Abstract

<p><a href="http://www.osa-jon.org/virtual_issue.cfm?vid=16">Feature Issue on High Availability in Optical Networks</a></p>A resource provisioning method for optical backbone networks running IP or multiprotocol label switching (MPLS) is presented. Trunk and hose models are well-known bandwidth provisioning models, but both have significant disadvantages if applied to large-scale networks. The management complexity of the trunk model highly increases with the size of the network, and the bandwidth efficiency of the hose model is often excessively low. We propose an intermediate solution between the hose and trunk models. By dividing the network into clusters and using a cluster-based traffic description, an appropriate equilibrium can be found between management complexity and overprovisioning.

© 2006 Optical Society of America

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  1. A. Jüttner, I. Szabó, and A. Szentesi, 'On bandwith efficiency of the hose resource managment model in virtual private networks,' in Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2003) (IEEE, 2003), pp. 386-395.
  2. M. Minoux, 'Network synthesis and optimum network design problems: models, solution methods and applications,' Networks 13, 313-360 (1989).
  3. M. Pióro, A. Myslek, A. Jüttner, J. Harmatos, and A. Szentesi, 'Topological design of MPLS networks,' in Global Telecommunications Conference (GLOBECOM 2001) (IEEE, 2001), pp. 12-16.
  4. M. Pióro and P. Gajowniczek, 'Solving multicommodity integral flow problems by simulated allocation,' Telecommun. Syst. 1, 17-28 (1997).
  5. T. Cinkler, T. Henk, and G. Gordos, 'Stochastic algorithms for design of thrifty single-failure-protected networks,' in Proceedings of Design of Reliable Communications Networks DRCN 2000 (2000).
  6. M. Maliosz and T. Cinkler, 'Methods for optical VPN design over multifiber wavelength routing networks,' in Proceedings of the 7th IFIP Working Conference on Optical Design & Modelling (ONDM) (Elsevier, 2003).
  7. A. Feldmann, A. Greenberg, C. Lund, N. Reingold, J. Rexford, and F. True, 'Deriving traffic demands for operational IP networks: methodology and experience,' in ACM SIGCOMM 2000 (Association for Computing Machinery, 2003), pp. 257-270.
  8. N. Duffield, C. Lund, and M. Thorup, 'Estimating flow distributions from sampled flow statistics,' in ACM SIGCOMM 2003 (Association for Computing Machinery, 2003), pp. 325-336.
  9. Y. Zhang, M. Roughan, C. Lund, and D. Donoho, 'An information-theoretic approach to traffic matrix estimation,' in (ACM SIGCOMM 2003 (Association for Computing Machinery, 2003), pp. 301-312
  10. J. A. Fingerhut, S. Suri, and J. S. Turner, 'Designing least-cost nonblocking broadband networks,' J. Algorithms 24, 287-309 (1997).
    [CrossRef]
  11. J. A. Fingerhut, 'Approximation algorithms for configuring nonblocking communication networks,' Ph.D. dissertation (Washington University, 1994).
  12. N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. V. der Merwe, 'A flexible model for resource management in virtual private networks,' in ACM SIGCOMM '99 (Association for Computing Machinery, 1999), pp. 95-108.
  13. A. Kumar, R. Rastogi, A. Silberschatz, and B. Yener, 'Algorithms for provisioning virtual private networks in the hose model,' in ACM SIGCOMM 2001 (Association for Computing Machinery, 2001), pp. 135-148.
  14. G. 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 Communications Societies (INFOCOM 2002) (IEEE, 2002), pp. 131-139.
  15. S. Raghunath, K. Chandrayana, and S. Kalyanaraman, 'Edge-based QoS provisioning for point-to-set assured services,' in International Conference on Communications (ICC '02) (IEEE, 2002), pp. 1128-1134.
  16. T. Erlebach and M. Ruegg, 'Optimal bandwidth reservation in hose-model VPNs with multi-path routing,' in Twenty-Third Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2004) (IEEE, 2004), pp. 2275-2282.
  17. M. Berkelaar and J. Dirks, 'lplowbarsolve 4.0,' ftp://ftp.es.ele.tue.nl/pub/lplowbarsolve.
  18. 'AT&Tx2019's internet backbone network,' http://www.cybergeography.org/atlas/morelowbarisplowbarmaps.html (2000).
  19. S. Bhattacharyya, C. Diot, J. Jetcheva, and N. Taft, 'POP-level and access-link-level traffic dynamics in a tier-1 POP,' in Internet Measurement Workshop (IMW) (Association for Computing Machinery, 2001), pp. 39-53.
  20. B. G. Józsa, D. Orincsay, and A. Kern, 'On the use of routing optimization for virtual private network design,' in Proceedings of the 7th IFIP Working Conference on Optical Network Design and Modelling (ONDM) (Elsevier, 2003).
  21. R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications (Prentice-Hall, 1993).

