A framework for quantifying complexity and understanding its sources : application to tow large-scale systems

The motivation for this work is to quantify the complexity of complex systems and to understand its sources. To study complexity, we develop a theoretical framework where the complex system of interest is embedded in a broader system: a complex large-scale system. In order to understand and show how the complexity of the system is impacted by the complexity of its environment, three layers of complexity are defined: the internal complexity which is the complexity of the complex system itself, the external complexity which is the complexity of the environment of the system (i.e., the complexity of the large- scale system in which the system is embedded) and the interface complexity which is defined at the interface of the system and its environment. For each complexity we suggest metrics and apply them to two examples. The examples of complex systems used are two surveillance radars: the first one is an Air Traffic Control radar, the second one is a maritime surveillance radar. The two large-scale systems in which the radars are embedded are therefore the air and the maritime transportation system. The internal complexity metrics takes into account the number of links, the number of elements, the function and hierarchy of the elements. The interface complexity metric is based upon the information content of the probability of failure of the system as it is used in its environment. The External complexity metric deals with the risk configuration of large- scale systems emphasizing the reliability and the tendency to catastrophe of the system.