Abstract

This paper investigates the issue of survivable routing to prevent arbitrary single-link failures in WDM networks when the traffic information is partially known. Two novel protection schemes called valiant-load-balancing- (VLB-) based hop constraint segment protection (VLB-HCSP) and hop constraint minimizing leaf nodes (HCMLN) are proposed and evaluated. Simulation results confirm our expectation that VLB-HCSP can achieve a desirable compromise between cost and failure recovery time compared with the previous VLB-based method, while HCMLN performs even more inspiringly for being able to provide both a low-cost budget and a fast recovery at the same time, in contrast to VLB-HCSP and the other existing schemes.

© 2009 Optical Society of America

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  1. B. Mukherjee, Optical Communication Networks (McGraw-Hill, 1997).
  2. A. Medina, N. Taft, K. Salamatian, S. Bhattacharyya, and C. Diot, “Traffic matrix estimation: existing techniques and new directions,” in Proceedings of ACM SIGCOMM (ACM, 2002), pp. 161-174.
  3. A. Gupta, J. Kleinberg, A. Kumar, R. Rastogi, and B. Yener, “Provisioning a virtual private network: a network design problem for multicommodity flow,” in ACM Symposium on Theory of Computing (ACM, 2001), pp. 389-398.
  4. R. Zhang-Shen and N. McKeown, “Designing a predictable Internet backbone network,” in Proceedings of HotNets III (2004).
  5. M. Kodialam, T. V. Lakshman, and S. Sengupta, “Efficient and robust routing of highly variable traffic,” in Proceedings of 3rd Workshop on Hot Topics in Networks (2004).
  6. N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. van der Merwe, “A flexible model for resource management in virtual private networks,” in Proceedings of ACM SIGCOMM (ACM, 1999), pp. 95-108.
  7. A. Juttner, I. Szabo, and A. Szentesi, “On bandwidth efficiency of the hose resource management model in virtual private network,” in Twenty-Second Annual Conference of the IEEE Computer and Communications Societies (IEEE, 2003), pp. 385-395.
  8. A. Kumar, R. Rastogi, A. Silberschatz, and B. Yener, “Algorithms for provisioning virtual private networks in the hose model,” in Proceedings of ACM SIGCOMM (ACM, 2001), pp. 135-146.
  9. R. Zhang-Shen and N. McKeown, “Designing a fault-tolerant network using valiant load-balancing,” in The 27th Conference on Computer Communications (IEEE, 2008), pp. 2360-2368.
  10. 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).
    [CrossRef]
  11. G. F. Italiano, R. Rastogi, and B. Yener, “Restoration algorithms for virtual private networks in the hose model,” in Twenty-First Annual Joint Conference of the IEEE Computer and Communication Societies (IEEE, 2002), pp. 131-139.
  12. Y. L. Liu, Y. S. Sun, and M. C. Chen, “Traffic engineering for hose-model VPN provisioning,” in IEEE Global Telecommunications Conference (IEEE, 2005), pp. 1080-1085.
  13. P. Ho, J. Tapolcai, and T. Cinkler, “Segment shared protection in mesh communications networks with bandwidth guaranteed tunnels,” IEEE/ACM Trans. Netw. 12, 1105-1118 (2004).
    [CrossRef]
  14. D. Xu, Y. Xiong, and C. Qiao, “Novel algorithms for shared segment protection,” IEEE J. Sel. Areas Commun. 21, 1320-1331 (2003).
    [CrossRef]
  15. F. Harary, Graph Theory (Addison-Wesley, 1972).
  16. K. Zhu and B. Mukherjee, “Traffic grooming in an optical WDM mesh network,” IEEE J. Sel. Areas Commun. 20, 122-133 (2002).
    [CrossRef]
  17. E. Modiano and P. J. Lin, “Traffic grooming in WDM networks,” IEEE Commun. Mag. 39(7), 124-129 (2001).
    [CrossRef]
  18. H. B. Wen, R. X. He, L. M. Li, and S. Wang, “Dynamic traffic-grooming algorithms in wavelength-division-multiplexing mesh networks,” J. Opt. Netw. 2, 100-111 (2003).
  19. C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks--shared protection,” IEEE J. Sel. Areas Commun. 21, 1367-1383 (2003).
    [CrossRef]
  20. M. Kodialam, T. V. Lakshman, J. B. Orlin, and S. Sengupta, “Preconfiguring IP-over-optical networks to handle router failures and unpredictable traffic,” IEEE J. Sel. Areas Commun. 25, 934-947 (2007).
  21. L. Valiant and G. Brebner, “Universal scheme for parallel communications,” in Proceedings of the 13th Annual Symposium on Theory Computing (ACM, 1981), pp. 263-277.

