Cost function considerations in hierarchical growth of lightwave networks

In this paper the potential usefulness of hierarchical networks is investigated from the viewpoint of growth of light-wave networks. To that end, a simple cost function is defined and used to measure the benefit of using hierarchical networks. Simple closed-form relationships developed for the cost function indicate that the most significant reduction occurs going from a single level network to a 2 level network, and the cost function reduces from the order of N/sup 2/ to N/sup 3/2/ where N is the number of nodes. When other network parameters are also considered (such as the amount of fiber required), star/ring hybrid networks are shown to be a good choice among different possibilities for 2 level networks.<>