, 1231-1240 (2003).

Doucette, J.

J. Doucette and W. D. Grover, ''Capacity design studies of span-restorable mesh transport networks with shared-risk link group (SRLG) effects,'' in Proceedings of OPTICOMM (SPIE, 2002), pp. 25-38.

Douville, R.

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, ''Routing and wavelength assignments of scheduled light-path demands,'' IEEE J. Sel. Areas Commun. 21, 1231-1240 (2003).

Fan, Y.

B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, ''Routing and wavelength assignment under a scheduled traffic model in reconfigurable WDM optical networks,'' in Proceedings of Broadnets'05 (IEEE, 2005), pp. 15-24.

Gagnaire, M.

J. Kuri, N. Puech, and M. Gagnaire, ''Diverse routing of scheduled light path demands in an optical transport network,'' in Proceedings of Fourth International Workshop on the Design of Reliable Communication Networks (DRCN 2003) (IEEE, 2003), pp. 69-76.

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, ''Routing and wavelength assignments of scheduled light-path demands,'' IEEE J. Sel. Areas Commun. 21, 1231-1240 (2003).

Grover, W. D.

W. D. Grover, Mesh-Based Survivable Networks: Options and Strategies for Optical, MPLS, SONET, and ATM Networking (Prentice-Hall, 2003).

J. Doucette and W. D. Grover, ''Capacity design studies of span-restorable mesh transport networks with shared-risk link group (SRLG) effects,'' in Proceedings of OPTICOMM (SPIE, 2002), pp. 25-38.

M. Clouqueur and W. D. Grover, ''Mesh-restorable networks with complete dual failure restorability and with selectively enhanced dual-failure restorability properties,'' in Proceedings of OPTICOMM (SPIE, 2002), pp. 1-12.

Gurusamy, M.

C. V. Saradhi, L. K. Wei, and M. Gurusamy, ''Provisioning fault-tolerant scheduled light-path demands in WDM mesh networks,'' in Proceedings of the First International Conference on Broadband Networks (BroadNets 2004) (IEEE Computer Society, 2004), pp. 150-159.

Ho, P.-H.

H. T. Mouftah and P.-H. Ho, Optical Networks: Architecture and Survivability (Kluwer, 2003).

Jue, J. P.

S. Yuan and J. P. Jue, ''Shared protection routing algorithm for optical network,'' Opt. Networks Mag. 3, 32-39 (2002).

Kuri, J.

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, ''Routing and wavelength assignments of scheduled light-path demands,'' IEEE J. Sel. Areas Commun. 21, 1231-1240 (2003).

J. Kuri, ''Optimization problems in WDM optical transport networks with scheduled light-path demands,'' Ph.D. thesis (ENST Paris, 2003).

J. Kuri, N. Puech, and M. Gagnaire, ''Diverse routing of scheduled light path demands in an optical transport network,'' in Proceedings of Fourth International Workshop on the Design of Reliable Communication Networks (DRCN 2003) (IEEE, 2003), pp. 69-76.

Li, T.

T. Li and B. Wang, ''Efficient online algorithms for dynamic shared path protection in optical WDM networks,'' Photon. Network Commun. 9, 207-222 (2005).

T. Li and B. Wang, ''On survivable service provisioning in WDM optical networks under a scheduled traffic model,'' in Proceedings of IEEE Globecom'05 (IEEE, 2005), pp. 1900-1904.

T. Li and B. Wang, ''On optimal survivability design in WDM optical networks under a scheduled traffic model,'' in Proceedings of the 5th IEEE International Workshop on Design of Reliable Communication Networks (DRCN) (IEEE, 2005), pp. 23-30.

T. Li and B. Wang, ''Cost-effective shared path protection in WDM optical mesh networks with partial wavelength conversion,'' Photon. Network Commun. 8, 251-266 (2004).

B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, ''Routing and wavelength assignment under a scheduled traffic model in reconfigurable WDM optical networks,'' in Proceedings of Broadnets'05 (IEEE, 2005), pp. 15-24.

Luo, X.

