Dimensioning telephone networks with budget constraints

Abstract

We present a theoretical study of a modified version of the dimensioning problem for telephone networks where the network does not contain any existing capacity and where the available capital is severely limited, a situation which can occur in private networks as well as in the public networks of developing countries. In the latter, case, the budget constraint is generally of paramount importance. This has two effects. First, the grade of service constraint is replaced by a budget constraint. Another difference from the original problem arises because the network may be operating under overload most of the time. This paper examines some cases of overload for which the link ordering is maintained. The main result of this paper is the derivation of a set of equations similar to the classical optimality equations that lead to the ECCS method, but for the modified version of the problem. As a consequence, we expect that it will be possible to obtain a fast iterative heuristic algorithm similar to the one currently used to solve the classical problem. A number of other points of theoretical interest are also discussed, mainly with the objective of gaining insight into the structure of the modified problem.