A numerical approach of the analysis of optical container filling

We study the performance of the optical network architecture NGreen which is based on an optical slotted ring. The random part of the end to end delay comes from the times needed to build an optical container from arriving Data Units and the insertion of the optical container on the ring. Here, to study the first problem, we build a Discrete Time Markov Chain to model the filling of the optical container with Data Units. We take into account a deadline (to have a small latency) and a constraint on a minimal filling of the container (to be energy efficient). We obtain through a numerical analysis using an ad-hoc algorithm we proved, the distribution of the container filling and the distribution of the time needed to build a container. We also compare the algorithm speed with two well known algorithms to compute the steady-state distribution of Markov chains.