# Analytical Model for the Duty Cycle in Solar-Based EH-WSN for Environmental Monitoring
## 2 Related Work
Next, this node determines which sender can transmit first (decision process that may include priorities to distinguish between normal and urgent data), and broadcasts a receiver beacon containing the identity of the selected sender as well as a network allocation vector (NAV) indicating the next wakeup time of the receiver. Moreover, the NAV value can be adjusted by the receiver according to its own energy profile. After capturing a beacon message, all senders except the one selected by the receiver switch to sleep mode, thus guaranteeing contention avoidance. It is shown that this protocol improves throughput, especially in the case of critical data. The last subset of MAC layer solutions for EH-WSN falls into the category of transmitter-initiated asynchronous protocols. One example is DeepSleep [51], which consists of a MAC enhancement scheme on the baseline IEEE 802.11 power saving mode (PS). DeepSleep was developed in the light of the forthcoming M2M (Machine To Machine) networks, which are expected to consist of large amounts of energy-harvesting devices. Large number of devices means high level of contention in the original IEEE 802.11, and hence high energy expenditure in idle listening, packet overhearing and collisions. Whereas this can be supported by personal devices such as mobile telephones and portable computers, as they can be recharged frequently, it is not deemed appropriate for autonomous wireless networks featuring long operation periods. Basically, DeepSleep introduces two enhancements: it grants higher channel access priority to devices with lower energy levels (this is done by reducing their contention window during backoff intervals), and it randomly defers the wakeup times of high-priority devices in order to reduce contention among them. In summary, DeepSleep improves performance (outage probability, packet loss rate and transmission delay) under self-sustained operation. Another solution is the EL-MAC (Energy Level MAC) protocol proposed in [52], which assumes that energy-harvesting devices are secondary users in a cognitive radio network. In essence, EL-MAC benefits low-energy nodes by allowing all nodes to compute an access probability and a contention window size on the basis of their residual energy. The access probability defines the probability that a node wishing to transmit decides to sense the channel; if not, channel-sensing is postponed and the node switches to sleep mode. The contention window size is the maximum number of CSMA/CA contention slots selected by the node once it has decided to sense the channel and transmit. Obviously, secondary users with lower energy levels will compute higher access probabilities and smaller contention windows. Finally, another relevant contribution in this category is the RF-MAC protocol [53], which also retains the essential concepts of CSMA/CA. RF-MAC adapts CSMA/CA to the specificities of sensor nodes that harvest radio frequency (RF) energy. The design is based on a experimental study that demonstrates how the location and number of RF transmitters, as well as the chosen frequency, impact node charging time. As in previous protocols, some parameters of the CSMA/CA mechanism are dynamically varied in order to balance energy delivery to sensor nodes with overall communication performance. Examples of these parameters are the slot time, the inter-frame spacing and the contention window size. As stated in the previous section, the protocols just described are based on heuristic approaches to the problem of optimizing network performance under self-sustained operation. In contrast, in this paper we follow an analytical approach. In the next section, we start by developing an accurate energy consumption model for the LPL mechanism implemented in TinyOS sensor nodes.