Minimum cost routing for static network models

This paper develops techniques which can be applied to long range planning studies for the domestic long haul communications network. The problem studied is how to select a path through the network for each point-to-point demand for communications channels, so that the total network cost is minimized. The problem is to minimize total network cost, subject to multicommodity flow requirements and concave link cost functions. Finding an exact solution is difficult because of the concavity of the cost functions and the complexity (100 to 200 nodes and 200 to 300 links) of the network structure. A specialized technique is developed to provide locally optimal solutions to the problem, one of minimizing a concave function over a convex constraint set. When the link cost displays a fixed charge, a modification of the iterative algorithm provides acceptable a modification of the iterative algorithm provides acceptable solutions. Even though the global optimum cannot be found amidst the immense number of local optima, several sample problems demonstrate the value of the techniques developed. A companion paper will extend this work to the dynamic routing problem, of deciding how to route future demands and install transmission facilities so as to minimize the present worth of expenditures during the study interval. The methods and goals of these modeling efforts will be discussed in the companion paper.