We consider the performance modeling and evaluation of network systems powered with renewable energy sources such as solar and wind energy. Such energy sources largely depend on environmental conditions, which are hard to predict accurately. As such, it may only make sense to require the network systems to support a soft quality of service (QoS) guarantee, i.e., to guarantee a service requirement with a certain high probability. In this paper, we intend to build a solid mathematical foundation to help better understand the stochastic energy constraint and the inherent correlation between QoS and the uncertain energy supply. We utilize a calculus approach to model the cumulative amount of charged energy and the cumulative amount of consumed energy. We derive upper and lower bounds on the remaining energy level based on a stochastic energy charging rate and a stochastic energy discharging rate. By building the bridge between energy consumption and task execution (i.e., service), we study the QoS guarantee under the constraint of uncertain energy sources. We further show how performance bounds can be improved if some strong assumptions can be made.
In the deterministic group, Zafer @cite_1 use deterministic network calculus to model traffic arrival and traffic departure. They use a power-rate function to link the traffic departure rate and energy consumption rate. By considering the special features of specific power-rate functions, they formulate and solve the optimal transmission scheduling problem under the given energy constraints. Their work only focuses on single-node analysis and assumes that traffic arrivals and service rates are deterministic. Kansal @cite_10 propose a so-termed to help energy management of a sensor node and determine the performance levels that the sensor node can support. The basic idea of the harvesting theory is to use a leaky bucket model to represent energy supply and energy depletion. Moser @cite_20 describe energy-aware scheduling and prove the conditions for a scheduling algorithm to be optimal in a system whose energy storage is replenished .
@cite_10 @cite_1 @cite_20
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We investigate performance limits of a multiple access communication system with energy harvesting nodes where the utility function is taken to be the long-term average sum-throughput. We assume a causal structure for energy arrivals and study the problem in the continuous time regime. For this setting, we first characterize a storage dam model that captures the dynamics of a battery with energy harvesting and variable transmission power. Using this model, we next establish an upper bound on the throughput problem as a function of battery capacity. We also formulate a nonlinear optimization problem to determine optimal achievable power policies for transmitters. Applying a calculus of variations technique, we then derive Euler-Lagrange equations as necessary conditions for optimum power policies in terms of a system of coupled partial integro-differential equations. Based on a Gauss-Seidel algorithm, we devise an iterative algorithm to solve these equations. We also propose a fixed-point algorithm for the symmetric multiple access setting in which the statistical descriptions of energy harvesters are identical. To further support our iterative algorithms, along with the analysis, comprehensive numerical results are also obtained. Wireless systems comprised of rechargeable nodes have a significantly prolonged lifetime and are sustainable. A distinct characteristic of these systems is the fact that the nodes can harvest energy throughout the duration in which communication takes place. As such, transmission policies of the nodes need to adapt to these harvested energy arrivals. In this paper, we consider optimization of point-to-point data transmission with an energy harvesting transmitter which has a limited battery capacity, communicating in a wireless fading channel. We consider two objectives: maximizing the throughput by a deadline, and minimizing the transmission completion time of the communication session. We optimize these objectives by controlling the time sequence of transmit powers subject to energy storage capacity and causality constraints. We, first, study optimal offline policies. We introduce a directional water-filling algorithm which provides a simple and concise interpretation of the necessary optimality conditions. We show the optimality of an adaptive directional water-filling algorithm for the throughput maximization problem. We solve the transmission completion time minimization problem by utilizing its equivalence to its throughput maximization counterpart. Next, we consider online policies. We use stochastic dynamic programming to solve for the optimal online policy that maximizes the average number of bits delivered by a deadline under stochastic fading and energy arrival processes with causal channel state feedback. We also propose near-optimal policies with reduced complexity, and numerically study their performances along with the performances of the offline and online optimal policies under various different configurations. In this paper, we investigate the optimal packet scheduling problem in a two-user multiple access communication system, where the transmitters are able to harvest energy from the nature. Under a deterministic system setting, we assume that the energy harvesting times and harvested energy amounts are known before the transmission starts. For the packet arrivals, we assume that packets have already arrived and are ready to be transmitted at the transmitter before the transmission starts. Our goal is to minimize the time by which all packets from both users are delivered to the destination through controlling the transmission powers and transmission rates of both users. We first develop a generalized iterative backward waterfilling algorithm to characterize the maximum departure region of the transmitters for any given deadline T. Then, based on the sequence of maximum departure regions at energy arrival instants, we decompose the transmission completion time minimization problem into convex optimization problems and solve the overall problem efficiently. In this paper, we consider a source node that operates over a time varying channel with energy harvesting capability. The goal of the source is to maximize the average number of successfully delivered packets per time slot. The source is able to choose whether to transmit a packet or defer the transmission in each time slot. The decision which is chosen by the source depends on the channel information available and the length of the energy queue. We formulate the problem of finding the optimal policy as a Markovian decision problem. We show some properties of the value function that represents the discounted number of successfully delivered packets per time slot. We prove that the optimal policy is a threshold type policy depending on the state of the channel and the length of the energy queue. We also derive an upper bound for the average number of packets per time slots successfully received by the destination. We show using numerical results that this bound is a tight bound on the performance of the optimal policy. And we consider the case of time varying channel but without channel state information (CSI). Then, we study the impact of channel time varying nature and the availability of CSI. In this case, we show that the optimal policy is a greedy policy. The performance of this greedy policy is also calculated.