Topology Engineering of Communication Systems

Connected linear graphs are introduced as symbolic models of communication systems. Their nodes of rank one, two, and larger symbolize terminal stations, repeater stations and exchanges of different sizes, respectively. Their branches symbolize circuits, lines or trunks. Connectivity between these system elements imposes a quantitative relationship between the types and numbers of system elements. Matched sets of system elements are sets which meet specific requirements regarding the number of terminal stations which must be interconnected, the number of circuits which can be used or the desired degree of invulnerability of a communication network. From these relationships an algorithm has been developed for the tabulation of matched sets of symbolic system elements (i.e., nodes), and tables of matched sets of nodes have been prepared both manually and with an automatic computer. The use of these tables is explained by practical examples dealing with synthesis problems of communication systems, which have to meet such requirements as described above. An algorithm is presented which permits the direct computation of matched sets of nodes of different ranks for: 1) trees containing specified numbers of terminal nodes; 2) trees containing a specified total number of nodes; and 3) networks with specified indexes of connectivity. Tables are given of matched sets of nodes computed with a 220 Burrough's computer and corresponding networks are shown. Applications of these tables to the synthesis of communication systems are discussed and practical examples using these tables.