1997 (2)

M. Pióro and P. Gajowniczek, 'Solving multicommodity integral flow problems by simulated allocation,' Telecommun. Syst. 1, 17-28 (1997).

J. A. Fingerhut, S. Suri, and J. S. Turner, 'Designing least-cost nonblocking broadband networks,' J. Algorithms 24, 287-309 (1997).
[CrossRef]

1989 (1)

M. Minoux, 'Network synthesis and optimum network design problems: models, solution methods and applications,' Networks 13, 313-360 (1989).

Ahuja, R. K.

R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications (Prentice-Hall, 1993).

Berkelaar, M.

M. Berkelaar and J. Dirks, 'lplowbarsolve 4.0,' ftp://ftp.es.ele.tue.nl/pub/lplowbarsolve.

Bhattacharyya, S.

S. Bhattacharyya, C. Diot, J. Jetcheva, and N. Taft, 'POP-level and access-link-level traffic dynamics in a tier-1 POP,' in Internet Measurement Workshop (IMW) (Association for Computing Machinery, 2001), pp. 39-53.

Chandrayana, K.

S. Raghunath, K. Chandrayana, and S. Kalyanaraman, 'Edge-based QoS provisioning for point-to-set assured services,' in International Conference on Communications (ICC '02) (IEEE, 2002), pp. 1128-1134.

Cinkler, T.

T. Cinkler, T. Henk, and G. Gordos, 'Stochastic algorithms for design of thrifty single-failure-protected networks,' in Proceedings of Design of Reliable Communications Networks DRCN 2000 (2000).

M. Maliosz and T. Cinkler, 'Methods for optical VPN design over multifiber wavelength routing networks,' in Proceedings of the 7th IFIP Working Conference on Optical Design & Modelling (ONDM) (Elsevier, 2003).

der Merwe, J. E. V.

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. V. der Merwe, 'A flexible model for resource management in virtual private networks,' in ACM SIGCOMM '99 (Association for Computing Machinery, 1999), pp. 95-108.

Diot, C.

S. Bhattacharyya, C. Diot, J. Jetcheva, and N. Taft, 'POP-level and access-link-level traffic dynamics in a tier-1 POP,' in Internet Measurement Workshop (IMW) (Association for Computing Machinery, 2001), pp. 39-53.

Dirks, J.

M. Berkelaar and J. Dirks, 'lplowbarsolve 4.0,' ftp://ftp.es.ele.tue.nl/pub/lplowbarsolve.

Donoho, D.

Y. Zhang, M. Roughan, C. Lund, and D. Donoho, 'An information-theoretic approach to traffic matrix estimation,' in (ACM SIGCOMM 2003 (Association for Computing Machinery, 2003), pp. 301-312

Duffield, N.

N. Duffield, C. Lund, and M. Thorup, 'Estimating flow distributions from sampled flow statistics,' in ACM SIGCOMM 2003 (Association for Computing Machinery, 2003), pp. 325-336.

Duffield, N. G.

