# Reliable Fault Tolerant-Based Multipath Routing Model for Industrial Wireless Control Systems
## 3 Methodology and System Model
### Simulation Setup
In the first step, set Edge1= \((R1,R2)\), Edge2= \((\emptyset,\emptyset)\), and subset of planned routers \(\mathbb{N}_{R}^{(i)}=\emptyset\) for \(i\)th field device. 8:while\(\text{\emph{Edge1}}\ \
eq\ AP\), \(\text{\emph{Edge2}}\ \
eq\ AP\)do
9: Let P1=P2=\(\infty\)
10:for Non-free Edge k, \(k\in 1,2\)do
11: Use the set of vertices \(\mathbb{N}_{V}\) to figure out different vertex of \(R_{3,k}\) which satisfying the terms and conditions:
12: TC1: H (\(R_{3,k}\), Edge(1)) = 1;
13: TC2: H (\(R_{3,k}\), Edge(2)) = 1;
14: TC3: \(R_{3,k}\)= argmin \(H(j,A1)+H(j,A2)\). \(j\in\mathbb{N}_{R}\) and \(j\in\mathbb{N}_{R}^{(i)}\)
15: Then, count routing hops number from \(R_{3,k}\) to access points A1 and A2, i.e., Pk=H(\(R_{3,k}\), A1) + H(\(R_{3,k}\), A2). 16:endfor
17:if\(P1\leq P2\)then
18:\(R_{3}\)=\(R_{3,1}\), R1= Edge (1), and R2= Edge (2);
19:else
20:\(R_{3}\)=\(R_{3,2}\), R1= Edge (1), and R2= Edge (2);
21:endif
22:\(\



### Fault Model

The evaluation of MPR fault tolerance characteristics is done by simulating fault model in the wireless network. The fault model is mainly based on link failures, which lead to packet loss in the failing link. The data packet drops are simulated by introducing random link failures on different links in the MPR model for random periods of time. The link failure is introduced to the network in the primary and alternative pathways. This is performed in two ways. First, by referring to Figure 5 the links joining nodes 8 to 1 on the primary path and 3 to 1 on the first alternative path are down at random times for random duration. Second, the link joining nodes 2 to 1 on the second alternative path is down for intermittent periods of time after the links in the primary path and the first alternative path are fault free. It is worth noting that any routing path is only usable if it is free of link failures. The evaluation parameters such as ANL, ENL, and PDR in the presence and absence of packet drops due to link faults are thoroughly discussed in Section 4. ## 4 Results and Discussion

In this section, the evaluation of the proposed modifications for the Kunzel [26], Han [25], and QLRR [4] protocols are presented. The proposed multipath routing (MPR) model shown in Section 3.3 was applied to Kunzel, Han, and QLRR algorithms to produce MPRKunzel, MPRHan, and MPRQLRR, respectively. The performance of the proposed model was compared with the original algorithm by evaluating average network latency (ANL), expected network lifetime (ENL), and packet delivery rate (PER). These three factors play essential roles in determining the reliability of IWSNs. ### Average Network Latency (ANL)

The evaluation of the proposed model was performed by comparing its performance with the three algorithms mentioned above. The gray boxplots in Figure 6 depict the average network latency of the WirelessHART network simulated with the [PERSON] [25] algorithm. The simulation was performed with the original Han network layout and the MPR proposed network topology, a fault tolerance-based model. It can be observed that implementing the MPR model with [PERSON]'s algorithm has significantly improved the network performance by reducing the average network latency. The boxplots show approximate reductions of 1.25 s and 1 s in the median and mean ANL, respectively. On the other hand, [PERSON]'s [26] approach was developed using Q-Learning to build graph routes for WSANs which utilizes a centralized management scheme. They adapted a Q-learning algorithm that uses and adjusts agents' weights to reliably build graphs. In this work, the proposed MPR model was implemented on the original [PERSON] algorithm. Thereafter, the performance was evaluated in terms of average network latency, as indicated in the blue boxplots in Figure 6. The proposed MPR model has led to a significant reduction in the average network latency.