The impact of tree selection on the design of networks with multipoint connections

We consider the design of networks that support point-to-multipoint calls with load sharing. In the case of point-to-point connections, there is an obviously good (natural) choice of candidate sets of predefined paths to use for the routing. For multipoint connections, there is no such obviously good choice of trees to form the candidate sets. For this reason, we need to investigate the impact of tree selection on the network revenue and dimensioning and eventually find a simple criterion for tree selection. For both routing and dimensioning problems, we find that a key factor affecting the result is whether or not the trees have many links in common, a result that follows from the form of the induced costs for the trees. We also find that the appropriate choice of trees for dimensioning (many links in common) is the opposite from the best choice for the routing problem (few links in common). This raises some further questions about the modeling of the dimensioning and the calculation of induced costs