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This paper considers a space-time interconnection architecture (STIA) based on optical devices and proposes its introduction in data center networks. The power consumption of the STIA is modeled, accounting for the energy proportionality of the optical devices in the STIA. Using such a model, a STIA-based network is designed using three different topologies, tree, folded Clos, and flattened butterfly, and optimized for power efficiency. Results show that, for a fixed topology, small-size STIAs are an energy-efficient solution for data center networks and allow a power reduction of more than an order of magnitude with respect to the Ethernet-based network. The comparison for the same bisection bandwidth shows that folded Clos and flattened butterfly outperform tree, whose power consumption is strongly dependent on the oversubscription ratio selected.