TY - GEN
T1 - A stochastic primal-dual algorithm for joint flow control and MAC design in multi-hop wireless networks
AU - Zhang, Junshan
AU - Zheng, Dong
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
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U2 - 10.1109/CISS.2006.286489
DO - 10.1109/CISS.2006.286489
M3 - Conference contribution
AN - SCOPUS:44049086389
SN - 1424403502
SN - 9781424403509
T3 - 2006 IEEE Conference on Information Sciences and Systems, CISS 2006 - Proceedings
SP - 339
EP - 344
BT - 2006 IEEE Conference on Information Sciences and Systems, CISS 2006 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2006 40th Annual Conference on Information Sciences and Systems, CISS 2006
Y2 - 22 March 2006 through 24 March 2006
ER -