Fair Allocation of Utilities in Multirate Multicast Networks

We study fairness in a multicast network. We assume that the source hierarchically encodes its signal and the hierarchical structure is predetermined. We study fair allocation of utilities, where utility of a bandwidth can be the number of layers or the bandwidth itself, or any other function of the bandwidth depending on system requirements. The utility function is not strictly increasing in general. Fairness issues become vastly diierent in this case as opposed to that when the utility function is strictly increasing. Computation of lexicographically optimal utility allocation becomes NP-hard in this case, while lexicographically optimal utility allocation is polynomial complexity computable when the utility function is strictly increasing. Furthermore, maxmin fair utility allocation may not exist in the general case. We introduce a new notion of fairness, maximal fairness. We propose a polynomial complexity algorithm for computation of maximally fair utility allocation. Even though, maximal fairness is a weaker notion of fairness, it coincides with lexicographic optimality and maxmin fairness, when maxmin fair utility allocation exists. So the algorithm for computing maximally utility allocation computes maxmin fair utility allocation, when the latter exists.