The key goal in optical network design is to introduce intelligence in the network and deliver capacity when and where it is needed. It is critical to understand the dependencies between network topology properties and the achievable network throughput. Real topology data of optical networks is scarce and often large sets of synthetic graphs are used to evaluate their performance including proposed routing algorithms. These synthetic graphs are typically generated via the Erdos-Renyi (ER) and Barabasi-Albert (BA) models. Both models lead to distinct structural properties of the synthetic graphs, including the degree and diameter distributions. In this paper, we show that these two commonly used approaches are not adequate for the modelling of real optical networks. The structural properties of optical core networks are strongly influenced by the internodal distances. These, in turn, impact the signal-to-noise ratio, which is distance-dependent. The analysis of optical network performance must, therefore, include spatial awareness to better reflect the graph properties of optical core network topologies. In this work, a new variant of the BA model, taking into account the inter-nodal signal-to-noise ratio, is proposed. It is shown that this approach captures both the effects of graph structure and physical properties to generate better networks than traditional methods. The proposed model is compared to spatially agnostic approaches, in terms of the wavelength requirements and the total information throughput, and highlights how intelligent choices can significantly increase network throughputs whilst saving fibre.
One of the key performance metrics for optical networks is the maximum achievable throughput for a given network. Determining it however, is an NP-hard optimisation problem, often solved via computationally expensive integer linear programming (ILP) formulations, infeasible to implement as objectives, even on very small node scales of a few tens of nodes. Alternatively heuristics are used, although these too require considerable computation time for large numbers of networks. There is, thus, a need for ultra-fast and accurate performance evaluation of optical networks. For the first time, we propose the use of a geometric deep learning model, message passing neural networks (MPNN), to learn the relationship between, node and edge features, the structure and the maximum achievable throughput of networks. We demonstrate that MPNNs can accurately predict the maximum achievable throughput while reducing the computational time by up to 5-orders of magnitude compared to the ILP for small networks (10-15 nodes) and compared to the heuristic for large networks (25-100 nodes) -proving their suitability for the design and optimisation of optical networks on different time-and distance-scales.
Designing optical networks for maximum throughput, under diverse traffic demands, is an NP-hard problem. We parameterise the relationship between demand and topology through a polynomial-time objective function, and show it is highly correlated to network throughput, enabling topology design, optimally tailored to the traffic demand.
One of the key performance metrics for optical networks is the maximum achievable throughput. Determining it however, is an NP-hard optimisation problem, often solved via computationally expensive integer linear programming (ILP) formulations. Heuristics, in conjunction with sequential loading, are scalable but non-exact. There is, thus, a need for ultra-fast performance evaluation of optical networks. For the first time, we propose message passing neural networks (MPNN), to learn the relationship between the structure and the maximum achievable throughput of optical networks. We demonstrate that MPNNs can accurately predict the maximum achievable throughput while reducing the computational time by 5-orders of magnitude compared to the ILP.
We introduce a polynomial-time distributed message passing algorithm for routing and wavelength assignment. Exact global solutions are obtained for small-scale networks and improvements are demonstrated on network scales beyond the reach of established global algorithms.
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