Stochastic network utility maximisation - A tribute to Kelly's paper published in this journal a decade ago

Since the seminal work by Kelly on distributed network resource allocation using the language of network utility maximisation (NUM) a decade ago, there have been extensive research efforts generalising and applying NUM to model, analyse and design various network protocols and architectures. Some of these works combine the distributed optimisation approach with stochastic network models to study NUM under network dynamics occurring at the session, packet and constraint levels. We survey these works by presenting the key questions, results and methodologies in this emerging theory of stochastic network utility maximisation, followed by discussion on related work and future research challenges.