Distributed Network Utility maximization in Multi-hop Wireless Networks: Noisy Feedback, Loss Channel and Stability

Distributed solutions play a critical role in making the network utility maximization (NUM) framework attractive in practical networks where a centralized solution is often infeasible and non-scalable. The implementation of such distributed algorithms hinges heavily on the information feedback, which, unfortunately, is often obtained using error-prone measurement mechanisms in practical systems and also suffers from other random errors in its transmissions

We study distributed NUM in multi-hop wireless networks. First we focus on the impact of noisy feedback on the distributed NUM algorithms based on the Lagrangian dual method. Assuming strong duality, we study both cases when the stochastic gradients are unbiased or biased. Using a combination of tools in stochastic approximation, Martingale theory and convex analysis, we develop a general theory on the stochastic stability of these algorithms in the presence of noisy feedback. We also examine the rate of convergence for the unbiased case, and show the limit process corresponding to the normalized iterate sequence is a stationary reflected linear diffusion process (not necessarily a Gaussian diffusion process). Then, we investigate the impact of lossy channel on distributed NUM and propose effective NUM accordingly.

Junshan Zhang received his Ph.D. degree from the School of ECE at Purdue University in 2000. He joined the EE Department at Arizona State University in August 2000, where he is currently an Associate Professor. His research interests fall in the general area of wireless networks, spanning from the networking layer to the physical layer. His current research focuses on fundamental aspects of sensor/ad-hoc networks, including cross-layer optimization and design, network management, network information theory, stochastic analysis. He is a recipient of the ONR Young Investigator Award in 2005 and the NSF CAREER award in 2003. He has served as TPC co-chair for IPCCC'06 and TPC vice chair for ICCCN'06, and he will be the general chair for IEEE Communication Theory Workshop 2007. He has served as an Associate Editor for IEEE Transactions on Wireless Communications since 2004.