LAUSR

In this paper, we address the energy harvesting tradeoff for minimizing the average packet delay in wireless energy harvesting multi-hop networks with inter-session network coding (NC) and successive interference cancellation. Unlike the previous works, conventionally making a tradeoff between the transmission delay and the energy consumption in a wireless network, here by minimizing the ratio of the scheduling length to the harvesting energy remained, we present a cross-layer formulation for a joint routing, network coding, and scheduling problem in a wireless energy transfer network to make the length-energy tradeoff while satisfying the traffic demands from the upper layer. With the realistic signal-to-interference-plus-noise ratio model, the formulation is also to address a conflict-free scheduling problem on the NC components, and to specify an energy harvesting and consuming model for these components in detail. Then, for the combinatorial nonlinear problem resulted, we develop a Lyapunov optimization-based scheme conducting a dynamic scheduling policy that can approach the optimal length-energy tradeoff while keeping the network stable. Specifically, the mixed integer nonlinear programming model, including, especially, the fractional objective is first transformed and decomposed into a master subproblem and a pricing subproblem with a column generation (CG) method to avoid enumerating all the possible configures, and then resolved iteratively through the Lyapunov optimization algorithm. To further reduce the complexity, the CG method on finding feasible configures is operated within a limited number of iteration and stopped when no significant improvements can be obtained. Finally, with the numerical results, we show that the proposed algorithm can effectively reduce the scheduling length, while reserving the time long enough to harvest the energy for the wireless networks with and without NC, and verify the tradeoff on the performance metrics as $[O(V), O(1/V)]$ , which provides engineering insights for a practical system design.