B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, ''Routing and wavelength assignment under a scheduled traffic model in reconfigurable WDM optical networks,'' in Proceedings of Broadnets'05 (IEEE, 2005), pp. 15-24.

Miyao, Y.

Y. Miyao and H. Saito, ''Optimal design and evaluation of survivable WDM transport networks,'' IEEE J. Sel. Areas Commun. 16, 1190-1198 (1998).

Mouftah, H. T.

H. T. Mouftah and P.-H. Ho, Optical Networks: Architecture and Survivability (Kluwer, 2003).

Mukherjee, B.

M. Tornatore, A. Pattavina, J. Zhang, B. Mukherjee, and C. Ou, ''Efficient shared-path protection exploiting the knowledge of connection-holding time,'' in Optical Fiber Communications Conference (OFC'05) (Optical Society of America, 2005), paper OThk2.

H. Zang, C. Ou, and B. Mukherjee, ''Path-protection routing and wavelength assignment (RWA) in WDM mesh networks under duct-layer constraints,'' IEEE/ACM Trans. Netw. 11, 248-258 (2003).

H. Zang, C. Ou, and B. Mukherjee, ''Path-protection routing and wavelength-assignment in WDM mesh networks under shared-risk-group constraints,'' in Proc. SPIE 4585, 49-60 (2001).

H. Zang and B. Mukherjee, ''Connection management for survivable wavelength-routed WDM mesh networks,'' Opt. Networks Mag. Special Issue on Protection and Survivability in Optical Networks 2(4), 17-28 (2001).

Ou, C.

M. Tornatore, A. Pattavina, J. Zhang, B. Mukherjee, and C. Ou, ''Efficient shared-path protection exploiting the knowledge of connection-holding time,'' in Optical Fiber Communications Conference (OFC'05) (Optical Society of America, 2005), paper OThk2.

H. Zang, C. Ou, and B. Mukherjee, ''Path-protection routing and wavelength assignment (RWA) in WDM mesh networks under duct-layer constraints,'' IEEE/ACM Trans. Netw. 11, 248-258 (2003).

H. Zang, C. Ou, and B. Mukherjee, ''Path-protection routing and wavelength-assignment in WDM mesh networks under shared-risk-group constraints,'' in Proc. SPIE 4585, 49-60 (2001).

Pattavina, A.

M. Tornatore, A. Pattavina, J. Zhang, B. Mukherjee, and C. Ou, ''Efficient shared-path protection exploiting the knowledge of connection-holding time,'' in Optical Fiber Communications Conference (OFC'05) (Optical Society of America, 2005), paper OThk2.

Puech, N.

J. Kuri, N. Puech, and M. Gagnaire, ''Diverse routing of scheduled light path demands in an optical transport network,'' in Proceedings of Fourth International Workshop on the Design of Reliable Communication Networks (DRCN 2003) (IEEE, 2003), pp. 69-76.

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, ''Routing and wavelength assignments of scheduled light-path demands,'' IEEE J. Sel. Areas Commun. 21, 1231-1240 (2003).

Ramamurthy, B.

A. Todimala and B. Ramamurthy, ''A dynamic partitioning sub-path protection routing technique in WDM mesh networks,'' in International Conference on Computer Communications (ICCC'02) (ICCC Press, 2002), 327-340.

Saito, H.

Y. Miyao and H. Saito, ''Optimal design and evaluation of survivable WDM transport networks,'' IEEE J. Sel. Areas Commun. 16, 1190-1198 (1998).

Saradhi, C. V.

C. V. Saradhi, L. K. Wei, and M. Gurusamy, ''Provisioning fault-tolerant scheduled light-path demands in WDM mesh networks,'' in Proceedings of the First International Conference on Broadband Networks (BroadNets 2004) (IEEE Computer Society, 2004), pp. 150-159.

Todimala, A.

A. Todimala and B. Ramamurthy, ''A dynamic partitioning sub-path protection routing technique in WDM mesh networks,'' in International Conference on Computer Communications (ICCC'02) (ICCC Press, 2002), 327-340.

