A mathematical measure for flexibility in communication networks

For communication networks research, flexibility of network design and networking solutions is considered a competitive advantage. However, this advantage is typically only claimed on an argumentative level and neither formally supported nor thoroughly investigated. To support the claim of flexibility and to make the flexibility of different solutions comparable, its degree must be quantified and thus made measurable. In this work, we propose a mathematical basis to quantify a degree of flexibility achieved by communication networks.We motivate that flexibility can be cast to the "size" of a set of achievable demand changes. Consequently, we propose the use of mathematical measure theory to quantify achieved networking flexibility. We derive several implications on the basic structure of flexibility, extend the insights towards a utility of flexibility and develop systematic approaches for both analytical and empirical measurement of flexibility. We apply the insights to several use-cases, showing that flexibility is in fact not as straight-forward to argue as it seems at first glance.