Achieving 100% Throughput in Reconfigurable Optical Networks

We study the maximum throughput properties of dynamically reconfigurable optical networks having wavelength and port constraints. Using stability as the throughput performance metric, we outline the single-hop and multi-hop stability regions of the network. We describe throughput-optimal dynamic algorithms employing joint WDM reconfiguration and electronic layer routing decisions. Our approach is a generalization of the BvN decomposition technique that has been so effective at expressing any stabilizable rate matrix for input-queued switches as a convex combination of service configurations. We consider generalized decompositions for physical topologies with wavelength and port constraints. For the case of a single wavelength per optical fiber, we link the decomposition problem to a corresponding Routing and Wavelength Assignment (RWA) problem. We characterize the stability region of the reconfigurable network, employing both single-hop and multi- hop routing, in terms of the RWA problem applied to the same physical topology. We derive expressions for two geometric properties of the stability region: maximum stabilizable uniform arrival rate, and maximum scaled doubly substochastic region. These geometric properties provide a measure of the performance gap between a network having a single wavelength per optical fiber and its wavelength-unconstrained version. They also provide a measure of the performance gap between algorithms employing single-hop versus multi-hop electronic routing.