Abstract

We address the problem of generating physical realistic optical transport network topologies. This type of network has characteristics that differ from scale-free networks, such as the Internet. Based on the analysis of a set of real transport topologies, we identify and assess relevant characteristics. A method to generate realistic topologies is proposed. The proposed method is validated by comparing the characteristics of computer-generated and real-world optical transport networks.

© 2009 Optical Society of America

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  49. H. Tangmunarunkit, R. Govindan, S. Jamin, S. Shenker, W. Willinger, “Network topology generators: degree-based vs. structural,” in Proc. of the Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communication, SIGCOMM ’02, vol. 32, no. 4, New York, NY, USA: ACM, Aug. 2002, pp. 147–159.

2007

C. T. Politi, H. Haunstein, D. A. Schupke, S. Duhovnikov, G. Lehmann, A. Stavdas, M. Gunkel, J. Martensson, A. Lord, “Integrated design and operation of a transparent optical network: a systematic approach to include physical layer awareness and cost function,” IEEE Commun. Mag., vol. 45, no. 2, pp. 40–47, Feb. 2007.
[CrossRef]

A.-L. Barabasi, “The architecture of complexity,” IEEE Control Syst., vol. 27, no. 4, pp. 33–42, Aug. 2007.
[CrossRef]

2005

M. Naldi, “Connectivity of Waxman topology models,” Comput. Commun., vol. 29, no. 1, pp. 24–31, 2005.
[CrossRef]

2004

2003

S. Ramamurthy, L. Sahasrabuddhe, B. Mukherjee, “Survivable WDM mesh networks,” J. Lightwave Technol., vol. 21, no. 4, pp. 870–883, Apr. 2003.
[CrossRef]

G. Siganos, M. Faloutsos, P. Faloutsos, C. Faloutsos, “Power laws and the as-level Internet topology,” IEEE/ACM Trans. Netw., vol. 11, no. 4, pp. 514–524, Aug. 2003.
[CrossRef]

A.-L. Barabasi, E. Bonabeau, “Scale-free networks,” Sci. Am., vol. 288, no. 5, pp. 50–59, May 2003.
[CrossRef]

2002

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, M. Pickavet, P. Lagasse, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

1988

B. Waxman, “Routing of multipoint connections,” IEEE J. Sel. Areas Commun., vol. 6, no. 9, pp. 1617–1622, Dec. 1988.
[CrossRef]

Barabasi, A.-L.

A.-L. Barabasi, “The architecture of complexity,” IEEE Control Syst., vol. 27, no. 4, pp. 33–42, Aug. 2007.
[CrossRef]

A.-L. Barabasi, E. Bonabeau, “Scale-free networks,” Sci. Am., vol. 288, no. 5, pp. 50–59, May 2003.
[CrossRef]

Bhattacharjee, S.

E. Zegura, K. Calvert, S. Bhattacharjee, “How to model an internetwork,” in Proc. of the 15th Annu. Joint Conf. of the IEEE Computer Societies. Networking the Next Generation. INFOCOM ’96, vol. 2, Mar. 1996, pp. 594–602.

Bonabeau, E.

A.-L. Barabasi, E. Bonabeau, “Scale-free networks,” Sci. Am., vol. 288, no. 5, pp. 50–59, May 2003.
[CrossRef]

Byers, J.

A. Medina, A. Lakhina, I. Matta, J. Byers, “Brite: an approach to universal topology generation,” in Proc. of the 9th Int. Symp. on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, MASCOTS ’01, Aug. 2001, pp. 346–353.

Calvert, K.

E. Zegura, K. Calvert, S. Bhattacharjee, “How to model an internetwork,” in Proc. of the 15th Annu. Joint Conf. of the IEEE Computer Societies. Networking the Next Generation. INFOCOM ’96, vol. 2, Mar. 1996, pp. 594–602.

Careglio, D.

M. Klinkowski, F. Herrero, D. Careglio, J. Sol-Pareta, “Adaptive routing algorithms for optical packet switching networks,” in Proc. of the Conf. on Optical Network Design and Modelling, ONMD ’05, Feb 2005, pp. 235–241.