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. V. der Merwe, 'A flexible model for resource management in virtual private networks,' in ACM SIGCOMM '99 (Association for Computing Machinery, 1999), pp. 95-108.

Erlebach, T.

T. Erlebach and M. Ruegg, 'Optimal bandwidth reservation in hose-model VPNs with multi-path routing,' in Twenty-Third Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2004) (IEEE, 2004), pp. 2275-2282.

Feldmann, A.

A. Feldmann, A. Greenberg, C. Lund, N. Reingold, J. Rexford, and F. True, 'Deriving traffic demands for operational IP networks: methodology and experience,' in ACM SIGCOMM 2000 (Association for Computing Machinery, 2003), pp. 257-270.

Fingerhut, J. A.

J. A. Fingerhut, S. Suri, and J. S. Turner, 'Designing least-cost nonblocking broadband networks,' J. Algorithms 24, 287-309 (1997).
[CrossRef]

J. A. Fingerhut, 'Approximation algorithms for configuring nonblocking communication networks,' Ph.D. dissertation (Washington University, 1994).

Gajowniczek, P.

M. Pióro and P. Gajowniczek, 'Solving multicommodity integral flow problems by simulated allocation,' Telecommun. Syst. 1, 17-28 (1997).

Gordos, G.

T. Cinkler, T. Henk, and G. Gordos, 'Stochastic algorithms for design of thrifty single-failure-protected networks,' in Proceedings of Design of Reliable Communications Networks DRCN 2000 (2000).

Goyal, P.

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. V. der Merwe, 'A flexible model for resource management in virtual private networks,' in ACM SIGCOMM '99 (Association for Computing Machinery, 1999), pp. 95-108.

Greenberg, A.

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. V. der Merwe, 'A flexible model for resource management in virtual private networks,' in ACM SIGCOMM '99 (Association for Computing Machinery, 1999), pp. 95-108.

A. Feldmann, A. Greenberg, C. Lund, N. Reingold, J. Rexford, and F. True, 'Deriving traffic demands for operational IP networks: methodology and experience,' in ACM SIGCOMM 2000 (Association for Computing Machinery, 2003), pp. 257-270.

Harmatos, J.

M. Pióro, A. Myslek, A. Jüttner, J. Harmatos, and A. Szentesi, 'Topological design of MPLS networks,' in Global Telecommunications Conference (GLOBECOM 2001) (IEEE, 2001), pp. 12-16.

Henk, T.

T. Cinkler, T. Henk, and G. Gordos, 'Stochastic algorithms for design of thrifty single-failure-protected networks,' in Proceedings of Design of Reliable Communications Networks DRCN 2000 (2000).

Italiano, G.

G. 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 Communications Societies (INFOCOM 2002) (IEEE, 2002), pp. 131-139.

Jetcheva, J.

S. Bhattacharyya, C. Diot, J. Jetcheva, and N. Taft, 'POP-level and access-link-level traffic dynamics in a tier-1 POP,' in Internet Measurement Workshop (IMW) (Association for Computing Machinery, 2001), pp. 39-53.

Józsa, B. G.

B. G. Józsa, D. Orincsay, and A. Kern, 'On the use of routing optimization for virtual private network design,' in Proceedings of the 7th IFIP Working Conference on Optical Network Design and Modelling (ONDM) (Elsevier, 2003).

Jüttner, A.

M. Pióro, A. Myslek, A. Jüttner, J. Harmatos, and A. Szentesi, 'Topological design of MPLS networks,' in Global Telecommunications Conference (GLOBECOM 2001) (IEEE, 2001), pp. 12-16.

A. Jüttner, I. Szabó, and A. Szentesi, 'On bandwith efficiency of the hose resource managment model in virtual private networks,' in Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2003) (IEEE, 2003), pp. 386-395.

Kalyanaraman, S.

S. Raghunath, K. Chandrayana, and S. Kalyanaraman, 'Edge-based QoS provisioning for point-to-set assured services,' in International Conference on Communications (ICC '02) (IEEE, 2002), pp. 1128-1134.

