Some properties of the capacity value function

Abstract

In a previous paper [B. A. Chiera and P. G. Taylor, Probab. Engrg. Inform. Sci., 16 (2002), pp. 513-522], 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 p..