Stochastic Online Control for Energy-Harvesting Wireless Networks with Battery Imperfections

In energy harvesting (EH) network, the energy storage devices (i.e., batteries) are usually not perfect. In this paper, we consider a practical battery model with finite battery capacity, energy (dis-)charging loss, and energy dissipation. Taking into account such battery imperfections, we rely on the Lyapunov optimization technique to develop a stochastic online control scheme that aims to maximize the utility of data rates for EH multi-hop wireless networks. It is established that the proposed algorithm can provide a feasible and efficient data admission, power allocation, routing and scheduling solution, without requiring any statistical knowledge of the stochastic channel, data-traffic, and EH processes. Numerical results demonstrate the merit of the proposed scheme

Network Resource Allocation via Stochastic Subgradient Descent: Convergence Rate

This paper considers a general stochastic resource allocation problem that arises widely in wireless networks, cognitive radio, networks, smart-grid communications, and cross-layer design. The problem formulation involves expectations with respect to a collection of random variables with unknown distributions, representing exogenous quantities such as channel gain, user density, or spectrum occupancy. We consider the constant step-size stochastic dual subgradient descent (SDSD) method that has been widely used for online resource allocation in networks. The problem is solved in dual domain which results in a primal resource allocation subproblem at each time instant. The goal here is to characterize the non-asymptotic behavior of such stochastic resource allocations in an almost sure sense. It is well known that with a step size of $\epsilon$, {SDSD} converges to an $\mathcal{O}(\epsilon)$-sized neighborhood of the optimum. In practice however, there exists a trade-off between the rate of convergence and the choice of $\epsilon$. This paper establishes a convergence rate result for the SDSD algorithm that precisely characterizes this trade-off. {Towards this end, a novel stochastic bound on the gap between the objective function and the optimum is developed. The asymptotic behavior of the stochastic term is characterized in an almost sure sense, thereby generalizing the existing results for the {stochastic subgradient} methods.} For the stochastic resource allocation problem at hand, the result explicates the rate with which the allocated resources become near-optimal. As an application, the power and user-allocation problem in device-to-device networks is formulated and solved using the {SDSD} algorithm. Further intuition on the rate results is obtained from the verification of the regularity conditions and accompanying simulation results