Cheng, L.

L. Cheng, N. Hutchinson, M. Ito, “Realnet: a topology generator based on real Internet topology,” in Proc. of the 22nd Int. Conf. on Advanced Information Networking and Applications, AINAW ’08, Mar. 2008, pp. 526–532.

Cheyns, J.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, M. Pickavet, P. Lagasse, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

Colle, D.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, M. Pickavet, P. Lagasse, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

De Maesschalck, S.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, M. Pickavet, P. Lagasse, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

Demeester, P.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, M. Pickavet, P. Lagasse, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

J.-P. Vasseur, M. Pickavet, P. Demeester, Network Recovery: Protection and Restoration of Optical, SONET-SDH, IP, and MPLS. San Francisco, CA, USA: Morgan Kaufmann, 2004.

Develder, C.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, M. Pickavet, P. Lagasse, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

Doar, M.

M. Doar, “A better model for generating test networks,” in Proc. of the IEEE Global Telecommunications Conf., GLOBECOM ’96, Nov. 1996, pp. 86–93.

Duhovnikov, S.

C. T. Politi, H. Haunstein, D. A. Schupke, S. Duhovnikov, G. Lehmann, A. Stavdas, M. Gunkel, J. Martensson, A. Lord, “Integrated design and operation of a transparent optical network: a systematic approach to include physical layer awareness and cost function,” IEEE Commun. Mag., vol. 45, no. 2, pp. 40–47, Feb. 2007.
[CrossRef]

Faloutsos, C.

G. Siganos, M. Faloutsos, P. Faloutsos, C. Faloutsos, “Power laws and the as-level Internet topology,” IEEE/ACM Trans. Netw., vol. 11, no. 4, pp. 514–524, Aug. 2003.
[CrossRef]

M. Faloutsos, P. Faloutsos, C. Faloutsos, “On power-law relationships of the Internet topology,” in Proc. of the Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communication, SIGCOMM ’99, New York, NY, USA: ACM, 1999, pp. 251–262.

Faloutsos, M.

G. Siganos, M. Faloutsos, P. Faloutsos, C. Faloutsos, “Power laws and the as-level Internet topology,” IEEE/ACM Trans. Netw., vol. 11, no. 4, pp. 514–524, Aug. 2003.
[CrossRef]

M. Faloutsos, P. Faloutsos, C. Faloutsos, “On power-law relationships of the Internet topology,” in Proc. of the Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communication, SIGCOMM ’99, New York, NY, USA: ACM, 1999, pp. 251–262.

Faloutsos, P.

G. Siganos, M. Faloutsos, P. Faloutsos, C. Faloutsos, “Power laws and the as-level Internet topology,” IEEE/ACM Trans. Netw., vol. 11, no. 4, pp. 514–524, Aug. 2003.
[CrossRef]

M. Faloutsos, P. Faloutsos, C. Faloutsos, “On power-law relationships of the Internet topology,” in Proc. of the Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communication, SIGCOMM ’99, New York, NY, USA: ACM, 1999, pp. 251–262.

Govindan, R.

H. Tangmunarunkit, R. Govindan, S. Jamin, S. Shenker, W. Willinger, “Network topology generators: degree-based vs. structural,” in Proc. of the Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communication, SIGCOMM ’02, vol. 32, no. 4, New York, NY, USA: ACM, Aug. 2002, pp. 147–159.

Groebbens, A.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, M. Pickavet, P. Lagasse, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

Grover, W. D.

W. D. Grover, Mesh-Based Survivable Networks: Options and Strategies for Optical, MPLS, SONET, and ATM Networking. NJ: Prentice Hall, 2004.

Gunes, M. H.

M. H. Gunes, K. Sarac, “Inferring subnets in router-level topology collection studies,” in IMC ’07: Proc. of the 7th ACM SIGCOMM Conf. on Internet Measurement, New York, NY, USA: ACM, 2007, pp. 203–208.