2007 (1)

M. Kodialam, T. V. Lakshman, J. B. Orlin, and S. Sengupta, “Preconfiguring IP-over-optical networks to handle router failures and unpredictable traffic,” IEEE J. Sel. Areas Commun. 25, 934-947 (2007).

2004 (1)

P. Ho, J. Tapolcai, and T. Cinkler, “Segment shared protection in mesh communications networks with bandwidth guaranteed tunnels,” IEEE/ACM Trans. Netw. 12, 1105-1118 (2004).
[CrossRef]

2003 (4)

D. Xu, Y. Xiong, and C. Qiao, “Novel algorithms for shared segment protection,” IEEE J. Sel. Areas Commun. 21, 1320-1331 (2003).
[CrossRef]

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).
[CrossRef]

H. B. Wen, R. X. He, L. M. Li, and S. Wang, “Dynamic traffic-grooming algorithms in wavelength-division-multiplexing mesh networks,” J. Opt. Netw. 2, 100-111 (2003).

C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks--shared protection,” IEEE J. Sel. Areas Commun. 21, 1367-1383 (2003).
[CrossRef]

2002 (1)

K. Zhu and B. Mukherjee, “Traffic grooming in an optical WDM mesh network,” IEEE J. Sel. Areas Commun. 20, 122-133 (2002).
[CrossRef]

2001 (1)

E. Modiano and P. J. Lin, “Traffic grooming in WDM networks,” IEEE Commun. Mag. 39(7), 124-129 (2001).
[CrossRef]

Bhattacharyya, S.

A. Medina, N. Taft, K. Salamatian, S. Bhattacharyya, and C. Diot, “Traffic matrix estimation: existing techniques and new directions,” in Proceedings of ACM SIGCOMM (ACM, 2002), pp. 161-174.

Brebner, G.

L. Valiant and G. Brebner, “Universal scheme for parallel communications,” in Proceedings of the 13th Annual Symposium on Theory Computing (ACM, 1981), pp. 263-277.

Chen, M. C.

Y. L. Liu, Y. S. Sun, and M. C. Chen, “Traffic engineering for hose-model VPN provisioning,” in IEEE Global Telecommunications Conference (IEEE, 2005), pp. 1080-1085.

Cinkler, T.

P. Ho, J. Tapolcai, and T. Cinkler, “Segment shared protection in mesh communications networks with bandwidth guaranteed tunnels,” IEEE/ACM Trans. Netw. 12, 1105-1118 (2004).
[CrossRef]

Diot, C.

A. Medina, N. Taft, K. Salamatian, S. Bhattacharyya, and C. Diot, “Traffic matrix estimation: existing techniques and new directions,” in Proceedings of ACM SIGCOMM (ACM, 2002), pp. 161-174.

Duffield, N. G.

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. van der Merwe, “A flexible model for resource management in virtual private networks,” in Proceedings of ACM SIGCOMM (ACM, 1999), pp. 95-108.

Goyal, P.

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. van der Merwe, “A flexible model for resource management in virtual private networks,” in Proceedings of ACM SIGCOMM (ACM, 1999), pp. 95-108.

Greenberg, A.

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. van der Merwe, “A flexible model for resource management in virtual private networks,” in Proceedings of ACM SIGCOMM (ACM, 1999), pp. 95-108.

Gupta, A.

A. Gupta, J. Kleinberg, A. Kumar, R. Rastogi, and B. Yener, “Provisioning a virtual private network: a network design problem for multicommodity flow,” in ACM Symposium on Theory of Computing (ACM, 2001), pp. 389-398.

Harary, F.

F. Harary, Graph Theory (Addison-Wesley, 1972).

He, R. X.

Ho, P.

P. Ho, J. Tapolcai, and T. Cinkler, “Segment shared protection in mesh communications networks with bandwidth guaranteed tunnels,” IEEE/ACM Trans. Netw. 12, 1105-1118 (2004).
[CrossRef]

Italiano, G. F.

G. F. Italiano, R. Rastogi, and B. Yener, “Restoration algorithms for virtual private networks in the hose model,” in Twenty-First Annual Joint Conference of the IEEE Computer and Communication Societies (IEEE, 2002), pp. 131-139.

Juttner, A.

A. Juttner, I. Szabo, and A. Szentesi, “On bandwidth efficiency of the hose resource management model in virtual private network,” in Twenty-Second Annual Conference of the IEEE Computer and Communications Societies (IEEE, 2003), pp. 385-395.

Kleinberg, J.

