A mathematical framework for measuring network flexibility

In the field of networking research, increased flexibility of new system architecture proposals, protocols, or algorithms is often stated to be a competitive advantage over its existing counterparts. However, this advantage is usually claimed only on an argumentative level and neither formally supported nor thoroughly investigated due to the lack of a unified flexibility framework. As we will show in this paper, the flexibility achieved by a system implementation can be measured, which consequently can be used to make different networking solutions quantitatively comparable with each other. The idea behind our mathematical model is to relate network flexibility to the achievable subset of the set of all possible demand changes, and to use measure theory to quantify it. As increased flexibility might come with additional system complexity and cost, our framework provides a cost model which measures how expensive it is to operate a flexible system. The introduced flexibility framework contains different normalization strategies to provide intuitive meaning to the network flexibility value as well, and also provides guidelines for generating demand changes with (non)uniform demand utilities. Finally, our network flexibility framework is applied on two different use-cases, and the benefits of a quantitative flexibility analysis compared to pure intuitive arguments are demonstrated.