PROPERTIES AND ALGORITHMS FOR A TRAFFIC MATRIX DETERMINATION PROBLEM (TELECOMMUNICATIONS NETWORKS, TRANSPORTATION POLYTOPE, KRUITHOF'S METHOD, QUADRATIC NORM)

Novel telecommunication networks are either being proposed or built. In order to design these networks reasonable estimates of traffic must be made. Often, separate data is available for the total traffic estimates (or marginal sums) and the individual point to point traffic estimates as a traffic matrix. Moreover, in many cases, the individual estimates do not add up to the marginal sums, and the marginal sums are believed to be more reliable. This necessitates finding a new traffic matrix "close" to the original matrix so as to match the given marginal sums. The "closeness" could be justified based on theory, principle or geometric notions.; This problem structure has applications in many different fields including transportation, statistics and economics, and has been studied extensively in the literature. Most of the theoretical and computational results in the literature are for entropy measure. The object of this report is to develop new models and methods for geometric measures (such as L(,1), L(,2) and L(,(INFIN)) norms) and to introduce new theoretical and computational results for geometric measures. Efficient implementation of these different methods on computers and their computational experience are also reported.