# Analytical Model for the Duty Cycle in Solar-Based EH-WSN for Environmental Monitoring
## 2 Related Work
This can be done over synchronous or asynchronous/hybrid solutions, though the latter have attracted most proposals. The duty cycle can be adjusted either by modifying the duty period or the sleep period (or both), under a variety of criteria that span several QoS metrics as well as energy efficiency. For instance, some protocols dynamically adjust the duty cycle based on the traffic load and/or topology information in order to achieve acceptable balances between QoS parameters (throughput, latency, reliability) and energy consumption. This is the case of BoostMAC [25], MaxMAC [26], Scheduled Channel Polling MAC (SCP-MAC) [27], Energy-Aware Adaptive LPL (EA-ALPL) [28], ASLEEP [29], Demand Wakeup MAC (DW-MAC) [30] and, more recently, DISense [31] and Cross Layer Adaptation of Check Intervals (CLAC) [32]. Some of these protocols are in fact mechanisms built on top of other known protocols. For instance, EA-ALPL is built on top of B-MAC, and CLAC is implemented on top of BoX-MAC-2 and the Collection Tree Protocol (CTP) [33]. These two protocols are, respectively,the MAC and network layer solutions adopted in TinyOS/MicaZ nodes. Other contributions proposing adaptive duty cycles are [34; 35; 36]. More information on MAC protocols for battery-powered wireless sensor networks can be found in [6; 37; 38; 39; 40; 41]. However, it is commonly accepted that these protocols are inappropriate under the energy-harvesting paradigm. As stated in the previous section, the primary objective in the design of EH-WSN is to optimize performance while preserving self-sustained operation. EH-WSN are subject to the time-varying nature of energy sources, fact that may result into periods of insufficient energy along the network lifecycle. For this reason, MAC protocols for EH-WSN try to couple traffic activity in transmission-reception pairs with peaks of energy in the participating nodes, while at the same time minimizing the impact on delay or throughput. Whereas these new requirements make MAC protocol design even more complex, the benefits in terms of longer network lifetimes or perpetual operation are invaluable. As stated in [1], synchronous MAC protocols are not deemed appropriate for EH-WSN because tight schedules are not compatible with the temporal and spatial variability of energy sources. Thus, the focus is on asynchronous protocols. The authors in [1] classify asynchronous MAC protocols for EH-WSN into three categories depending on the element that initiates the communication process: sink-initiated, receiver-initiated and sender-initiated asynchronous protocols. Next, these categories are described in more detail. In sink-initiated asynchronous MAC protocols, it is the sink that triggers the communication process by polling sensor nodes. Particularly, in [42] a probabilistic polling approach is adopted, which takes into account the unpredictability of energy sources. More specifically, the sink sets a contention probability in every polling packet to indicate the probability that any sensor node in receiving state should send its data packet. Upon receiving the polling packet, a sensor node generates an internal random number and decides to transmit the data packet if the generated number is below the contention probability; otherwise, the node remains in receiving state or switches to charging state if its residual energy falls below a predetermined value. Ideally, only one out of the set of sensor nodes in receiving state should transmit after having received the polling packet; precisely, the core algorithm executed by the sink consists of adapting the contention probability from poll to poll in order to achieve this goal. This approach is formulated in [42] for single-hop WSN; then, its multi-hop extension is proposed in [43]. In [44], an adaptive MAC protocol that maintains energy efficiency and quality of service for an IEEE 802.15.4 standard-based IoT network is proposed.