Design of survivable networks with vulnerability constraints

We consider the Network Design Problem with Vulnerability Constraints (NDPVC) which simultaneously addresses resilience against failures (network survivability) and bounds on the lengths of each communication path (hop constraints). Solutions to the NDPVC are subgraphs containing a path of length at most Hst for each commodity {s, t} and a path of length at most Hst′ between s and t after at most k−1 edge failures. We first show that a related and well known problem from the literature, the Hop-Constrained Survivable Network Design Problem (kHSNDP), that addresses the same two measures produces solutions that are too conservative in the sense that they might be too expensive in practice or may even fail to provide feasible solutions. We also explain that the reason for this difference is that Mengerian-like theorems not hold in general when considering hop-constraints. Three graph theoretical characterizations of feasible solutions to the NDPVC are derived and used to propose integer linear programming formulations. In a computational study we compare these alternatives with respect to the lower bounds obtained from the corresponding linear programming relaxations and their capability of solving instances to proven optimality. In addition, we show that in many cases, the solutions produced by solving the NDPVC are cheaper than those obtained by the related kHSNDP.

[1]  Geoffrey Exoo.  On a measure of communication network vulnerability , 1982, Networks.

[2]  Michael Poss,et al.  Benders Decomposition for the Hop-Constrained Survivable Network Design Problem , 2013, INFORMS J. Comput..

[3]  Luís Gouveia,et al.  Using Variable Redefinition for Computing Lower Bounds for Minimum Spanning and Steiner Trees with Hop Constraints , 1998, INFORMS J. Comput..

[4]  Ehab Al-Shaer,et al.  On the impact of loss and delay variation on Internet packet audio transmission , 2006, Comput. Commun..

[5]  Jean-François Cordeau,et al.  Formulations for the nonbifurcated hop-constrained multicommodity capacitated fixed-charge network design problem , 2015, Comput. Oper. Res..

[6]  T. Magnanti,et al.  Modeling and heuristic worst-case performance analysis of the two-level network design problem , 1994 .

[7]  J. G. Klincewicz,et al.  Optimization Issues in Quality of Service , 2006, Handbook of Optimization in Telecommunications.

[8]  M. Stoer.  Design of Survivable Networks , 1993 .

[9]  Jean-Claude Bermond,et al.  Surveys in Combinatorics: GRAPHS AND INTERCONNECTION NETWORKS: DIAMETER AND VULNERABILITY , 1983 .

[10]  Ali Ridha Mahjoub,et al.  Design of Survivable Networks: A survey , 2005, Networks.

[11]  Marc Necker,et al.  The Sensitivity of TCP to Sudden Delay Variations in Mobile Networks , 2004, NETWORKING.

[12]  Luís Gouveia,et al.  Lexicographical minimization of routing hops in hop-constrained node survivable networks , 2016, Telecommun. Syst..

[13]  Luidi Simonetti,et al.  Hop‐level flow formulation for the survivable network design with hop constraints problem , 2013, Networks.

[14]  Ivana Ljubić,et al.  A branch-and-cut-and-price algorithm for vertex-biconnectivity augmentation , 2010 .

[15]  Arif Ghafoor,et al.  Jitter-minimized reliability-maximized management of networks , 2011, Int. J. Netw. Manag..

[16]  Amaro de Sousa,et al.  Compact Models for Hop-Constrained Node Survivable Network Design: An Application to MPLS , 2006 .

[17]  K. Menger.  Zur allgemeinen Kurventheorie , 1927 .