Francesco Conte, Gabriele Oliva and Roberto Setola, "Time-Varying Input-output Inoperability Model," International Journal on Infrastructure Systems, vol. 19, n. 1, pag. 4757, 2013. (doi:10.1061/(ASCE)IS.1943-555X.0000099.)
Representing interdependent Critical Infrastructures is mandatory to implement protection policies and strategies. Although many interdependency models have been provided in these years, the Input-output Inoperability Model (IIM) is an actual standard. Such a model is able to emphasize cascading effects induced in a complex scenario by dependencies and interdependencies; however the financial origin of data and the stationariety assumption greatly reduce the applicability of the framework. The latter aspect is a very crude approximation, since the coupling of different infrastructures and sectors is expected to increase in long-lasting critical situations with respect to the effect expected during normal operative conditions. In this paper we propose an extension of IIM model introducing some peculiar behaviors induced by the different backup strategies and, consequently, time varying interdependency coefficients. Such coefficients are defined to explicitly take into account the severity and duration of negative phenomena. Some remarkable results are obtained from a complex case study, including several infrastructures on the Italian territory, emphasizing the interesting feature of the proposed methodology.