Mathematical decomposition techniques for distributed cross-layer optimization of data networks

Abstract — Network performance can be increased if the traditionally separated network layers are jointly optimized. Recently, network utility maximization has emerged as a powerful framework for studying such cross-layer issues. In this paper we review and explain three distinct techniques that can be used to engineer utility-maximizing protocols: primal, dual, and cross decomposition. The techniques suggest layered, but loosely coupled, network architectures and protocols where different resource allocation updates should be run at different timescales. The decomposition methods are applied to the design of fully distributed protocols for two wireless network technologies: networks with orthogonal channels and network-wide resource constraints, as well as wireless networks where the physical layer uses spatial-reuse TDMA. Numerical examples are included to demonstrate the power of the approach. Index Terms — Wireless networks, optimization, congestion control, power control, scheduling, cross-layer protocol design