Some Properties of the Capacity Value Function

In a previous paper [5], two of the authors developed a method for ascribing a value to an extra unit of capacity on a telecommunications link. Specifically, they expressed the value of an extra unit of capacity as a function of current capacity, current occupancy and a planning horizon. The intention was to use this function as an ingredient in a bandwidth reallocation scheme for ensuring efficient operation of a telecommunications network. Unfortunately, direct evaluation of the function requires numerical inversion of a Laplace transform expressed in terms of Charlier polynomials, a task that is beyond the processing capabilities of typical switches in today’s telecommunications networks. Because of this, it is desirable to have more easily computable methods of either calculating or approximating the capacity value function. We develop two approaches to this problem: the first is a recursive method of computing the Laplace transform of the capacity value function and the second is a linear approximation to the capacity value function itself.