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 stochastic group, Markov chain models have been used extensively. Susu @cite_4 use a discrete-time Markov chain in which states represent different energy levels. Some work @cite_5 uses a Markov chain model to capture the influence of clouds and wind on solar radiation intensity. Relevant to stochastic energy modeling, there are many efforts to predict a stochastic energy supply. Lu @cite_17 assess three prediction techniques: regression analysis, moving average, and exponential smoothing. Recas @cite_12 propose a weather-conditioned moving average () model, which adapts to long-term seasonal changes and short-term sudden weather changes. Moser @cite_20 introduce energy variability curves to predict the power provided by a harvesting unit.
@cite_4 @cite_5 @cite_12 @cite_20 @cite_17
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Environmental energy is becoming a feasible alternative for many low-power systems, such as wireless sensor nodes. Designing an environmentally powered device faces several challenges: choosing the exact type of the energy harvester, the energy storage elements and determining the duty cycle of the application. With harvesting, the design process becomes even more difficult because it also has to take into account the unpredictability of the energy source. The contribution of this paper is a methodology that facilitates the analysis of energy harvesting nodes. The existing modeling strategies for battery powered systems are not suitable because they do not capture the uncertainty of the power source. Also, the metrics of interest for battery powered devices are different, as opposed to the harvesting powered ones: in the former case we search to maximize the system lifetime, while in the latter case a more expressive goal is to increase the system availability. A queuing analytical model is presented to investigate the performances of different sleep and wakeup strategies in a solar-powered wireless sensor mesh network where a solar cell is used to charge the battery in a sensor mesh node. While the solar radiation process (and, hence, the energy generation process in a solar cell) is modeled by a stochastic process (i.e., a Markov chain), a linear battery model with relaxation effect is used to model the battery capacity recovery process. Developed based on a multidimensional discrete-time Markov chain, the presented model is used to analyze the performances of different sleep and wakeup strategies in a sensor mesh node. The packet dropping and packet blocking probabilities at a node are the major performance metrics. The numerical results obtained from the analytical model are validated by extensive simulations. In addition, using the queuing model, based on a game-theoretic formulation, we demonstrate how to obtain the optimal parameters for a particular sleep and wakeup strategy. In this case, we formulate a bargaining game by exploiting the trade-off between packet blocking and packet dropping probabilities due to the sleep and wakeup dynamics in a sensor mesh node. The Nash solution is obtained for the equilibrium point of sleep and wakeup probabilities. The presented queuing model, along with the game-theoretic formulation, would be useful for the design and optimization of energy-efficient protocols for solar-powered wireless sensor mesh networks under quality-of-service (QoS) constraints Energy harvesting sensor nodes (EHSNs) have stringent low-energy consump- tion requirements, but they need to concurrently execute several types of tasks (processing, sensing, actuation, etc.). Furthermore, no accurate models exist to predict the energy harvest- ing income in order to adapt at run-time the executing set of prioritized tasks. In this article, we propose a novel power-aware task scheduler for EHSNs, namely, HOLLOWS: Head-of- Line Low-Overhead Wide-priority Service. HOLLOWS uses an energy-constrained prioritized queue model to describe the residence time of tasks entering the system and dynamically selects the set of tasks to execute, according to system accuracy requirements and expected energy. Moreover, HOLLOWS includes a new energy harvesting prediction algorithm, that is, weather-conditioned moving average (WCMA), which we have developed to estimate the solar panel energy income. We have tested HOLLOWS using the real-life working conditions of Shimmer, a sensor node for structural health monitoring. Our results indicate that HOLLOWS accurately predicts the energy available in Shimmer to guarantee a certain damage monitoring quality for long-term autonomous scenarios. Also, HOLLOWS is able to adjust the use of the incoming energy harvesting to achieve high accuracy for rapid event damage assessment (after earthquakes, fires, etc.). Energy harvesting has recently emerged as a feasible option to increase the operating time of sensor networks. If each node of the network, however, is powered by a fluctuating energy source, common power management solutions have to be reconceived. This holds in particular if real-time responsiveness of a given application has to be guaranteed. Task scheduling at the single nodes should account for the properties of the energy source, capacity of the energy storage as well as deadlines of the single tasks. We show that conventional scheduling algorithms (like e.g. EDF) are not suitable for this scenario. Based on this motivation, we have constructed optimal scheduling algorithms that jointly handle constraints from both energy and time domain. Further we present an admittance test that decides for arbitrary task sets, whether they can be scheduled without deadline violations. To this end, we introduce the concept of energy variability characterization curves (EVCC) which nicely captures the dynamics of various energy sources. Simulation results show that our algorithms allow significant reductions of the battery size compared to Earliest Deadline First scheduling.