A stochastic primal-dual algorithm for joint flow control and MAC design in multi-hop wireless networks

Junshan Zhang, Dong Zheng

Research output: Chapter in Book/Report/Conference proceedingConference contribution

23 Scopus citations

Abstract

We study stochastic rate control for joint flow control and MAC design in multi-hop wireless networks with random access. Most existing studies along this avenue are based on deterministic convex optimization and the corresponding distributed algorithms developed therein involve deterministic feedback control. In a multi-hop wireless network, however, the feedback signal is obtained using error-prone measurement mechanisms and therefore noisy in nature. A fundamental open question is that under what conditions these algorithms would converge to the optimal solutions in the presence of noisy feedback signals, and this is the main subject of this paper. Specifically, we first formulate rate control in multi-hop random access networks as a network utility maximization problem where the link constraints are given in terms of the persistence probabilities. Using the Lagrangian dual decomposition method, we devise a distributed primal-dual algorithm for joint flow control and MAC design. Then, we focus on the convergence properties of this algorithm under noisy feedback information. We show that the proposed primal-dual algorithm converges (almost surely) to the optimal solutions only if the estimators of gradients are asymptotically unbiased. We also characterize the corresponding rate of convergence, and our findings reveal that in general the limit process of the interpolated process, corresponding to the normalized iterate sequence generated from the primal-dual algorithm, is a reflected linear diffusion process, not necessarily the Gaussian diffusion process.

Original languageEnglish (US)
Title of host publication2006 IEEE Conference on Information Sciences and Systems, CISS 2006 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages339-344
Number of pages6
ISBN (Print)1424403502, 9781424403509
DOIs
StatePublished - Jan 1 2006
Event2006 40th Annual Conference on Information Sciences and Systems, CISS 2006 - Princeton, NJ, United States
Duration: Mar 22 2006Mar 24 2006

Publication series

Name2006 IEEE Conference on Information Sciences and Systems, CISS 2006 - Proceedings

Other

Other2006 40th Annual Conference on Information Sciences and Systems, CISS 2006
CountryUnited States
CityPrinceton, NJ
Period3/22/063/24/06

ASJC Scopus subject areas

  • Computer Science(all)

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    Zhang, J., & Zheng, D. (2006). A stochastic primal-dual algorithm for joint flow control and MAC design in multi-hop wireless networks. In 2006 IEEE Conference on Information Sciences and Systems, CISS 2006 - Proceedings (pp. 339-344). [4067830] (2006 IEEE Conference on Information Sciences and Systems, CISS 2006 - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CISS.2006.286489