A Theory and an Algorithm for Fault Diagnosis by Measuring Transmission Numbers in a Directed Network

In location problems, the outtransmission and intransmission numbers are important indices to evaluate a directed network. We formulate and consider a new problem of fault diagnosis in a system modeled by a directed network in which to each edge a positive real number called the length of edge is assigned and to each vertex a positive real number called the weight of vertex is assigned. By a fault in a directed network, we mean any increase in the length of an edge with respect to its nominal length. A theory and an algorithm for detecting a fault edge in a directed network in which the above indices, i.e. outtransmission and/or intransmission numbers, are measurable, are presented