Kern, A.

B. G. Józsa, D. Orincsay, and A. Kern, 'On the use of routing optimization for virtual private network design,' in Proceedings of the 7th IFIP Working Conference on Optical Network Design and Modelling (ONDM) (Elsevier, 2003).

Kumar, A.

A. Kumar, R. Rastogi, A. Silberschatz, and B. Yener, 'Algorithms for provisioning virtual private networks in the hose model,' in ACM SIGCOMM 2001 (Association for Computing Machinery, 2001), pp. 135-148.

Lund, C.

A. Feldmann, A. Greenberg, C. Lund, N. Reingold, J. Rexford, and F. True, 'Deriving traffic demands for operational IP networks: methodology and experience,' in ACM SIGCOMM 2000 (Association for Computing Machinery, 2003), pp. 257-270.

Y. Zhang, M. Roughan, C. Lund, and D. Donoho, 'An information-theoretic approach to traffic matrix estimation,' in (ACM SIGCOMM 2003 (Association for Computing Machinery, 2003), pp. 301-312

N. Duffield, C. Lund, and M. Thorup, 'Estimating flow distributions from sampled flow statistics,' in ACM SIGCOMM 2003 (Association for Computing Machinery, 2003), pp. 325-336.

Magnanti, T. L.

R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications (Prentice-Hall, 1993).

Maliosz, M.

M. Maliosz and T. Cinkler, 'Methods for optical VPN design over multifiber wavelength routing networks,' in Proceedings of the 7th IFIP Working Conference on Optical Design & Modelling (ONDM) (Elsevier, 2003).

Minoux, M.

M. Minoux, 'Network synthesis and optimum network design problems: models, solution methods and applications,' Networks 13, 313-360 (1989).

Mishra, P.

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. V. der Merwe, 'A flexible model for resource management in virtual private networks,' in ACM SIGCOMM '99 (Association for Computing Machinery, 1999), pp. 95-108.

Myslek, A.

M. Pióro, A. Myslek, A. Jüttner, J. Harmatos, and A. Szentesi, 'Topological design of MPLS networks,' in Global Telecommunications Conference (GLOBECOM 2001) (IEEE, 2001), pp. 12-16.

Orincsay, D.

B. G. Józsa, D. Orincsay, and A. Kern, 'On the use of routing optimization for virtual private network design,' in Proceedings of the 7th IFIP Working Conference on Optical Network Design and Modelling (ONDM) (Elsevier, 2003).

Orlin, J. B.

R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications (Prentice-Hall, 1993).

Pióro, M.

M. Pióro and P. Gajowniczek, 'Solving multicommodity integral flow problems by simulated allocation,' Telecommun. Syst. 1, 17-28 (1997).

M. Pióro, A. Myslek, A. Jüttner, J. Harmatos, and A. Szentesi, 'Topological design of MPLS networks,' in Global Telecommunications Conference (GLOBECOM 2001) (IEEE, 2001), pp. 12-16.

Raghunath, S.

S. Raghunath, K. Chandrayana, and S. Kalyanaraman, 'Edge-based QoS provisioning for point-to-set assured services,' in International Conference on Communications (ICC '02) (IEEE, 2002), pp. 1128-1134.

Ramakrishnan, K. K.

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. V. der Merwe, 'A flexible model for resource management in virtual private networks,' in ACM SIGCOMM '99 (Association for Computing Machinery, 1999), pp. 95-108.

Rastogi, R.

G. 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 Communications Societies (INFOCOM 2002) (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 ACM SIGCOMM 2001 (Association for Computing Machinery, 2001), pp. 135-148.

Reingold, N.

A. Feldmann, A. Greenberg, C. Lund, N. Reingold, J. Rexford, and F. True, 'Deriving traffic demands for operational IP networks: methodology and experience,' in ACM SIGCOMM 2000 (Association for Computing Machinery, 2003), pp. 257-270.

