Stability and Benefits of Suboptimal Utility Maximization

Network utility maximization has been widely used to model resource allocation and network architectures. However, in practice, often it cannot be solved optimally due to complexity reasons. Thus motivated, we address the following two questions in this paper: 1) Can suboptimal utility maximization maintain queue stability? 2) Can underoptimization of utility objective function in fact benefit other network design objectives? We quantify the following intuition: A resource allocation that is suboptimal with respect to a utility maximization formulation maintains maximum flow-level stability when the utility gap is sufficiently small and information delay is bounded, and it can still provide a guaranteed size of stability region otherwise. Utility-suboptimal rate allocation can also enhance other network performance metrics, e.g., it may reduce link saturation. These results provide a theoretical support for turning attention from optimal but complex solutions of network optimization to those that are simple even though suboptimal.