## 5 Related Work  
Related works have been organized according to three different evaluation techniques: measurement, simulation and analytical modeling. The measurement method analyzes the reliability directly using an actual sensor node (mote). Researches on measurement usually determine the reliability of a WSN based on the rate of number of sent messages and number of received messages in sink node. For example, [PERSON] and [PERSON] [4] evaluated the impact of the physical and MAC layers on the reliability of a WSN. Additionally, they evaluated the WSN reliability in different conditions (e.g., indoor and outdoor). In another example, [PERSON] and [PERSON] [32] used measurement to discover the link reliability. Next, they apply these results to evaluate the reliability of a WSN with re-transmissions and multipath routing. Existing works on assessing the WSN reliability through simulation use models for simulating propagation and interferences in the signal. There are propagation models that do not consider packet lost caused by the environment [33] and specific models for WSNs that consider irregular propagation and interference by other elements (e.g., Radio Irregularity Model [5]). These models are added to the simulators to allow to better evaluate situations of packet lost, collision or errors in the WSN. For instance, [PERSON] _et al._[6] proposed a WSN congestion control protocol called Priority-based Congestion Control Protocol (PCCP). Through simulation, it was possible to evaluate the benefits of avoiding and decreasing the packet lost in the WSNs, increasing the reliability of the sensor nodes. Figure 21: Reliability of the region in three different positions. The last technique (analytical modeling) assesses the reliability or availability of WSNs when we know the fault rate and the probabilities of their occurring. We can use three different ways to evaluate the reliability using analytical modeling: Fault Tree, Markov Chain and RBD. Fault Tree is a graphical model (using logic gates) that represents events (with conditions to happen) and their consequences, which lead to the system failure [9]. Markov Chain considers that the system has states (e.g., working state and failure state) and its state varies with the time. It can be represented by a directed graph, where the vertices are states and the edges show the possibilities of change between states. Additionally, the edges have a probability (assigned on the label) of transition from one state to another. [PERSON] _et al._[9] proposed a methodology for evaluating the reliability and availability of WSNs using Fault Tree. The proposed methodology evaluates different kinds of networks (e.g., single hop or multiple hop). However, this approach does not consider the routing protocols. Instead of this, the network is converted into a graph and the depth-first search is used to find a path between the sensor nodes. The model proposed in this paper is close to one introduced by [PERSON] [9]. However, this proposal considers that the routing protocol is essential to create the paths between the sensor nodes and sink node instead of using depth-first search. Besides that, our proposal also introduces the notion of region, which can be evaluated individually. Finally, the battery level is considered the main reason to sensor node faults and its value is obtained by evaluating the power consumption. [PERSON] _et al._[7] evaluated the WSN reliability using Markov Chain and RBD and show how to increase the network reliability by replacing the faulty sensor nodes. However, WSNs usually do not allow to repair or replace the sensor nodes due to the environment hostility (e.g., close to volcanoes) or difficulty to their access (e.g., dense forests). [PERSON] _et al._[8] used RBD for evaluating the reliability of two transport protocols, namely Event-to-sink Reliable Transport (ESRT) [34] and Reliable Multi-Segment Transport (RMST) [35], where the packets are sent in broadcast and paths have the same reliability level.