Current networks implement Service Level Agreements (SLA) by careful configuration of both routing and queue scheduling policies. Network modeling is a critical component of Quality of Service (QoS) optimization. Furthermore, we shed some light on the relationship between graph structure and the difficulty of data-driven routing of flows, an aspect that has not been considered in the existing work in the area. We find that, in many networks, an MLP is competitive with a generic GNN that does not use our mechanism. We extensively evaluate the proposed approach by means of an Internet routing case study using 17 Service Provider topologies and two flow routing schemes. We show that our proposed method yields substantial gains over existing graph learning methods that constrain the routing unnecessarily. In this paper, we propose a novel approach based on Graph Neural Networks (GNNs) for the MCNF problem which uses distinctly parametrized message functions along each link, akin to a relational model where all edge types are unique. The widely-used objective that we focus on is the maximum utilization of any link in the network, given traffic demands and a routing strategy.
Among them, the Multi-Commodity Network Flow (MCNF) problem is of particular interest given its generality, since it concerns the distribution of multiple flows (also called demands) of different sizes between several sources and sinks. Due to the appeal of data-driven optimization, these problems have increasingly been approached using graph learning methods. Network flow problems, which involve distributing traffic over a network such that the underlying infrastructure is used effectively, are ubiquitous in transportation and logistics.
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