Minimizing the Number of ADMs in SONET Rings with Maximum Throughput

Abstract

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, more 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 a full use of the bandwidth and uses the minimum possible number of ADMs under this constraint. 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(W log W + N) ADMs (compared to NW ADMs for the basic architecture in [1]) which is optimal for W = O(N / log N). We further improve this result to $O(W log \overline{W} + N)$ ADMs, where $\overline{W} = o(W)$.