An Asynchronous Fixed-Point Algorithm for Resource Sharing With Coupled Objectives

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Distributed resource allocation and sharing can often be formulated as a utility maximization problem, with the objective being the sum of user utilities minus a coupled cost. A traditional distributed solution to such problems, called “consistency pricing,” decouples the objective function via dual decomposition, which is then iteratively solved by the subgradient method. However, such gradient-based approaches may require many iterations of message passing to converge, which may not be sufficient in large-scale real-time applications. In this paper, we propose a new fixed-point-like distributed solution to resource sharing problems with coupled objective functions. While preserving the simple pricing interpretation, our approach speeds up convergence by exploiting the structural difference between user utilities and the coupled cost function. We theoretically analyze the asynchronous algorithm convergence conditions based on contraction mapping. Through a detailed case study of cloud bandwidth reservation based on real-world workload traces, we demonstrate the benefits of the proposed algorithm over state-of-the-art distributed optimization techniques including gradient descent, dual decomposition, and ADMM. In addition, we also extend the proposed algorithm to approach a more general class of consensus optimization problems with not only a coupled objective function, but also a certain class of coupled constraints.