# Trusted Energy-Aware Hierarchical Routing (TEAHR) for Wireless Sensor Networks
## 2 Related Studies
### Trust Models and Their Classification
Trust metrics are characteristics that indicate the trustworthiness of a sensor node that is resourceful. These may be the packet forwarding ratio, data trustworthiness, energy level, and cooperation degree per node, where each quality indicator is weighted with an essential factor for Trust to calculate. In the probability trust model, we also need to consider the direct and indirect Trust. The direct observations and recommendations are  
Figure 2: Trust model ([PERSON] et al., 2015). used to calculate direct and indirect Trust. Overall, Trust (T) can be a weighted sum of the direct \(T_{d}\) and indirect \(T_{i}\) as follows:  
\[T=w_{d}\times T_{d}+w_{i}\times T_{i} \tag{3}\]  
\(T_{Wd}\) is direct weight, and \(w_{i}\) is indirect weight. As in WSN, where the trusts aggregate from different sources, and finally, the trust level of the recommenders is considered in the weighted average:  
\[T_{agg}=\frac{\sum_{j=1}^{m}w_{j}\times T_{j}}{\sum_{j=1}^{m}w_{j}} \tag{4}\]  
\(T_{agg}\) is the aggregated trust value, \(T_{j}\) is the trust value from the \(j\)-th recommender, \(w_{j}\) is the weight assigned to the \(j\)-th recommender's trust value, and \(m\) is the number of recommenders. A simple approach is to model the trust score T of a node using a weighted-sum model. \[T=\sum_{i=1}^{n}w_{i}\times m_{i} \tag{5}\]  
where \(w_{i}\) is the weight of the \(i\)-th metrics and \(m_{i}\) is the value of the \(i\)-th metrics. In order to track the relevance of trust scores, tools like Trust Update mechanisms are highly required. Trust scores can adapt by making updates in their values on new interactions or behaviors and developing methods to forgive nodes as well as penalize based on the change of actions. Trust scores are used in certain network decisions, such as routing and data aggregation or node cooperation (these will be discussed later). Nodes with a high trust score should be given priority for particular jobs, whereas those that are untrusted might end up being quarantined or scrutinized further. [PERSON] et al. (2016) Trust-Oriented Routing in Mobile Ad Hoc Networks (MANET) proposed a trust-based routing framework for establishing routes with neighboring nodes, increasing AODV security levels by using historical node data to calculate the cooperation level, including both direct and indirect recommendations, and recompensing cross-recommendations. It is confirmed by a sequence of tests that such a version improved over TSAODV, called original AODV and TSR, across all scenarios in this study, but significantly when different parameters regarding the total number of nodes and distribution node velocity are changed. Research on it strengthens the weighted trust model and uses Machine Learning Algorithms (MLAs) that update weights depending on the network state, so this adaptivity improves the accuracy of trust evaluation. A crucial illustrative example was found in a series of studies by [PERSON] et al. These advances are discussed by (2017), which showed better network performance and security. Authors [PERSON] et al. Present behavior trust, data trust, and Historical Trust. The comprehensive Trust is calculated through a weighted approach, where each type of Trust contributes to the overall trustworthiness of a node. The formula for comprehensive Trust could be represented as _comprehensives_ = \(w_{1}\times T_{behavior}\)+ \(w_{2}\times T_{data}\)+ \(w_{3}\times T_{historial}\), where \(w_{1}\), \(w_{2}\), and \(w_{3}\) are the weights assigned to each trust component, respectively. [PERSON] et al. (2018) have introduced a model that evaluates both communication trust and data trust. Communication trust is derived from direct and indirect observations of a node's forwarding behavior, while data trust is computed using the median of sensor data. The direct Trust could be calculated as follows:  
\[T_{direct}=\frac{successful\ forward}{total\ forwards} \tag{6}\]  
Moreover, the Indirect Trust uses the weighted Dempster-Shaffer theory. The authors [PERSON] et al.