Achieving Low-Delay and Fast-Convergence in Stochastic Network Optimization: A Nesterovian Approach

Due to the rapid growth of mobile data demands, there have been significant interests in stochastic resource control and optimization for wireless networks. Although significant advances have been made in stochastic network optimization theory, to date, most of the existing approaches are plagued by either slow convergence or unsatisfactory delay performances. To address these challenges, in this paper, we develop a new stochastic network optimization framework inspired by the Nesterov accelerated gradient method. We show that our proposed Nesterovian approach offers utility-optimality, fast-convergence, and significant delay reduction in stochastic network optimization. Our contributions in this paper are three-fold: i) we propose a Nesterovian joint congestion control and routing/scheduling framework for both single-hop and multi-hop wireless networks; ii) we establish the utility optimality and queueing stability of the proposed Nesterovian method, and analytically characterize its delay reduction and convergence speed; and iii) we show that the proposed Nesterovian approach offers a three-way performance control between utility-optimality, delay, and convergence.