Branch-and-price algorithm for a combined problem of virtual path establishment and traffic packet routing in a layered communication network

This paper considers a combined problem of establishing virtual paths (VPs) and routing traffic (packet) demands through the virtual paths in a layered communication network where each physical link is subject to its capacity constraints. The problem is modeled as a path-based formulation for which a branch-and-price solution algorithm is derived. The solution algorithm is composed of an efficient pricing algorithm, and also a branching rule based on a variable dichotomy, which does not destroy the structure of the associated pricing problems. Computational experiments are performed to test the efficiency of the algorithm, which show that the algorithm works quite well in finding optimal solutions (for the test instances) within reasonable time. Its immediate application may be made to a centralized network management on mid-term global reconfiguration and long-term VP planning.

[1]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[2]  Hisashi Kobayashi,et al.  Modeling and analysis , 1978 .

[3]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[4]  Joel Sokol,et al.  Virtual Path Design in Service-Specific ATM Networks , 2000, J. Heuristics.

[5]  Elwood S. Buffa,et al.  Graph Theory with Applications , 1977 .

[6]  Ori Gerstel,et al.  Efficient support for client/server applications over heterogeneous ATM network , 1998, TNET.

[7]  Reuven Cohen,et al.  Connection management and rerouting in ATM networks , 1994, Proceedings of INFOCOM '94 Conference on Computer Communications.

[8]  C S Sung,et al.  Branch-and-price algorithm for a multicast routing problem , 1999, J. Oper. Res. Soc..

[9]  C. Siva Ram Murthy,et al.  A new algorithm for virtual path network design in ATM networks , 1999, Comput. Commun..

[10]  Johnny W. Wong,et al.  Resource management with virtual paths in ATM networks , 1996 .

[11]  Laurence A. Wolsey,et al.  An exact algorithm for IP column generation , 1994, Oper. Res. Lett..

[12]  Martin de Prycker,et al.  Asynchronous Transfer Mode, Solution for Broadband Isdn , 1991 .

[13]  Reuven Cohen,et al.  On the cost of virtual private networks , 2000, TNET.

[14]  Geir Dahl,et al.  Routing Through Virtual Paths in Layered Telecommunication Networks , 1999, Oper. Res..

[15]  Kwang-Ting Cheng,et al.  Virtual path assignment and virtual circuit routing in ATM networks , 1993, Proceedings of GLOBECOM '93. IEEE Global Telecommunications Conference.

[16]  Rainer Händel,et al.  Integrated broadband networks : an introduction to ATM-based networks , 1991 .

[17]  Jennifer Ryan,et al.  Path assignment for call routing: An application of tabu search , 1993, Ann. Oper. Res..

[18]  Aurel A. Lazar,et al.  Virtual path control for ATM networks with call level quality of service guarantees , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

[19]  Yannis Viniotis,et al.  Deterministic algorithm for VP assignment in ATM networks , 1996, Comput. Commun..

[20]  Aurel A. Lazar,et al.  Virtual path control for ATM networks with call level quality of service guarantees , 1998, TNET.

[21]  Sungsoo Park,et al.  An Integer Programming Approach to the Bandwidth Packing Problem , 1996 .

[22]  Jennifer Ryan,et al.  A column generation algorithm for bandwidth packing , 1993, Telecommun. Syst..

[23]  Martin W. P. Savelsbergh,et al.  Branch-and-Price: Column Generation for Solving Huge Integer Programs , 1998, Oper. Res..

[24]  Ori Gerstel,et al.  The layout of virtual paths in ATM networks , 1996, TNET.

[25]  Avishai Wool,et al.  Optimal layouts on a chain ATM network , 1998, Discret. Appl. Math..

[26]  Ue-Pyng Wen,et al.  Optimizing the system of virtual paths by tabu search , 2001, Eur. J. Oper. Res..

[27]  Johan Hellstrand,et al.  Solving the Uncapacitated Network Design Problem by a Lagrangean Heuristic and Branch-and-Bound , 1998, Oper. Res..

[28]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[29]  Imrich Chlamtac,et al.  Optimizing the system of virtual paths , 1994, TNET.

[30]  Sanghyun Ahn,et al.  Virtual path layout design on ATM networks , 1994, Proceedings of INFOCOM '94 Conference on Computer Communications.

[31]  Thomas L. Magnanti,et al.  Network Design and Transportation Planning: Models and Algorithms , 1984, Transp. Sci..

[32]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .