An efficient method for determining economical configurations of elementary packet-switched networks

The packet-switched network design problem can be formulated as a capacity and flow assignment (CFA) problem. The CFA problem is investigated for an elementary network consisting of one tandem switch and n local switches. It is regarded as the structural unit of a hierarchical network. It is assumed that any line speed is available and the cost of each line is a linear function of its speed with a fixed charge for installation. This CFA problem is shown to be equivalent to a 0-1 integer programming problem with a discontinuous cost function. A threshold rule and a row-wise or column-wise improvement (RCI) iteration are proposed to solve the problem. The threshold rule assigns all the traffic between two local switches to a direct route if the required traffic exceeds a predetermined threshold value, and otherwise to a tandem route. The RCI iteration searches the vertices of the unit cube of 2n-dimensional Euclidean space by a procedure roughly like the simplex method. Whenever the network has external traffic, direct application of the threshold rule ensures a global optimum. When there is no external traffic, a simple modification of the RCI iteration yields almost a global optimum within 2n steps