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A heuristic method of optimizing the design of a very large communications network is described. The procedure is employed to configure the routes of 5552 communications service requests involving 1633 nodes. A FORTRAN 4 program was developed to solve for actual needs of the Defense Communications Agency for leased-line service employing the Telpak tariff structure. (Author), Sponsored in part by Defense Communications Agency, Washington, D.C.

Properties of lossy communication nets are studied in the paper. Optimum flows in general and special lossy nets are discussed. Methods for the calculations of terminal capacities in the nets are presented. (Author)

28-71-C-0002AF-515AESDTR-72-160(*data transmission systems, *recursive functions), approximation(mathematics), probability, set theory, mathematical models, systems engineering, reliability(electronics)communication networks, systems analysis, telecommunicationA recursive scheme for computing system availability from component element availabilities is developed and displayed. It requires only the knowledge of all minimal sets of components needed for successful system operation. It does not rely on any series, parallel or bridge structure but is applicable to the most general redundant systems. The scheme can be truncated at any level of recursion to yield good approximations. Included is a discussion of how the level of truncation depends on the number of system components, their availabilities and the desired accuracy. (Author)

Two main topics are discussed in the report. One is a necessary and sufficient condition for two symmetric matrices to be realized as the terminal capacity matrix (TCM) and the expected value terminal capacity matrix (EVTCM) of a tree communication net. The other one is concerned with a necessary and sufficient condition for a symmetric matrix to be realizable as the EVTCM of a tree net. It is shown that there exists a certain tree net which can never be equivalent to a non-tree net under the same TCM and EVTCM, except when all edges of both nets have reliability one. A necessary and sufficient conditon is given for a matrix to be realizable as the reliability matrix (RM) of a tree net. Although the RM is a special case of the first topic, it plays an important role in the EVTCM of a tree. It is proved that if a matrix whose nondiagonal elements are less than one is realizable as the RM of a tree, its topology is unique. Making use of the realiability matrix, a necessary and sufficient conditon for the first problem is developed. (Modified author abstract)