Rexford, J.

A. Feldmann, A. Greenberg, C. Lund, N. Reingold, J. Rexford, and F. True, 'Deriving traffic demands for operational IP networks: methodology and experience,' in ACM SIGCOMM 2000 (Association for Computing Machinery, 2003), pp. 257-270.

Roughan, M.

Y. Zhang, M. Roughan, C. Lund, and D. Donoho, 'An information-theoretic approach to traffic matrix estimation,' in (ACM SIGCOMM 2003 (Association for Computing Machinery, 2003), pp. 301-312

Ruegg, M.

T. Erlebach and M. Ruegg, 'Optimal bandwidth reservation in hose-model VPNs with multi-path routing,' in Twenty-Third Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2004) (IEEE, 2004), pp. 2275-2282.

Silberschatz, A.

A. Kumar, R. Rastogi, A. Silberschatz, and B. Yener, 'Algorithms for provisioning virtual private networks in the hose model,' in ACM SIGCOMM 2001 (Association for Computing Machinery, 2001), pp. 135-148.

Suri, S.

J. A. Fingerhut, S. Suri, and J. S. Turner, 'Designing least-cost nonblocking broadband networks,' J. Algorithms 24, 287-309 (1997).
[CrossRef]

Szabó, I.

A. Jüttner, I. Szabó, and A. Szentesi, 'On bandwith efficiency of the hose resource managment model in virtual private networks,' in Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2003) (IEEE, 2003), pp. 386-395.

Szentesi, A.

A. Jüttner, I. Szabó, and A. Szentesi, 'On bandwith efficiency of the hose resource managment model in virtual private networks,' in Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2003) (IEEE, 2003), pp. 386-395.

M. Pióro, A. Myslek, A. Jüttner, J. Harmatos, and A. Szentesi, 'Topological design of MPLS networks,' in Global Telecommunications Conference (GLOBECOM 2001) (IEEE, 2001), pp. 12-16.

Taft, N.

S. Bhattacharyya, C. Diot, J. Jetcheva, and N. Taft, 'POP-level and access-link-level traffic dynamics in a tier-1 POP,' in Internet Measurement Workshop (IMW) (Association for Computing Machinery, 2001), pp. 39-53.

Thorup, M.

N. Duffield, C. Lund, and M. Thorup, 'Estimating flow distributions from sampled flow statistics,' in ACM SIGCOMM 2003 (Association for Computing Machinery, 2003), pp. 325-336.

True, F.

A. Feldmann, A. Greenberg, C. Lund, N. Reingold, J. Rexford, and F. True, 'Deriving traffic demands for operational IP networks: methodology and experience,' in ACM SIGCOMM 2000 (Association for Computing Machinery, 2003), pp. 257-270.

Turner, J. S.

J. A. Fingerhut, S. Suri, and J. S. Turner, 'Designing least-cost nonblocking broadband networks,' J. Algorithms 24, 287-309 (1997).
[CrossRef]

Yener, B.

A. Kumar, R. Rastogi, A. Silberschatz, and B. Yener, 'Algorithms for provisioning virtual private networks in the hose model,' in ACM SIGCOMM 2001 (Association for Computing Machinery, 2001), pp. 135-148.

G. 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 Communications Societies (INFOCOM 2002) (IEEE, 2002), pp. 131-139.

Zhang, Y.

Y. Zhang, M. Roughan, C. Lund, and D. Donoho, 'An information-theoretic approach to traffic matrix estimation,' in (ACM SIGCOMM 2003 (Association for Computing Machinery, 2003), pp. 301-312

J. Algorithms (1)

J. A. Fingerhut, S. Suri, and J. S. Turner, 'Designing least-cost nonblocking broadband networks,' J. Algorithms 24, 287-309 (1997).
[CrossRef]

Networks (1)

M. Minoux, 'Network synthesis and optimum network design problems: models, solution methods and applications,' Networks 13, 313-360 (1989).

