  A Quantum Key Distribution (QKD) network is an infrastructure that allows the
realization of the key distribution cryptographic primitive over long distances
and at high rates with information-theoretic security. In this work, we
consider QKD networks based on trusted repeaters from a topology viewpoint, and
present a set of analytical models that can be used to optimize the spatial
distribution of QKD devices and nodes in specific network configurations in
order to guarantee a certain level of service to network users, at a minimum
cost. We give details on new methods and original results regarding such cost
minimization arguments applied to QKD networks. These results are likely to
become of high importance when the deployment of QKD networks will be addressed
by future quantum telecommunication operators. They will therefore have a
strong impact on the design and requirements of the next generation of QKD
devices.
