## 2 System Model
### Link Quality of Devices Estimation  
Links failure among the devices is the most common issue due to the limited battery lifetime of the devices, and it severely affects the data packet losses and network stability. In order to maintain reliable data packet delivery and network stability optimization, it is essential to rapidly and accurately detect the links' failure in the network. Therefore, the link quality of the intermediate device plays a significant role in the selection of the optimal path, which minimizes the data packet losses in the network. Consequently, this study exploits the concept of Expected Transmission Count (ETX) on the link, which is the number of transmissions and retransmissions required for the successful transmission of data packets to the destination device over the link [46]. Probe packets are sent to the link before data transmission, which does not include the data information. Therefore, the ETX value of the link is computed according to the forward delivery ratio \(p_{f}\) and reverse delivery ratio \(p_{r}\) through the probe packets, such as: \(1/(p_{f}\times p_{r})\). The link quality is estimated with ETX metric value, provides better performance in the light traffic networks. However, when the network condition is highly loaded, the ETX metric induces flooding of RREQ packets in the network for finding the optimal route. Therefore, to mitigate the flooding effect of RREQ packets in the network, this study presents the concept of High load-ETX (HETX) [47]. The HETX is the extended version of the ETX metric, which utilizes the current and previous time window rather than only the current time window (ETX). The time window employed in this study is ten times the probe packets. The window time is scaled into the discrete window time scale having equal size \([t_{i-1},t_{i}]\). The HETX value of the link is computed as below:  
\[\textit{HETX}=\frac{D_{(x,y)}}{p_{f}(t_{i})\times p_{r}(t_{i})}\frac{S_{p}}{\mu _{(x,\ y)}},t\in[t_{i},t_{i+1}] \tag{5}\]  
where \(D_{(x,y)}\) is denoted as the distance from the source to destination devices. \(S_{p}\) and \(\mu_{(x,\ y)}\) are defined as the packets size and rate of data packets transmission, respectively. All the network devices periodically broadcast probe packets for a window \(w_{i}\) at an interval of \(\tau\) seconds to evaluate the forward delivery ratio \(p_{f}(t_{i})\) and reverse delivery ratio \(p_{r}(t_{i})\). Every probe packet includes the number of probe packets and previous window information \(w_{i-1}\), which is received from the neighboring devices. Hence, the forward and reverse delivery ratios \(r(t_{i})=\text{Num}(t_{i-1},t_{i})/(w/\tau)\) are estimated with the use of the information contained in the probe packets. Here \(\text{Num}(t_{i-1},t_{i})\) refers to the number of probe packets received at the current and previous time window. The \(w/\tau\) refers to the number of probe packets sent before the data transmission. The link quality among the device is calculated with the HETX metric which reduces the flooding of RREQ packets in the network and thereby minimizes the chance of link failure and improves the overall network QoS performances.