Learning-NUM: Network Utility Maximization With Unknown Utility Functions and Queueing Delay

Network Utility Maximization (NUM) studies the problems of allocating traffic rates to network users in order maximize users’ total utility subject resource constraints. In this paper, we propose a new NUM framework, Learning-NUM, where functions are unknown apriori and function values can be observed only after corresponding is delivered destination, which means that feedback experiences queueing delay. The goal design policy gradually learns makes rate allocation scheduling/routing decisions so as obtained over finite time horizon $T$ . addition stochastic constraints, central challenge our problem lies delay observations, may unbounded depends on policy. We first show expected by best dynamic upper bounded solution static optimization problem. Without presence delay, an algorithm based ideas gradient estimation Max-Weight scheduling. To handle embed parallel-instance paradigm form achieves notation="LaTeX">$\tilde {O}(T^{3/4})$ -regret, i.e., difference between Furthermore, extend deal with case observations noisy it {O}(T^{7/8})$ -regret. Finally, demonstrate practical applicability Learning-NUM apply three application scenarios including database query, job scheduling video streaming. further conduct simulations evaluate empirical performance