# Reliable Fault Tolerant-Based Multipath Routing Model for Industrial Wireless Control Systems
## 3 Methodology and System Model
### Simulation Setup
The boxplot depicts the median of ANL, which has decreased from 2.8 s to 1.2 s. Similarly, the mean of ANL was reduced from 2.8 s to 1.25 s. As a result, the performance of the Kunzel protocol has been improved with the implementation of the MPR model as the ANL was reduced by 1.6 s.

Q-Learning reliable routing (QLRR) [4] creates a routing graph that is used by nodes to send data to a gateway. A weighted cost equation is used to select nodes and neighbors (graph edges) during the graph construction process. The green boxplots in Figure 6 depict the ANL of the MPR model over QLRR and the ANL of the QLRR itself. One can see in Figure 6; the MPRQLRR method results in expediting the data delivery rate by reducing the ANL. The QLRR originally has a median and mean ANL of approximately 2.5 s, which were further reduced to 1.5 s when the MPR method is applied. In this regard, it can be said that MPR has improved the network performance as the average network latency is decreased by a factor of 1 s.

In summary, the model proposed in this study has improved the network latency of all the base algorithms. Among the three protocols, the MPRKunzel outperforms the other two algorithms by having the least average network latency. On the other hand, the MPRQLRR results in an ANL median of 1.6 s, which outperforms the MPRHan, whose ANL median is 1.8 s. In other words, the MPRHan has the worst performance than others, as observed in Figure 6.

Figure 7 depicts the boxplot of the ANL when packet drops occur at different links of the MPR model. It can be observed that the proposed model is robust where the average network latency in all of the utilized algorithms was not very affected by the packet drop (PD). When the response is compared with the condition of no packet drop, the median and the mean of the data has no significant difference. Despite the small effect due to the packet drop, the ANL of the WSAN over the proposed MPR model still outperforms the original algorithm shown in Figure 6 as elaborated in Section 4.1. Figure 6: Average Network Latency (ANL) performance comparison. ### Expected Network Lifetime (ENL)

The lifetime of a wireless network is a significant factor in establishing a highly efficient network. It can be enhanced by controlling the power consumption of the nodes. In this subsection, an ENL evaluation of the proposed MPR with the associated routing algorithms is performed. The gray boxplots of Figure 8 show the expected network lifetime (ENL) of the simulation run using the WirelessHART simulator with Han [25] and MPR-based Han algorithms. The collected data are originally based on the estimated number of days, which was converted to years for simplicity. It can be observed in Figure 8 that implementing the proposed MPR model with Han and QLRR algorithms has drastically improved the network performance through increasing the expected network lifetime. As for the Han algorithm, the boxplot shows a vast increment of ENL mean, where MPRHan and Han have produced a mean of 10 years and 5.5 years, respectively. Likewise, the Kunzel [26] algorithm was further investigated with the association of MPR to evaluate the latter effect in terms of the expected network lifetime. The WirelessHART simulator was tested with the original Kunzel and the MPR-based Kunzel layouts, which in turn produced the expected network lifetime chart as depicted by the blue boxplots in Figure 8. One can see in the figure that the MPR model has enhanced the network lifetime expectation. Originally, running the WirelessHART simulator with the Kunzel algorithm led to an ENL mean of approximately 6.5 years. This number was significantly increased when MPR is used and has led to an increment of the ENL mean by 4 years. In other words, it can be observed from Figure 8 that MPR-based Kunzel and Kunzel produced ENL mean values of 10.5 years and 6.5 years, respectively. Moreover, the proposed model was further evaluated on the QLRR [4] algorithm for the expected network lifetime factor.