Necessary and Sufficient Conditions for the Rearrangeability of WSW1 Switching Fabrics

This paper considers the three-stage switching fabrics of the wavelength-space-wavelength architecture, called the WSW1 switching fabrics, for elastic optical nodes. Seven control algorithms for simultaneous connection routing are described. One algorithm is designed for the WSW1 switching fabric with two inputs and two outputs, four algorithms for the WSW1 switching fabric with three inputs and outputs, and two algorithms for nodes with a capacity greater than 3. We establish the necessary conditions for rearrangeability and prove sufficient rearrangeable conditions for the proposed algorithms. In cases where the switching fabric capacity is a multiple of 3, the sufficient conditions obtained for the proposed algorithms are the best known and close to the necessary conditions.