Optimal Sleep-Wake Policies for an Energy Harvesting Sensor Node Vinay Joseph, Vinod Sharma and Utpal Mukherji Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, India. Email:{vinay,vinod,utpal}@ece.iisc.ernet.in Abstract—We study a sensor node with an energy harvesting source. In any slot, the sensor node is in one of two modes: Wake or Sleep. The generated energy is stored in a buffer. The sensor node senses a random field and generates a packet when it is awake. These packets are stored in a queue and transmitted in the wake mode using the energy available in the energy buffer. We obtain energy management policies which minimize a linear combination of the mean queue length and the mean data loss rate. Then, we obtain two easily implementable suboptimal policies and compare their performance to that of the optimal policy. Next, we extend the Throughput Optimal policy developed in our previous work to sensors with two modes. Via this policy, we can increase the throughput and stabilize the data queue by allowing the node to sleep in some slots and to drop some generated packets. This policy requires minimal statistical knowledge of the system. We also modify this policy to decrease the switching costs. Keywords: Energy harvesting sensor nodes, Sleep-Wake Poli- cies, Throughput Optimal Policies. I. I NTRODUCTION Sensor networks consist of a large number of small, inex- pensive sensor nodes. These nodes have small batteries with limited power and also have limited computational power and storage space. When the battery of a node is exhausted, it is not replaced and the node dies. When sufficient number of nodes die, the network may not be able to perform its designated task. Various studies have been conducted to increase the life time of the battery of a node by reducing the energy intensive tasks, e.g., reducing the number of bits to transmit ([9], [2]), making a node go into power saving modes (sleep/listen) periodically ([15]), using energy efficient routing ([17], [12]) and MAC ([18]). A general survey on sensor networks is [1] which provides more references on these issues. The life time of the battery itself can be increased by energy harvesting techniques ([5], [8]). Common energy harvesting devices are solar cells, wind turbines and piezo-electric cells, which extract energy from the environment. Among these, solar energy harvesting seems to have emerged as a technology of choice ([8], [10]). Unlike for a battery operated sensor node, now there is potentially an infinite amount of energy available to the node. However, the source of energy and the energy harvesting device may be such that the energy cannot be generated at all times (e.g., a solar cell). Furthermore, the rate of generation of energy can be limited. Thus, one may need to modify the energy consumption profile of the sensor node so that the node can perform satisfactorily for a long time, e.g., can operate in energy neutral operation ([5]). In our previous work ([13], [14]), for data gathering appli- cations, throughput optimal and mean delay optimal energy management policies were identified which made the system work in energy neutral operation. It was found that having energy storage allows larger stability region as well as lower mean delays. MACs for such sensor nodes have also been studied in [13]. In this paper, we extend this work to also include sleep mode which may be needed when energy neutral operation is not possible (necessary conditions for which were identified in [14]). In the following, we survey the literature on sensor net- works with energy harvesting nodes. Early papers on energy harvesting in sensor networks are [6] and [11]. A good recent contribution is [5]. It provides various deterministic theoretical models for energy generation and energy consumption profiles and provides conditions for energy neutral operation. In [4], the authors study optimal sleep-wake cycles such that event detection probability is maximized. In [7], finite state Markov models of solar energy harvesting are formulated, certain sleep-wake strategies are proposed and policy parameters optimized using Game Theory. A recent survey is [8] which also summarizes the results in [7]. In this paper, we consider a sensor node with an energy harvesting source that has two modes: Wake and Sleep. The sleep mode is a power saving mode in which the sensor only harvests energy and performs no other functions so that the energy consumption is negligible. We find an optimal policy that minimizes a linear combination of the mean queue length and the mean data loss rate. Next, we obtain a throughput optimal policy which is much easier to compute and does not require distributions of the system parameters. We find the optimal fraction of time the sensor should sleep and then specify a policy to schedule the sleep slots of the sensor. Interestingly, for stability of data queue, the throughput optimal policy may require dropping a fraction of packets after sensing and processing them. The results we obtain for a single node will be used in a sensor network later on. In contrast to finite state Markov models in [7], we have more general stationary stochastic models and our emphasis is on showing the existence of optimal policies and obtaining easily computable optimal and suboptimal policies. This paper is organized as follows. Section II describes