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Any properly designed network coding technique can result in increased throughput and reliability of multi-hop wireless networks by taking advantage of the broadcast nature of wireless medium. In many inter-flow network coding schemes nodes are encouraged to overhear neighbours traffic in order to improve coding opportunities at the transmitter nodes. A study of these schemes reveal that some of the overheard packets are not useful for coding operation and thus this forced overhearing increases energy consumption dramatically. In this paper, we formulate network coding aware sleep/wakeup scheduling as a semi Markov decision process (SMDP) that leads to an optimal node operation. In the proposed solution for SMDP, the network nodes learn when to switch off their transceiver in order to conserve energy and when to stay awake to overhear some useful packets. One of the main challenges here is the delay in obtaining reward signals by nodes. We employ a modified Reinforcement Learning (RL) method based on continuous-time Q-learning to overcome this challenge in the learning process. Our simulation results confirm the optimality of the new methodology.

Network coding is all about combining a variety of packets and forwarding as much packets as possible in each transmission operation. The network coding technique improves the throughput efficiency of multi-hop wireless networks by taking advantage of the broadcast nature of wireless channels. However, there are some scenarios where the coding cannot be exploited due to the stochastic nature of the packet arrival process in the network. In these cases, the coding node faces two critical choices: forwarding the packet towards the destination without coding, thereby sacrificing the advantage of network coding, or, waiting for a while until a coding opportunity arises for the packets. Current research works have addressed this challenge for the case of a simple and restricted scheme called reverse carpooling where it is assumed that two flows with opposite directions arrive at the coding node. In this paper the issue is explored in a general sense based on the COPE architecture requiring no assumption about flows in multi-hop wireless networks. In particular, we address this sequential decision making problem by using the solid framework of optimal stopping theory, and derive the optimal stopping rule for the coding node to choose the optimal action to take, i.e. to wait for more coding opportunity or to stop immediately (and send packet). Our simulation results validate the effectiveness of the derived optimal stopping rule and show that the proposed scheme outperforms existing methods in terms of network throughput and energy consumption.

Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Gr\"unwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate., Comment: 21 pages

We consider cooperative communications with energy harvesting (EH) relays, and develop a distributed power control mechanism for the relaying terminals. Unlike prior art which mainly deal with single-relay systems with saturated traffic flow, we address the case of bursty data arrival at the source cooperatively forwarded by multiple half-duplex EH relays. We aim at optimizing the long-run average delay of the source packets under the energy neutrality constraint on power consumption of each relay. While EH relay systems have been predominantly optimized using either offline or online methodologies, we take on a more realistic learning-theoretic approach. Hence, our scheme can be deployed for real-time operation without assuming acausal information on channel realizations, data/energy arrivals as required by offline optimization, nor does it rely on precise statistics of the system processes as is the case with online optimization. We formulate the problem as a partially observable identical payoff stochastic game (PO-IPSG) with factored controllers, in which the power control policy of each relay is adaptive to its local source-to-relay/relay-to-destination channel states, its local energy state as well as to the source buffer state information. We derive a multi-agent reinforcement learning algorithm which is convergent to a locally optimal solution of the formulated PO-IPSG. The proposed algorithm operates without explicit message exchange between the relays, while inducing only little source-relay signaling overhead. By simulation, we contrast the delay performance of the proposed method against existing heuristics for throughput maximization. It is shown that compared with these heuristics, the systematic approach adopted in this paper has a smaller sub-optimality gap once evaluated against a centralized optimal policy armed with perfect statistics., Comment: 13 pages, 6 figures, IEEE Transactions on Vehicular Technology