Gunkel, M.

C. T. Politi, H. Haunstein, D. A. Schupke, S. Duhovnikov, G. Lehmann, A. Stavdas, M. Gunkel, J. Martensson, A. Lord, “Integrated design and operation of a transparent optical network: a systematic approach to include physical layer awareness and cost function,” IEEE Commun. Mag., vol. 45, no. 2, pp. 40–47, Feb. 2007.
[CrossRef]

Haunstein, H.

C. T. Politi, H. Haunstein, D. A. Schupke, S. Duhovnikov, G. Lehmann, A. Stavdas, M. Gunkel, J. Martensson, A. Lord, “Integrated design and operation of a transparent optical network: a systematic approach to include physical layer awareness and cost function,” IEEE Commun. Mag., vol. 45, no. 2, pp. 40–47, Feb. 2007.
[CrossRef]

Herrero, F.

M. Klinkowski, F. Herrero, D. Careglio, J. Sol-Pareta, “Adaptive routing algorithms for optical packet switching networks,” in Proc. of the Conf. on Optical Network Design and Modelling, ONMD ’05, Feb 2005, pp. 235–241.

Hutchinson, N.

L. Cheng, N. Hutchinson, M. Ito, “Realnet: a topology generator based on real Internet topology,” in Proc. of the 22nd Int. Conf. on Advanced Information Networking and Applications, AINAW ’08, Mar. 2008, pp. 526–532.

Ito, M.

L. Cheng, N. Hutchinson, M. Ito, “Realnet: a topology generator based on real Internet topology,” in Proc. of the 22nd Int. Conf. on Advanced Information Networking and Applications, AINAW ’08, Mar. 2008, pp. 526–532.

Jamin, S.

C. Jin, C. J. Qian, S. Jamin, “Inet: Internet topology generator,” Technical Report CSE-TR-433-00, EECS Department, University of Michigan, 2000.

H. Tangmunarunkit, R. Govindan, S. Jamin, S. Shenker, W. Willinger, “Network topology generators: degree-based vs. structural,” in Proc. of the Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communication, SIGCOMM ’02, vol. 32, no. 4, New York, NY, USA: ACM, Aug. 2002, pp. 147–159.

Jin, C.

C. Jin, C. J. Qian, S. Jamin, “Inet: Internet topology generator,” Technical Report CSE-TR-433-00, EECS Department, University of Michigan, 2000.

Klinkowski, M.

M. Klinkowski, F. Herrero, D. Careglio, J. Sol-Pareta, “Adaptive routing algorithms for optical packet switching networks,” in Proc. of the Conf. on Optical Network Design and Modelling, ONMD ’05, Feb 2005, pp. 235–241.

Korotky, S. K.

Lagasse, P.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, M. Pickavet, P. Lagasse, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

Lakhina, A.

A. Medina, A. Lakhina, I. Matta, J. Byers, “Brite: an approach to universal topology generation,” in Proc. of the 9th Int. Symp. on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, MASCOTS ’01, Aug. 2001, pp. 346–353.

Lehmann, G.

C. T. Politi, H. Haunstein, D. A. Schupke, S. Duhovnikov, G. Lehmann, A. Stavdas, M. Gunkel, J. Martensson, A. Lord, “Integrated design and operation of a transparent optical network: a systematic approach to include physical layer awareness and cost function,” IEEE Commun. Mag., vol. 45, no. 2, pp. 40–47, Feb. 2007.
[CrossRef]

Lievens, I.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, M. Pickavet, P. Lagasse, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

Lord, A.

C. T. Politi, H. Haunstein, D. A. Schupke, S. Duhovnikov, G. Lehmann, A. Stavdas, M. Gunkel, J. Martensson, A. Lord, “Integrated design and operation of a transparent optical network: a systematic approach to include physical layer awareness and cost function,” IEEE Commun. Mag., vol. 45, no. 2, pp. 40–47, Feb. 2007.
[CrossRef]

Magoni, D.