Tornatore, M.

M. Tornatore, A. Pattavina, J. Zhang, B. Mukherjee, and C. Ou, ''Efficient shared-path protection exploiting the knowledge of connection-holding time,'' in Optical Fiber Communications Conference (OFC'05) (Optical Society of America, 2005), paper OThk2.

Wang, B.

T. Li and B. Wang, ''On survivable service provisioning in WDM optical networks under a scheduled traffic model,'' in Proceedings of IEEE Globecom'05 (IEEE, 2005), pp. 1900-1904.

T. Li and B. Wang, ''On optimal survivability design in WDM optical networks under a scheduled traffic model,'' in Proceedings of the 5th IEEE International Workshop on Design of Reliable Communication Networks (DRCN) (IEEE, 2005), pp. 23-30.

T. Li and B. Wang, ''Efficient online algorithms for dynamic shared path protection in optical WDM networks,'' Photon. Network Commun. 9, 207-222 (2005).

T. Li and B. Wang, ''Cost-effective shared path protection in WDM optical mesh networks with partial wavelength conversion,'' Photon. Network Commun. 8, 251-266 (2004).

B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, ''Routing and wavelength assignment under a scheduled traffic model in reconfigurable WDM optical networks,'' in Proceedings of Broadnets'05 (IEEE, 2005), pp. 15-24.

Wei, L. K.

C. V. Saradhi, L. K. Wei, and M. Gurusamy, ''Provisioning fault-tolerant scheduled light-path demands in WDM mesh networks,'' in Proceedings of the First International Conference on Broadband Networks (BroadNets 2004) (IEEE Computer Society, 2004), pp. 150-159.

Wu, T.-H.

T.-H. Wu, ''Emerging technologies for fiber network survivability,'' IEEE Commun. Mag. 33(2), 58-59, 62-74 (1995).

Xin, C.

B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, ''Routing and wavelength assignment under a scheduled traffic model in reconfigurable WDM optical networks,'' in Proceedings of Broadnets'05 (IEEE, 2005), pp. 15-24.

Yuan, S.

S. Yuan and J. P. Jue, ''Shared protection routing algorithm for optical network,'' Opt. Networks Mag. 3, 32-39 (2002).

Zang, H.

H. Zang, WDM Mesh Networks: Management and Survivability (Kluwer, 2003).

H. Zang, C. Ou, and B. Mukherjee, ''Path-protection routing and wavelength assignment (RWA) in WDM mesh networks under duct-layer constraints,'' IEEE/ACM Trans. Netw. 11, 248-258 (2003).

H. Zang, C. Ou, and B. Mukherjee, ''Path-protection routing and wavelength-assignment in WDM mesh networks under shared-risk-group constraints,'' in Proc. SPIE 4585, 49-60 (2001).

H. Zang and B. Mukherjee, ''Connection management for survivable wavelength-routed WDM mesh networks,'' Opt. Networks Mag. Special Issue on Protection and Survivability in Optical Networks 2(4), 17-28 (2001).

Zhang, J.

M. Tornatore, A. Pattavina, J. Zhang, B. Mukherjee, and C. Ou, ''Efficient shared-path protection exploiting the knowledge of connection-holding time,'' in Optical Fiber Communications Conference (OFC'05) (Optical Society of America, 2005), paper OThk2.

IEEE Commun. Mag. (1)

T.-H. Wu, ''Emerging technologies for fiber network survivability,'' IEEE Commun. Mag. 33(2), 58-59, 62-74 (1995).

IEEE J. Sel. Areas Commun. (2)

Y. Miyao and H. Saito, ''Optimal design and evaluation of survivable WDM transport networks,'' IEEE J. Sel. Areas Commun. 16, 1190-1198 (1998).

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, ''Routing and wavelength assignments of scheduled light-path demands,'' IEEE J. Sel. Areas Commun. 21, 1231-1240 (2003).