Telecommun. Syst. (1)

M. Pióro and P. Gajowniczek, 'Solving multicommodity integral flow problems by simulated allocation,' Telecommun. Syst. 1, 17-28 (1997).

Other (18)

T. Cinkler, T. Henk, and G. Gordos, 'Stochastic algorithms for design of thrifty single-failure-protected networks,' in Proceedings of Design of Reliable Communications Networks DRCN 2000 (2000).

M. Maliosz and T. Cinkler, 'Methods for optical VPN design over multifiber wavelength routing networks,' in Proceedings of the 7th IFIP Working Conference on Optical Design & Modelling (ONDM) (Elsevier, 2003).

A. Feldmann, A. Greenberg, C. Lund, N. Reingold, J. Rexford, and F. True, 'Deriving traffic demands for operational IP networks: methodology and experience,' in ACM SIGCOMM 2000 (Association for Computing Machinery, 2003), pp. 257-270.

N. Duffield, C. Lund, and M. Thorup, 'Estimating flow distributions from sampled flow statistics,' in ACM SIGCOMM 2003 (Association for Computing Machinery, 2003), pp. 325-336.

Y. Zhang, M. Roughan, C. Lund, and D. Donoho, 'An information-theoretic approach to traffic matrix estimation,' in (ACM SIGCOMM 2003 (Association for Computing Machinery, 2003), pp. 301-312

M. Pióro, A. Myslek, A. Jüttner, J. Harmatos, and A. Szentesi, 'Topological design of MPLS networks,' in Global Telecommunications Conference (GLOBECOM 2001) (IEEE, 2001), pp. 12-16.

A. Jüttner, I. Szabó, and A. Szentesi, 'On bandwith efficiency of the hose resource managment model in virtual private networks,' in Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2003) (IEEE, 2003), pp. 386-395.

J. A. Fingerhut, 'Approximation algorithms for configuring nonblocking communication networks,' Ph.D. dissertation (Washington University, 1994).

N. G. Duffield, P. Goyal, A. Greenberg, P. Mishra, K. K. Ramakrishnan, and J. E. V. der Merwe, 'A flexible model for resource management in virtual private networks,' in ACM SIGCOMM '99 (Association for Computing Machinery, 1999), pp. 95-108.

A. Kumar, R. Rastogi, A. Silberschatz, and B. Yener, 'Algorithms for provisioning virtual private networks in the hose model,' in ACM SIGCOMM 2001 (Association for Computing Machinery, 2001), pp. 135-148.

G. 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 Communications Societies (INFOCOM 2002) (IEEE, 2002), pp. 131-139.

S. Raghunath, K. Chandrayana, and S. Kalyanaraman, 'Edge-based QoS provisioning for point-to-set assured services,' in International Conference on Communications (ICC '02) (IEEE, 2002), pp. 1128-1134.

T. Erlebach and M. Ruegg, 'Optimal bandwidth reservation in hose-model VPNs with multi-path routing,' in Twenty-Third Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2004) (IEEE, 2004), pp. 2275-2282.

M. Berkelaar and J. Dirks, 'lplowbarsolve 4.0,' ftp://ftp.es.ele.tue.nl/pub/lplowbarsolve.

'AT&Tx2019's internet backbone network,' http://www.cybergeography.org/atlas/morelowbarisplowbarmaps.html (2000).

S. Bhattacharyya, C. Diot, J. Jetcheva, and N. Taft, 'POP-level and access-link-level traffic dynamics in a tier-1 POP,' in Internet Measurement Workshop (IMW) (Association for Computing Machinery, 2001), pp. 39-53.

B. G. Józsa, D. Orincsay, and A. Kern, 'On the use of routing optimization for virtual private network design,' in Proceedings of the 7th IFIP Working Conference on Optical Network Design and Modelling (ONDM) (Elsevier, 2003).

R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications (Prentice-Hall, 1993).

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