D. Magoni, “Nem: a software for network topology analysis and modeling,” in Proc. of the 10th IEEE Int. Symp. on Modeling, Analysis and Simulation of Computer and Telecommunications Systems, MASCOTS ’02, Oct. 2002, pp. 364–371.

Martensson, J.

C. T. Politi, H. Haunstein, D. A. Schupke, S. Duhovnikov, G. Lehmann, A. Stavdas, M. Gunkel, J. Martensson, A. Lord, “Integrated design and operation of a transparent optical network: a systematic approach to include physical layer awareness and cost function,” IEEE Commun. Mag., vol. 45, no. 2, pp. 40–47, Feb. 2007.
[CrossRef]

Matta, I.

A. Medina, A. Lakhina, I. Matta, J. Byers, “Brite: an approach to universal topology generation,” in Proc. of the 9th Int. Symp. on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, MASCOTS ’01, Aug. 2001, pp. 346–353.

Medina, A.

A. Medina, A. Lakhina, I. Matta, J. Byers, “Brite: an approach to universal topology generation,” in Proc. of the 9th Int. Symp. on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, MASCOTS ’01, Aug. 2001, pp. 346–353.

Monteiro, P.

J. Pedro, A. Teixeira, P. Monteiro, J. Pires, “On a Portuguese backbone network of reference,” in Proc. of the Symp. on Enabling Optical Networks and Sensors, SEON ’05, June 2005, pp. 80–84.

Mukherjee, B.

S. Ramamurthy, L. Sahasrabuddhe, B. Mukherjee, “Survivable WDM mesh networks,” J. Lightwave Technol., vol. 21, no. 4, pp. 870–883, Apr. 2003.
[CrossRef]

Naldi, M.

M. Naldi, “Connectivity of Waxman topology models,” Comput. Commun., vol. 29, no. 1, pp. 24–31, 2005.
[CrossRef]

Palmer, C.

C. Palmer, J. Steffan, “Generating network topologies that obey power laws,” in Proc. of the IEEE Global Telecommunications Conf., GLOBECOM ’00, vol. 1, Nov. 2000, pp. 434–438.

Pedro, J.

J. Pedro, A. Teixeira, P. Monteiro, J. Pires, “On a Portuguese backbone network of reference,” in Proc. of the Symp. on Enabling Optical Networks and Sensors, SEON ’05, June 2005, pp. 80–84.

Pickavet, M.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, M. Pickavet, P. Lagasse, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

J.-P. Vasseur, M. Pickavet, P. Demeester, Network Recovery: Protection and Restoration of Optical, SONET-SDH, IP, and MPLS. San Francisco, CA, USA: Morgan Kaufmann, 2004.

Pires, J.

J. Pedro, A. Teixeira, P. Monteiro, J. Pires, “On a Portuguese backbone network of reference,” in Proc. of the Symp. on Enabling Optical Networks and Sensors, SEON ’05, June 2005, pp. 80–84.

Politi, C. T.

C. T. Politi, H. Haunstein, D. A. Schupke, S. Duhovnikov, G. Lehmann, A. Stavdas, M. Gunkel, J. Martensson, A. Lord, “Integrated design and operation of a transparent optical network: a systematic approach to include physical layer awareness and cost function,” IEEE Commun. Mag., vol. 45, no. 2, pp. 40–47, Feb. 2007.
[CrossRef]

Qian, C. J.

C. Jin, C. J. Qian, S. Jamin, “Inet: Internet topology generator,” Technical Report CSE-TR-433-00, EECS Department, University of Michigan, 2000.

Ramamurthy, S.

S. Ramamurthy, L. Sahasrabuddhe, B. Mukherjee, “Survivable WDM mesh networks,” J. Lightwave Technol., vol. 21, no. 4, pp. 870–883, Apr. 2003.
[CrossRef]

Sahasrabuddhe, L.

S. Ramamurthy, L. Sahasrabuddhe, B. Mukherjee, “Survivable WDM mesh networks,” J. Lightwave Technol., vol. 21, no. 4, pp. 870–883, Apr. 2003.
[CrossRef]

Sarac, K.

