Stability analysis in a multi-channel quasi-ring optical network

In this paper we perform stability analysis of a quasi-ring optical network, the simplest configuration in which channel power excursions can self-propagate indefinitely. The quasi-ring is a network composed of two reconfigurable optical add-drop multiplexers (ROADMs) each equipped with a constant gain optical amplifier and a wavelength selective switch. Over the amplified spans, two sets of lightpaths (added/dropped by opposite ROADMs) are transmitted in mirror image of each other and form an overlapping ring. Using Lyapunov analysis and the small gain theorem, we derive sufficient stability conditions for the quasi-ring as well as an L₂ bound for the channel power excursions. These are functions of the amplifier gain coupling quantified by its Lipschitz constant. Numerical results that verify and compare the theoretical L₂ excursion bounds are provided. To accomplish this, we use Bell Lab´s A Transparent Optical Mesh (ATOM) simulator to set up dynamic network loading and input channel disturbance scenarios.