Optimal Mesh Routing in Four-Fibre WDM Rings

Introduction Optical ring networks will form the next step in the rollout of WDM in the telecommunications industry. Since it is important for network planning and design to know the wavelength requirements for different traffic patterns, this Letter describes the calculation of this quantity, assuming full mesh interconnection of every node in a four-fibre ring. There are N nodes in a ring, numbered consecutively from 0 to N −1. A ring has two protection fibres (which are not relevant here) and two working fibres. All paths are bi-directional and are generally carried by the two counterpropagating unidirectional working fibres [1]. Throughout, N λ is an upper bound on the optimum number of wavelengths required to interconnect all nodes in an N -node four-fibre ring with wavelength conversion. N Λ is similar, but it refers to a ring without wavelength conversion. Finally, N μ is a lower