IEEE/ACM Trans. Netw. (1)

H. Zang, C. Ou, and B. Mukherjee, ''Path-protection routing and wavelength assignment (RWA) in WDM mesh networks under duct-layer constraints,'' IEEE/ACM Trans. Netw. 11, 248-258 (2003).

Opt. Networks Mag. Special Issue on Protection and Survivability in Optical Networks (1)

H. Zang and B. Mukherjee, ''Connection management for survivable wavelength-routed WDM mesh networks,'' Opt. Networks Mag. Special Issue on Protection and Survivability in Optical Networks 2(4), 17-28 (2001).

Other (19)

S. Yuan and J. P. Jue, ''Shared protection routing algorithm for optical network,'' Opt. Networks Mag. 3, 32-39 (2002).

A. Todimala and B. Ramamurthy, ''A dynamic partitioning sub-path protection routing technique in WDM mesh networks,'' in International Conference on Computer Communications (ICCC'02) (ICCC Press, 2002), 327-340.

T. Li and B. Wang, ''Efficient online algorithms for dynamic shared path protection in optical WDM networks,'' Photon. Network Commun. 9, 207-222 (2005).

W. D. Grover, Mesh-Based Survivable Networks: Options and Strategies for Optical, MPLS, SONET, and ATM Networking (Prentice-Hall, 2003).

J. Kuri, ''Optimization problems in WDM optical transport networks with scheduled light-path demands,'' Ph.D. thesis (ENST Paris, 2003).

J. Kuri, N. Puech, and M. Gagnaire, ''Diverse routing of scheduled light path demands in an optical transport network,'' in Proceedings of Fourth International Workshop on the Design of Reliable Communication Networks (DRCN 2003) (IEEE, 2003), pp. 69-76.

M. Tornatore, A. Pattavina, J. Zhang, B. Mukherjee, and C. Ou, ''Efficient shared-path protection exploiting the knowledge of connection-holding time,'' in Optical Fiber Communications Conference (OFC'05) (Optical Society of America, 2005), paper OThk2.

C. V. Saradhi, L. K. Wei, and M. Gurusamy, ''Provisioning fault-tolerant scheduled light-path demands in WDM mesh networks,'' in Proceedings of the First International Conference on Broadband Networks (BroadNets 2004) (IEEE Computer Society, 2004), pp. 150-159.

B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, ''Routing and wavelength assignment under a scheduled traffic model in reconfigurable WDM optical networks,'' in Proceedings of Broadnets'05 (IEEE, 2005), pp. 15-24.

T. Li and B. Wang, ''On survivable service provisioning in WDM optical networks under a scheduled traffic model,'' in Proceedings of IEEE Globecom'05 (IEEE, 2005), pp. 1900-1904.

T. Li and B. Wang, ''On optimal survivability design in WDM optical networks under a scheduled traffic model,'' in Proceedings of the 5th IEEE International Workshop on Design of Reliable Communication Networks (DRCN) (IEEE, 2005), pp. 23-30.

The problems can easily be shown to be NP-complete.

Assume that demands in D′ are indexed from 1 to ∣D′∣.

M. Clouqueur and W. D. Grover, ''Mesh-restorable networks with complete dual failure restorability and with selectively enhanced dual-failure restorability properties,'' in Proceedings of OPTICOMM (SPIE, 2002), pp. 1-12.

J. Doucette and W. D. Grover, ''Capacity design studies of span-restorable mesh transport networks with shared-risk link group (SRLG) effects,'' in Proceedings of OPTICOMM (SPIE, 2002), pp. 25-38.

T. Li and B. Wang, ''Cost-effective shared path protection in WDM optical mesh networks with partial wavelength conversion,'' Photon. Network Commun. 8, 251-266 (2004).

H. Zang, WDM Mesh Networks: Management and Survivability (Kluwer, 2003).

H. T. Mouftah and P.-H. Ho, Optical Networks: Architecture and Survivability (Kluwer, 2003).

H. Zang, C. Ou, and B. Mukherjee, ''Path-protection routing and wavelength-assignment in WDM mesh networks under shared-risk-group constraints,'' in Proc. SPIE 4585, 49-60 (2001).

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