Diagrams of the functional vulnerability of flow network systems

The method of analysis of changes in functional capabilities of the flow network system after the damaging effects is considered. To describe the processes of streams of different interchangeable products to various peer users, the model of single-product network is used. The damage is defined as the total amount of unsatisfied demands. Damage estimates are calculated for all users and all possible cases of failure of physical or logical elements of the system. Optimal solutions of the sequence of problems of minimization of total relative damages are used as damage estimates. Based on the obtained results for various destruction configurations, the vulnerability diagrams of the initial network system are constructed. Diagrams allow an a priori analysis of both small and critical damages, due to which the flows to some users vanish. The proposed method can be used to study the structural and functional vulnerability of flow network systems.