Optimal Transport Flows for Distributed Production Networks

Abstract

Network flows often exhibit a hierarchical tree-like structure that can be attributed to the minimisation of dissipation. The common feature of such systems is a single source and multiple sinks (or vice versa). In contrast, here we study networks with only a single source and sink. These systems can arise from secondary purposes of the networks, such as blood sugar regulation through insulin production. Minimisation of dissipation in these systems lead to trivial behaviour. We show instead how optimising the transport time yields network topologies that match those observed in the insulin-producing pancreatic islets. These are patterns of periphery-to-center and center-to-periphery flows. The obtained flow networks are broadly independent of how the flow velocity depends on the flow flux, but continuous and discontinuous phase transitions appear at extreme flux dependencies. Lastly, we show how constraints on flows can lead to buckling of the branches of the network, a feature that is also observed in pancreatic islets.