Distributed network utility maximization (NUM) is receiving increasing interests for cross-layer optimization problems in multihop wireless networks. Traditional distributed NUM algorithms rely heavily on feedback information between different network elements, such as traffic sources and routers. Because of the distinct features of multihop wireless networks such as time-varying channels and dynamic network topology, the feedback information is usually inaccurate, which represents as a major obstacle for distributed NUM application to wireless networks. The questions to be answered include if distributed NUM algorithm can converge with inaccurate feedback and how to design effective distributed NUM algorithm for wireless networks. In this paper, we first use the infinitesimal perturbation analysis technique to provide an unbiased gradient estimation on the aggregate rate of traffic sources at the routers based on locally available information. On the basis of that, we propose a stochastic approximation algorithm to solve the distributed NUM problem with inaccurate feedback. We then prove that the proposed algorithm can converge to the optimum solution of distributed NUM with perfect feedback under certain conditions. The proposed algorithm is applied to the joint rate and media access control problem for wireless networks. Numerical results demonstrate the convergence of the proposed algorithm.
Bibliographical noteThis is the peer reviewed version of the following article: Liao, S., & He, J. (2014). Design and analysis of distributed utility maximization algorithm for multihop wireless network with inaccurate feedback. International journal of communication systems, 27(12), 4280-4299, which has been published in final form athttp://onlinelibrary.wiley.com/doi/10.1002/dac.2611. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
Funding: NSF of China through the grant 61072051 and 61072057; key science and technology project of Wuhan - grant (NO. 201110821234); research funds of CCNU from the colleges’ basic research and operation of MOE (NO.120002040246).
- dual decomposition
- gradient estimation
- infinitesimal perturbation analysis
- multihop wireless networks
- network utility maximization
- noise level