A. Gupta, J. Kleinberg, A. Kumar, R. Rastogi, and B. Yener, “Provisioning a virtual private network: a network design problem for multicommodity flow,” in ACM Symposium on Theory of Computing (ACM, 2001), pp. 389-398.

Kodialam, M.

M. Kodialam, T. V. Lakshman, J. B. Orlin, and S. Sengupta, “Preconfiguring IP-over-optical networks to handle router failures and unpredictable traffic,” IEEE J. Sel. Areas Commun. 25, 934-947 (2007).

M. Kodialam, T. V. Lakshman, and S. Sengupta, “Efficient and robust routing of highly variable traffic,” in Proceedings of 3rd Workshop on Hot Topics in Networks (2004).

Kumar, A.

A. Kumar, R. Rastogi, A. Silberschatz, and B. Yener, “Algorithms for provisioning virtual private networks in the hose model,” in Proceedings of ACM SIGCOMM (ACM, 2001), pp. 135-146.

A. Gupta, J. Kleinberg, A. Kumar, R. Rastogi, and B. Yener, “Provisioning a virtual private network: a network design problem for multicommodity flow,” in ACM Symposium on Theory of Computing (ACM, 2001), pp. 389-398.

Lakshman, T. V.

M. Kodialam, T. V. Lakshman, J. B. Orlin, and S. Sengupta, “Preconfiguring IP-over-optical networks to handle router failures and unpredictable traffic,” IEEE J. Sel. Areas Commun. 25, 934-947 (2007).

M. Kodialam, T. V. Lakshman, and S. Sengupta, “Efficient and robust routing of highly variable traffic,” in Proceedings of 3rd Workshop on Hot Topics in Networks (2004).

Li, L. M.

Lin, P. J.

E. Modiano and P. J. Lin, “Traffic grooming in WDM networks,” IEEE Commun. Mag. 39(7), 124-129 (2001).
[CrossRef]

Liu, Y. L.

Y. L. Liu, Y. S. Sun, and M. C. Chen, “Traffic engineering for hose-model VPN provisioning,” in IEEE Global Telecommunications Conference (IEEE, 2005), pp. 1080-1085.

McKeown, N.

R. Zhang-Shen and N. McKeown, “Designing a fault-tolerant network using valiant load-balancing,” in The 27th Conference on Computer Communications (IEEE, 2008), pp. 2360-2368.

R. Zhang-Shen and N. McKeown, “Designing a predictable Internet backbone network,” in Proceedings of HotNets III (2004).

Medina, A.

A. Medina, N. Taft, K. Salamatian, S. Bhattacharyya, and C. Diot, “Traffic matrix estimation: existing techniques and new directions,” in Proceedings of ACM SIGCOMM (ACM, 2002), pp. 161-174.

Mishra, P.

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. van der Merwe, “A flexible model for resource management in virtual private networks,” in Proceedings of ACM SIGCOMM (ACM, 1999), pp. 95-108.

Modiano, E.

E. Modiano and P. J. Lin, “Traffic grooming in WDM networks,” IEEE Commun. Mag. 39(7), 124-129 (2001).
[CrossRef]

Mukherjee, B.

C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks--shared protection,” IEEE J. Sel. Areas Commun. 21, 1367-1383 (2003).
[CrossRef]

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).
[CrossRef]

K. Zhu and B. Mukherjee, “Traffic grooming in an optical WDM mesh network,” IEEE J. Sel. Areas Commun. 20, 122-133 (2002).
[CrossRef]

B. Mukherjee, Optical Communication Networks (McGraw-Hill, 1997).

Orlin, J. B.

M. Kodialam, T. V. Lakshman, J. B. Orlin, and S. Sengupta, “Preconfiguring IP-over-optical networks to handle router failures and unpredictable traffic,” IEEE J. Sel. Areas Commun. 25, 934-947 (2007).

Ou, C.

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).
[CrossRef]

C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks--shared protection,” IEEE J. Sel. Areas Commun. 21, 1367-1383 (2003).
[CrossRef]

Qiao, C.

D. Xu, Y. Xiong, and C. Qiao, “Novel algorithms for shared segment protection,” IEEE J. Sel. Areas Commun. 21, 1320-1331 (2003).
[CrossRef]

Ramakrishnan, K. K.

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. van der Merwe, “A flexible model for resource management in virtual private networks,” in Proceedings of ACM SIGCOMM (ACM, 1999), pp. 95-108.

Rastogi, R.

A. Gupta, J. Kleinberg, A. Kumar, R. Rastogi, and B. Yener, “Provisioning a virtual private network: a network design problem for multicommodity flow,” in ACM Symposium on Theory of Computing (ACM, 2001), pp. 389-398.

