Abstract
In the past years, telecommunications networks have seen an important evolution with the advances in optical technologies and the explosive growth of the Internet. Several optical systems allow a very large transport capacity, and data traffic has dramatically increased. Telecommunications networks are now moving towards a model of high-speed routers interconnected by intelligent optical core networks. Moreover, there is a general consensus that the control plan of the optical networks should utilize IP-based protocols for dynamic provisioning and restoration of lightpaths. The interaction of the IP routers with the optical core networks permits to achieve end-to-end connections, and the lightpaths of the optical networks define the topology of the IP network. This new infrastructure has to be sufficiently survivable, so that network services can be restored in the event of a catastrophic failure. In this paper we consider a multilayer survivable network design problem that may be of practical interest for IP-over-optical neworks. We give an integer programming formulation for this problem and discuss the associated polytope. We describe some valid inequalities and study when these are facet defining. We discuss separation algorithms for these inequalities and introduce some reduction operations. We develop a Branch-and-Cut algorithm based on these results and present extensive computational results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abacus. http://www.oreas.de.
Barahona, F. (1992). “Separating from the Dominant of the Spanning Tree Polytope.” Operations Research Letters, 12, 201–203.
Barahona, F. and A.R. Mahjoub. (1995). “On Two-Connected Subgraph Polytopes.” Discrete Mathematics, 147, 19–34.
Bradner, S. IETF. (1995). “The Recommendation for the IP Next Generation Protocol.” (RFC1752).
Cunningham, W.H. (1985). “Optimal Attack and Reinforcement of a Network.” Journal of Association for Computing Machinery, 32, 549–561.
Elf, M., C. Gutwenger, M. Jünger, and G. Rinaldi. (2001). “Branch-and-Cut Algorithms for Combinatorial Optimization and Their Implementation in ABACUS.” In M. Jünger, and D. Naddef (eds.), Computational Combinatorial Optimization, LNCS 2241, pp. 157–222.
Goldberg, A.V. and R.E. Tarjan. (1988). “A New Approach to the Maximum-flow Problem.” Journal of the Association for Computing Machinery, 35, 921–940.
Gomory, R.E. and T.C. Hu. (1961). “Multi-Terminal Network Flows.” SIAM Journal on Applied Mathematics, 9, 551–570.
Gouveia, L., P. Patrício, A. de Sousa, and R. Valadas. (2003). “MPLS Over WDM Network Design with Packet Level QoS Constraints Based on ILP Models.” In Proceedings IEEE INFOCOM 2003, San Francisco.
Grötschel, M., C.L. Monma, and M. Stoer. (1995). “Design of Survivable Networks.” In M.O. Ball et al. (eds.), Handbooks in OR & MS 7, pp. 617–671.
Gusfield, D. (1990). ”Very Simple Methods for All Pairs Network Flow Analysis.” SIAM Journal on Computing, 19, 143–155.
Jensen, T. (2001). “Internet Protocol and Transport Protocols.” Telektronikk, 97, 20–38.
Kerivin, H. (2000). “Réseaux fiables et polyèdres.” PhD Thesis, University Blaise Pascal, Clermont-Ferrand, France.
Kerivin, H., A.R. Mahjoub, and C. Nocq. (2004). “(1, 2)-Survivable Networks: Facets and Branch-and-Cut.” In M. Grötschel (ed.), The Sharpest Cut, MPS/SIAM in Optimization, pp. 121–152.
Magnanti, T.L., P. Mirchandani, and R. Vachani, (1993). “The Convex Hull of Two Core Capacitated Network Design Problems.” Mathematical Programming, 60, 233–250.
Magnanti, T.L., P. Mirchandani, and R. Vachani. (1995). “Modeling and Solving the Two-Facility Capacitated Network Loading Problem.” Operations Research, 43, 142–157.
Mahjoub, A.R. (1994). “Two-Edge Connected Spanning Subgraphs and Polyhedra.” Mathematical Programming, 64, 199–208.
Postel, J. IETF. (1981). “Internet Protocol. DARPA Internet Program Protocol Specification.” (RFC791).
Postel, J. IETF. (1981).“Internet Control Message Protocol. DARPA Internet Program Protocol Specification.” (RFC792).
Postel, J. IETF. (1981). “Transmission Control Protocol. DARPA Internet Program Protocol Specification.” (RFC793).
Rajagopalan, B., D. Pendarakis, D. Saha, R.S. Ramamoorthy, and K. Bala. (2000). “IP Over Optical Networks: Architectural Aspects.” IEEE Communications Magazine, 94–102.
Reinelt, G. (1991). ”TSPLIB—A Traveling Salesman Problem Library.” ORSA Journal on Computing, 3, 376–384.
Ricciato, F., S. Salsano, A. Belmonte, and M. Listanti. (2002). ”Off-line Configuration of a MPLS over WDM Network under Time-Varying Offered Traffic.” In Proceedings IEEE INFOCOM 2002, New York, USA.
Schrijver, A. (2003). “Combinatorial Optimization: Polyhedra and Efficiency.” Algorithms and Combinatorics, 24, Springer-Verlag, Berlin.
Stoer, M. (1992). “Design of Survivable Networks.” Lectures Notes in Mathematics 1531, Springer-Verlag.
Stoer, M. and G. Dahl. (1994). “A Polyhedral Approach to Multicommodity Survivable Network Design.” Numerische Mathematik, 68, 149–167.
Thienel, S. (1995). “ABACUS—A Branch-And-CUt System.” PhD thesis, Universität zu Köln.
Wessäly, R. (2000). “DImensioning Survivable Capacitated NETworks(DISCNET).” PhD Thesis, Technische Universität Berlin.
Zouganeli, E. (2001). “Optical Network Functionality: From “Dumb Fat Pipes” to Bright Networking.” Telektronikk, 97, 346–354.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Borne, S., Gourdin, E., Liau, B. et al. Design of survivable IP-over-optical networks. Ann Oper Res 146, 41–73 (2006). https://doi.org/10.1007/s10479-006-0047-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-006-0047-2