Using Gilbert networks to reveal uncertainty in the planning of multi-user infrastructures

When cost is the main consideration and the costs are only determined by the total length of the network, the optimal network infrastructure roll-out between several nodes is determined by minimal spanning trees and Steiner minimal trees. We explain that when capacities also play a role in the cost function a minimal Gilbert network gives the cheapest network structure. However, these kinds of networks can only be determined when locations of participating nodes and required capacities are known in advance. When participating nodes are not yet determined, we provide a probabilistic extension to these networks that can minimise planners' regret, thus contributing to a more robust design for the network topology.