A. Kumar, R. Rastogi, A. Silberschatz, and B. Yener, “Algorithms for provisioning virtual private networks in the hose model,” in Proceedings of ACM SIGCOMM (ACM, 2001), pp. 135-146.

G. F. Italiano, R. Rastogi, and B. Yener, “Restoration algorithms for virtual private networks in the hose model,” in Twenty-First Annual Joint Conference of the IEEE Computer and Communication Societies (IEEE, 2002), pp. 131-139.

Sahasrabuddhe, L. H.

C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks--shared protection,” IEEE J. Sel. Areas Commun. 21, 1367-1383 (2003).
[CrossRef]

Salamatian, K.

A. Medina, N. Taft, K. Salamatian, S. Bhattacharyya, and C. Diot, “Traffic matrix estimation: existing techniques and new directions,” in Proceedings of ACM SIGCOMM (ACM, 2002), pp. 161-174.

Sengupta, S.

M. Kodialam, T. V. Lakshman, J. B. Orlin, and S. Sengupta, “Preconfiguring IP-over-optical networks to handle router failures and unpredictable traffic,” IEEE J. Sel. Areas Commun. 25, 934-947 (2007).

M. Kodialam, T. V. Lakshman, and S. Sengupta, “Efficient and robust routing of highly variable traffic,” in Proceedings of 3rd Workshop on Hot Topics in Networks (2004).

Silberschatz, A.

A. Kumar, R. Rastogi, A. Silberschatz, and B. Yener, “Algorithms for provisioning virtual private networks in the hose model,” in Proceedings of ACM SIGCOMM (ACM, 2001), pp. 135-146.

Sun, Y. S.

Y. L. Liu, Y. S. Sun, and M. C. Chen, “Traffic engineering for hose-model VPN provisioning,” in IEEE Global Telecommunications Conference (IEEE, 2005), pp. 1080-1085.

Szabo, I.

A. Juttner, I. Szabo, and A. Szentesi, “On bandwidth efficiency of the hose resource management model in virtual private network,” in Twenty-Second Annual Conference of the IEEE Computer and Communications Societies (IEEE, 2003), pp. 385-395.

Szentesi, A.

A. Juttner, I. Szabo, and A. Szentesi, “On bandwidth efficiency of the hose resource management model in virtual private network,” in Twenty-Second Annual Conference of the IEEE Computer and Communications Societies (IEEE, 2003), pp. 385-395.

Taft, N.

A. Medina, N. Taft, K. Salamatian, S. Bhattacharyya, and C. Diot, “Traffic matrix estimation: existing techniques and new directions,” in Proceedings of ACM SIGCOMM (ACM, 2002), pp. 161-174.

Tapolcai, J.

P. Ho, J. Tapolcai, and T. Cinkler, “Segment shared protection in mesh communications networks with bandwidth guaranteed tunnels,” IEEE/ACM Trans. Netw. 12, 1105-1118 (2004).
[CrossRef]

Valiant, L.

L. Valiant and G. Brebner, “Universal scheme for parallel communications,” in Proceedings of the 13th Annual Symposium on Theory Computing (ACM, 1981), pp. 263-277.

van der Merwe, J. E.

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. van der Merwe, “A flexible model for resource management in virtual private networks,” in Proceedings of ACM SIGCOMM (ACM, 1999), pp. 95-108.

Wang, S.

Wen, H. B.

Xiong, Y.

D. Xu, Y. Xiong, and C. Qiao, “Novel algorithms for shared segment protection,” IEEE J. Sel. Areas Commun. 21, 1320-1331 (2003).
[CrossRef]

Xu, D.

D. Xu, Y. Xiong, and C. Qiao, “Novel algorithms for shared segment protection,” IEEE J. Sel. Areas Commun. 21, 1320-1331 (2003).
[CrossRef]

Yener, B.

A. Gupta, J. Kleinberg, A. Kumar, R. Rastogi, and B. Yener, “Provisioning a virtual private network: a network design problem for multicommodity flow,” in ACM Symposium on Theory of Computing (ACM, 2001), pp. 389-398.

G. F. Italiano, R. Rastogi, and B. Yener, “Restoration algorithms for virtual private networks in the hose model,” in Twenty-First Annual Joint Conference of the IEEE Computer and Communication Societies (IEEE, 2002), pp. 131-139.

A. Kumar, R. Rastogi, A. Silberschatz, and B. Yener, “Algorithms for provisioning virtual private networks in the hose model,” in Proceedings of ACM SIGCOMM (ACM, 2001), pp. 135-146.

Zang, H.

