Minimization of the number of ADMs in SONET rings with maximum throughput with implications to the traffic grooming problem

SONET ADMs are dominant cost factors in WDM/SONET rings. Whereas most previous papers on the topic concentrated on the number of wavelengths assigned to a given set of lightpaths, recent papers argue that the number of ADMs is a more realistic cost measure. The minimization of this cost factor has been investigated in recent years, where single-hop and multi-hop communication models, with arbitrary traffic and uniform traffic loads have been investigated. As a first attempt to understand the trade-off between the number of wavelengths and the number of ADMs, we concentrate on the all-to-all, uniform traffic instance with multi-hop, splittable communication. We look for a solution which makes full use of the bandwidth and uses the minimum possible number of ADMs. We develop an architecture based on successive nested polygons and present a necessary and sufficient condition for a solution in this architecture to be feasible. This architecture leads to a solution using O(WlogW+N) ADMs where W is the number of wavelengths used, and N is the number of nodes in the ring. This is a substantial improvement compared to NW ADMs for the basic architecture in [O. Gerstel, P. Lin, G. Sasaki, Combined wdm and sonet network design, in: INFOCOM'99, Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies, vol. 2, 1999, pp. 734-743], and optimal for W=O(N/logN). We further improve this result to O(Wlog$/overline{W}$+N) ADMs, where $/overline{W}$=o(W). This architecture constitutes a solution for the traffic grooming problem, which is the subject of many recent works.