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.
Finally, related to analytical frameworks for performance modeling, there is a large body of research on energy-aware scheduling algorithms. For example, Niyato @cite_5 investigate the impact of different sleep and wake-up strategies on data communication among solar-powered wireless nodes. @cite_11 , Vigorito propose an adaptive duty-cycling algorithm that ensures operational power levels at wireless sensor nodes regardless of changing environmental conditions. @cite_13 , Gorlatova measure the energy availability in indoor environment and based on the measurement results they develop algorithms to determine energy allocation in systems with predictable energy inputs and in systems where energy inputs are stochastic. In the stochastic model, they assume that energy inputs are i.i.d. random variables. Unlike the above work, our analytical framework is generic and uses only abstract notations on energy charging discharging amount, traffic arrival amount, etc. As such, all the above work could be treated as a special case of our more general framework in which the abstract functions are replaced with concrete ones for specific applications.
@cite_5 @cite_13 @cite_11
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Accurate analytical expressions of delay and packet reception probabilities, and energy consumption of duty-cycled wireless sensor networks with random medium access control (MAC) are instrumental for the efficient design and optimization of these resource-constrained networks. Given a clustered network topology with unslotted IEEE 802.15.4 and preamble sampling MAC, a novel approach to the modeling of the delay, reliability, and energy consumption is proposed. The challenging part in such a modeling is the random MAC and sleep policy of the receivers, which prevents to establish the exact time of data packet transmission. The analysis gives expressions as function of sleep time, listening time, traffic rate and MAC parameters. The analytical results are then used to optimize the duty cycle of the nodes and MAC protocol parameters. The approach provides a significant reduction of the energy consumption compared to existing solutions in the literature. Monte Carlo simulations by ns2 assess the validity of the analysis. Increasingly many wireless sensor network deployments are using harvested environmental energy to extend system lifetime. Because the temporal profiles of such energy sources exhibit great variability due to dynamic weather patterns, an important problem is designing an adaptive duty-cycling mechanism that allows sensor nodes to maintain their power supply at sufficient levels (energy neutral operation) by adapting to changing environmental conditions. Existing techniques to address this problem are minimally adaptive and assume a priori knowledge of the energy profile. While such approaches are reasonable in environments that exhibit low variance, we find that it is highly inefficient in more variable scenarios. We introduce a new technique for solving this problem based on results from adaptive control theory and show that we achieve better performance than previous approaches on a broader class of energy source data sets. Additionally, we include a tunable mechanism for reducing the variance of the node's duty cycle over time, which is an important feature in tasks such as event monitoring. We obtain reductions in variance as great as two-thirds without compromising task performance or ability to maintain energy neutral operation. 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. This paper considers a two-user Gaussian interference channel with energy harvesting transmitters. Different than conventional battery powered wireless nodes, energy harvesting transmitters have to adapt transmission to availability of energy at a particular instant. In this setting, the optimal power allocation problem to maximize the sum throughput with a given deadline is formulated. The convergence of the proposed iterative coordinate descent method for the problem is proved and the short-term throughput maximizing offline power allocation policy is found. Examples for interference regions with known sum capacities are given with directional waterfilling interpretations. Next, stochastic data arrivals are addressed. Finally, online and or distributed near-optimal policies are proposed. Performance of the proposed algorithms are demonstrated through simulations.