C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks--shared protection,” IEEE J. Sel. Areas Commun. 21, 1367-1383 (2003).
[CrossRef]

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).
[CrossRef]

Zhang-Shen, R.

R. Zhang-Shen and N. McKeown, “Designing a fault-tolerant network using valiant load-balancing,” in The 27th Conference on Computer Communications (IEEE, 2008), pp. 2360-2368.

R. Zhang-Shen and N. McKeown, “Designing a predictable Internet backbone network,” in Proceedings of HotNets III (2004).

Zhu, K.

C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks--shared protection,” IEEE J. Sel. Areas Commun. 21, 1367-1383 (2003).
[CrossRef]

K. Zhu and B. Mukherjee, “Traffic grooming in an optical WDM mesh network,” IEEE J. Sel. Areas Commun. 20, 122-133 (2002).
[CrossRef]

IEEE Commun. Mag. (1)

E. Modiano and P. J. Lin, “Traffic grooming in WDM networks,” IEEE Commun. Mag. 39(7), 124-129 (2001).
[CrossRef]

IEEE J. Sel. Areas Commun. (4)

K. Zhu and B. Mukherjee, “Traffic grooming in an optical WDM mesh network,” IEEE J. Sel. Areas Commun. 20, 122-133 (2002).
[CrossRef]

D. Xu, Y. Xiong, and C. Qiao, “Novel algorithms for shared segment protection,” IEEE J. Sel. Areas Commun. 21, 1320-1331 (2003).
[CrossRef]

C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks--shared protection,” IEEE J. Sel. Areas Commun. 21, 1367-1383 (2003).
[CrossRef]

M. Kodialam, T. V. Lakshman, J. B. Orlin, and S. Sengupta, “Preconfiguring IP-over-optical networks to handle router failures and unpredictable traffic,” IEEE J. Sel. Areas Commun. 25, 934-947 (2007).

IEEE/ACM Trans. Netw. (2)

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).
[CrossRef]

P. Ho, J. Tapolcai, and T. Cinkler, “Segment shared protection in mesh communications networks with bandwidth guaranteed tunnels,” IEEE/ACM Trans. Netw. 12, 1105-1118 (2004).
[CrossRef]

J. Opt. Netw. (1)

Other (13)

G. F. Italiano, R. Rastogi, and B. Yener, “Restoration algorithms for virtual private networks in the hose model,” in Twenty-First Annual Joint Conference of the IEEE Computer and Communication Societies (IEEE, 2002), pp. 131-139.

Y. L. Liu, Y. S. Sun, and M. C. Chen, “Traffic engineering for hose-model VPN provisioning,” in IEEE Global Telecommunications Conference (IEEE, 2005), pp. 1080-1085.

F. Harary, Graph Theory (Addison-Wesley, 1972).

B. Mukherjee, Optical Communication Networks (McGraw-Hill, 1997).

A. Medina, N. Taft, K. Salamatian, S. Bhattacharyya, and C. Diot, “Traffic matrix estimation: existing techniques and new directions,” in Proceedings of ACM SIGCOMM (ACM, 2002), pp. 161-174.

A. Gupta, J. Kleinberg, A. Kumar, R. Rastogi, and B. Yener, “Provisioning a virtual private network: a network design problem for multicommodity flow,” in ACM Symposium on Theory of Computing (ACM, 2001), pp. 389-398.

R. Zhang-Shen and N. McKeown, “Designing a predictable Internet backbone network,” in Proceedings of HotNets III (2004).

M. Kodialam, T. V. Lakshman, and S. Sengupta, “Efficient and robust routing of highly variable traffic,” in Proceedings of 3rd Workshop on Hot Topics in Networks (2004).

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. van der Merwe, “A flexible model for resource management in virtual private networks,” in Proceedings of ACM SIGCOMM (ACM, 1999), pp. 95-108.

A. Juttner, I. Szabo, and A. Szentesi, “On bandwidth efficiency of the hose resource management model in virtual private network,” in Twenty-Second Annual Conference of the IEEE Computer and Communications Societies (IEEE, 2003), pp. 385-395.

A. Kumar, R. Rastogi, A. Silberschatz, and B. Yener, “Algorithms for provisioning virtual private networks in the hose model,” in Proceedings of ACM SIGCOMM (ACM, 2001), pp. 135-146.

R. Zhang-Shen and N. McKeown, “Designing a fault-tolerant network using valiant load-balancing,” in The 27th Conference on Computer Communications (IEEE, 2008), pp. 2360-2368.

L. Valiant and G. Brebner, “Universal scheme for parallel communications,” in Proceedings of the 13th Annual Symposium on Theory Computing (ACM, 1981), pp. 263-277.

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