A numerical strategy for telecommunications networks capacity planning under demand and price uncertainty

The massive use of Internet in the last twenty years has created a huge demand for telecommunications networks capacity. In this work, financial option pricing methods are applied to the problem of network investment decision timing. The main innovative aspect is the consideration of two uncertain factors: the capacity demand and the bandwidth price, the evolution of which is modeled by suitable stochastic processes. Thus, we consider the optimal decision problem of upgrading a line in terms of the (highly volatile) uncertain demand for capacity and the price. By using real options pricing methodology, a set of partial differential equation problems are posed and appropriate numerical methods based on characteristics methods combined with finite elements to approximate the solution are proposed. The combination with a dynamic programming strategy gives rise to a global algorithm to help in the decision of optimizing the value of the line.