Abstract
SONET (Synchronous Optical NETworks) add-drop multiplexers (ADMs) are the dominant cost factor in the WDM(Wavelength Division Multiplexing)/SONET rings. The number of SONET ADMs required by a set of traffic streams is determined by the routing and wavelength assignment of the traffic streams. Previous works took as input the traffic streams with routings given a priori and developed various heuristics for wavelength assignment to minimize the SONET ADM costs. However, little was known about the performance guarantees of these heuristics. This paper contributes mainly in two aspects. First, in addition to the traffic streams with pre-specified routing, this paper also studies minimizing the ADM requirement by traffic streams without given routings, a problem which is shown to be NP-hard. Several heuristics for integrated routing and wavelength assignment are proposed to minimize the SONET ADM costs. Second, the approximation ratios of those heuristics for wavelength assignment only and those heuristics for integrated routing and wavelength assignment are analyzed. The new Preprocessed Iterative Matching heuristic has the best approximation ratio: at most 3/2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Carpenter, S. Cosares, and I. Saniee, “Demand routing and slotting on ring networks,” DIMACS Technical Report 97-02, 1997.
O. Gerstel, P. Lin, and G. Sasaki, “Wavelength assignment in a WDM ring to minimize cost of embedded SONET rings,” in Proc. IEEE INFOCOM'98, San Francisco, CA, 1998, vol. 1, pp. 94–101.
O. Gerstel, P. Lin, and G. Sasaki, “Combined WDM and SONET Network Design,” in Proc. IEEE INFOCOM'99, New York, NY, 1999, vol. 2, pp. 734–743.
I. Haque, W. Kremer, and K. Raychauduri, “Self-healing rings in a synchronous environment,” in SONET/SDH: A Sourcebook of Synchronous Networking, C.A. Siller and M. Shafi (Eds.), IEEE Press, New York, 1996, pp. 131–139.
L.W. Liu, X.-Y. Li, P.-J. Wan, and O. Frieder, “Wavelength assignment in WDM rings to minimize SONET ADMs,” in Proc. INFOCOM 2000, Tel-Aviv, Israel, 2000, vol. 2, pp. 1020–1025.
P. Raghavan and E. Upfal, “Efficient routing in all-optical networks,” in Proc. 26th ACM Symp. Theory of Computing, 1994, pp. 134–143.
A. Schrijver, P.D. Seymour, and P. Winkler, “The ring loading problem,” SIAM J. Disc. Math., vol. 11, no. 1, pp. 1–14, 1998.
A. Tucker, “Coloring a family of circular arcs,” SIAM Journal of Applied Math, vol. 29, no. 3, pp. 493–502, 1975.
P.-J. Wan, G. Călinescu, L.-W. Liu, and O. Frieder, “Grooming of arbitrary traffic in SONET/WDM rings,” IEEE Journal of Selected Area on Communications, vol. 18, no. 10, pp. 1995–2003, 2000.
P. Wilfong and P. Winkler, “Ring routing and wavelength translation,” in Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, 1998, pp. 333–341.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Călinescu, G., Wan, PJ. Traffic Partition in WDM/SONET Rings to Minimize SONET ADMs. Journal of Combinatorial Optimization 6, 425–453 (2002). https://doi.org/10.1023/A:1019525904862
Issue Date:
DOI: https://doi.org/10.1023/A:1019525904862