Wavelength assignment in all-optical star-ring

This paper studies wavelength assignments in a class of all-optical networks without wavelength converters topologized as star-ring: some sub-rings connected by a backbone ring. In the static model, we give an upper bound 5L/2 and a lower bound 9L/4 of the necessary wavelengths to accommodate any requests with load L. These become (3L/2)divide;log₂ (N+(Σ_i=1 ⁿ)m_i)nlt;+max_1⩽i⩽n (L divide;log₂ m_inlt;)+2L and 0.5L( divide;log₂ (N+max_1⩽i⩽n (m_i ))nlt;+1) respectively in the dynamic model, where N is the number of nodes in the backbone ring and m_i is the number of nodes in the ith sub-ring (1⩽i⩽n)