Characterization of a simple communication network using Legendre transform

We describe an application of the Legendre transform to communication networks. The Legendre transform applied to max-plus algebra linear systems corresponds to the Fourier transform applied to conventional linear systems. Hence, it is a powerful tool that can be applied to max-plus linear systems and their identification. Linear max-plus algebra has been already used to describe simple data communication networks. We first extend the Legendre transform as the slope transform to non-concave/non-convex functions. We then use it to analyze a simple communication network. We also propose an identification method for its transfer characteristic, and we confirm the results using the ns-2 network simulator.