Operation state scheduling of relay nodes (RNs) in two-tiered wireless sensor networks is the focus of this paper. From multiple access control (MAC) viewpoint, the scheduling of transmit, receive, and sleep operation states of RNs is formulated as an optimization problem under the objective of energy cost minimization. This problem is computationally intractable to solve optimally for practical problem sizes. With the perspective of a synchronous and schedule access MAC protocol, the problem is tackled using dual decomposition and the solution is achieved collaboratively by RNs continually over the time. To make the solution practically possible, a stochastic approximation iteration is provided that results in an energy-aware MAC protocol with linear complexity. This protocol attains statistical convergence with respect to the time-varying channel state information in the time of its scope. Numerical results demonstrate the effectiveness of this protocol in terms of consumed energy in comparison with classical protocols as a result of eliminating idle listening in the network.
