Identification of the sensors configuration and flows control

The article is devoted to the development of strategies for identifying the location of special programmable devices (sensors) in network nodes for collecting, processing, analyzing information about the flow function in order to evaluate arc flows in that part of the network that is not directly observed. One of the ways to solve this problem is to search through possible placements, based on heuristic considerations. In work as a model of a flow network with sensors, a sparse underdetermined system of linear algebraic equations is used. The conditions for the uniqueness of the solution of a special kind of system obtained as a result of the use of a priori information from sensors installed in the monitored nodes of the network are determined. However, checking these conditions with a full search can only be used for small networks. The estimations limiting the number of viewed configurations of nodes are obtained and the interval of changing the number of monitored nodes that guarantee the complete observability of the network is justified. These results make it possible to increase the dimensionality of the problems being solved. Methods are developed for finding suboptimal solutions to establish the complete observability of the network for a given intensity threshold. Numerical results of constructing suboptimal solutions for various values of the intensity threshold are obtained. The results of visualization of the sensory configuration of the observed nodes are presented, which guarantee complete observability of the network. Conditions for effective applicability of exact methods are obtained for problems of the investigated class.