Necessary and sufficient condition for non-concave network utility maximisation

As the popularity of intellectual-property video services growing, users have raised their expectations on better quality of services. However, the existing traffic engineering solutions are not adequate to provide such desired quality to users. This paper aims to develop the distributed, user-utility-aware and optimisation-based traffic allocation mechanisms for real applications with non-concave utility functions, and then provide a solution to the problem. We formulate the traffic allocation problem as a network utility maximisation problem with link capacity constraints. This optimisation problem is challenging because of the non-concavity of the utility functions and the lack of global information. We overcome the difficulty by designing a class of fully distributed traffic allocation control laws, which requires a minimum communication workload. Moreover, we present a necessary and sufficient condition under which the proposed control laws converge to the globally optimal solution. Finally, we present numerical simulations to illustrate the theoretical results.