M. H. Gunes, K. Sarac, “Inferring subnets in router-level topology collection studies,” in IMC ’07: Proc. of the 7th ACM SIGCOMM Conf. on Internet Measurement, New York, NY, USA: ACM, 2007, pp. 203–208.

Schupke, D. A.

C. T. Politi, H. Haunstein, D. A. Schupke, S. Duhovnikov, G. Lehmann, A. Stavdas, M. Gunkel, J. Martensson, A. Lord, “Integrated design and operation of a transparent optical network: a systematic approach to include physical layer awareness and cost function,” IEEE Commun. Mag., vol. 45, no. 2, pp. 40–47, Feb. 2007.
[CrossRef]

Shenker, S.

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Figures (11)

Fig. 1
Fig. 1

Physical topology of the European Optical Network (EON). The nodes are interconnected with optical cables and distributed across a geographic area. Some regions are more densely populated with nodes and links than others. Regions with a cluster of nodes often present cycles (see the strong links).

Fig. 2
Fig. 2

Nodal degree relative frequency and the Poisson probability function, with λ = δ = 3.42 for the USA 100 network. We verified that real transport networks tend to follow a Poisson distribution for the nodal degree.

Fig. 3
Fig. 3

The minimum, average, and maximum values of (a) the nodal degree, (b) the number of hops, (c) the link-disjoint pairwise connectivity, and (d) the node-disjoint pairwise connectivity for 29 real-world network topologies.

Fig. 4
Fig. 4

A network generated by the Waxman model with α = 0.4 and β = 0.4 .

Fig. 5
Fig. 5

(a) The plane and regions. (b) Node placing, connection, and blocked areas. (c) Region interconnection. (d) A possible network topology over a six-region plane.

Fig. 6
Fig. 6

A plane is divided into R regions. A random number of nodes is assigned and placed in each region. After the nodes are interconnected, new links are added while the mean nodal degree is between δ min and δ max .

Fig. 7
Fig. 7

Waxman link probability (6) with α = 0.4 and β = 0.4 over a link length distribution. For the link length distribution we have considered 950 links of real-world networks presented in Table 1.

Fig. 8
Fig. 8

The minimum, average, and maximum (a) nodal degree, (b) number of hops, (c) link-disjoint pairwise connectivity, and (d) node-disjoint pairwise connectivity for the 29 computer-generated network topologies.

Fig. 9
Fig. 9

Nodal degree relative frequency and the Poisson probability function with λ = δ = 3.42 for a computer-generated topology with N = 100 and L = 171 (these values are identical to the USA 100 topology; see Fig. 2).

Fig. 10
Fig. 10

Comparison between the clustering coefficient of real and computer-generated networks. The minimum and maximum deviation between each pair of networks (real and computer generated) is 0 and 0.23, respectively. The average deviation is 0.07.

Fig. 11
Fig. 11

Example of a computer-generated network topology for N = 19 , L = 37 , A = 100 2 , R = 12 , d = 2 , ζ = 71 , α = 0.4 , and β = 0.4 . Possible cycles inside regions are shown as highlighted links.

Tables (3)

Tables Icon

Table 1 Real-World Reference Networks

Tables Icon

Table 2 Input Variables for the Proposed Method

Tables Icon

Table 3 Summary of the Values of Key Variables

Equations (9)

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

h = 2 N ( N 1 ) i = 1 N 1 j = i + 1 N h i j ,
Ω = 2 N ( N 1 ) i = 1 N 1 j = i + 1 N ω i j .
Θ = 2 N ( N 1 ) i = 1 N 1 j = i + 1 N θ i j .
c i = 2 t i δ i ( δ i 1 ) ,
c = 1 N i = 1 N c i .
P ( i , j ) = β exp d ( i , j ) ζ α ,
A r = Δ X r x Δ X r y ,
n max = A r d 2 .
T = φ ( δ max N δ min N 2 ) + 1 .