Generalized gradient scheduling for vector network utility maximization

Generalized network utility maximization (NUM), which has a multiple-variable vector utility function, is a key framework in network resource allocation that supports multi-class services with a different efficiency and fairness. We propose a generalized gradient scheduling (GS) that easily finds a solution to the generalized NUM problem by simplifying its objective function. The properties of the argument of the maximum and the directional derivative are applied to the simplification process. Achieving a generalized GS is a necessary condition for achieving a generalized NUM, and for a special case with scalar utility functions, the generalized GS and generalized NUM are equivalent problems. A practical application of the findings to uplink cellular networks is also presented in this paper.