Traffic Grooming in Bidirectional WDM Ring Networks

We study the minimization of ADMs (Add-Drop Multiplexers) in Optical WDM Networks with Bidirectional Ring topology considering symmetric shortest path routing and all-to-all unitary requests. We insist on the statement of the problem, which had not been clearly stated before in the bidirectional case. Optimal solutions had not been found up to date. In particular, we study the case C = 2 and C = 3 (giving either optimal constructions or near-optimal solutions) and the case C = k(k+ 1)/2 (giving optimal decompositions for specific congruence classes of N). We state a general Lower Bound for all the values of C and N, and we improve this Lower Bound for C = 2 and C = 3 (when N = 4t+ 3). We also include some comments about the simulation of the problem using Linear Programming.

[1]  A.L. Chiu,et al.  Traffic grooming algorithms for reducing electronic multiplexing costs in WDM ring networks , 2000, Journal of Lightwave Technology.

[2]  Ori Gerstel,et al.  Cost effective traffic grooming in WDM rings , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[3]  Jean-Claude Bermond,et al.  Traffic grooming on the path , 2007, Theor. Comput. Sci..

[4]  George N. Rouskas,et al.  Traffic grooming in WDM networks: past and future , 2002, IEEE Netw..

[5]  David Coudert,et al.  Optimal Solution of the Maximum All Request Path Grooming Problem , 2006, Advanced Int'l Conference on Telecommunications and Int'l Conference on Internet and Web Applications and Services (AICT-ICIW'06).

[6]  Peng-Jun Wan,et al.  Grooming of arbitrary traffic in SONET/WDM BLSRs , 2000, IEEE Journal on Selected Areas in Communications.

[7]  C. Colbourn,et al.  The CRC handbook of combinatorial designs , edited by Charles J. Colbourn and Jeffrey H. Dinitz. Pp. 784. $89.95. 1996. ISBN 0-8493-8948-8 (CRC). , 1997, The Mathematical Gazette.

[8]  David Coudert,et al.  Traffic grooming in unidirectional WDM ring networks using design theory , 2003, IEEE International Conference on Communications, 2003. ICC '03..

[9]  George N. Rouskas,et al.  On optimal traffic grooming in WDM rings , 2001, SIGMETRICS '01.

[10]  Biswanath Mukherjee,et al.  A Review of Traffic Grooming in WDM Optical Networks: Architectures and Challenges , 2002 .

[11]  Charles J. Colbourn,et al.  Grooming in unidirectional rings: K4-e designs , 2004, Discret. Math..

[12]  Eytan Modiano,et al.  Traffic grooming in WDM networks , 2001, IEEE Commun. Mag..

[13]  Xiang-Yang Li,et al.  Select line speeds for single-hub SONET/WDM ring networks , 2000, 2000 IEEE International Conference on Communications. ICC 2000. Global Convergence Through Communications. Conference Record.

[14]  Ori Gerstel,et al.  Combined WDM and SONET network design , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[15]  David Coudert,et al.  Traffic Grooming in Unidirectional Wavelength-Division Multiplexed Rings with Grooming Ratio C = 6 , 2005, SIAM J. Discret. Math..

[16]  David Coudert,et al.  On DRC‐covering of Kn by cycles , 2003 .

[17]  P. Hell,et al.  Graph Problems Arising from Wavelength-Routing in All-Optical Networks , 2004 .

[18]  Ori Gerstel,et al.  Wavelength assignment in a WDM ring to minimize cost of embedded SONET rings , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[19]  Charles J. Colbourn,et al.  Graph decompositions with application to wavelength add-drop multiplexing for minimizing SONET ADMs , 2003, Discret. Math..

[20]  Jean-Claude Bermond,et al.  Traffic Grooming in Unidirectional WDM Ring Networks: the all-to-all unitary case , 2003 .

[21]  David Coudert,et al.  Trac Grooming on the Path , 2005 .

[22]  Charles J. Colbourn,et al.  Minimizing drop cost for SONET/WDM networks with ⅛ wavelength requirements , 2001 .

[23]  Philip J. Lin,et al.  The ring grooming problem , 2004, Networks.

[24]  Eytan Modiano,et al.  Reducing electronic multiplexing costs in SONET/WDM rings with dynamically changing traffic , 2000, IEEE Journal on Selected Areas in Communications.

[25]  George N. Rouskas,et al.  A Survey of Virtual Topology Design Algorithms for Wavelength Routed Optical Networks , 1999 .