# Congestion Control and Traffic Differentiation for Heterogeneous 6 TiSCH Networks in IIoT
## 5 Performance Evaluations
### Single-Traffic Scenario  
First, we describe the effect of the proposed congestion control method on the network topology by sketching the DODAG created by RPL-OF0 [8] and CCTD in Figure 8a,b, respectively. Each DODAG structure in Figure 8 represents the routing topology recognized at the end of the simulations by tracking each child-parent pair in each end-to-end path through the node ID. As shown in the figure, the DODAG created by RPL-OF0 suffered from imbalanced load distribution among parent nodes. For instance, Node 21 had the burden to forward almost 43% of the total load of the network through its corresponding sub-tree, which was much less than other nodes with the same RANK, e.g., Nodes 20, \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Network size & 30 nodes \\ Propagation model & Shadowing (log-normal) \\ Standard deviation & 14 dB \\ Deployment area & 200 m \(\times\) 200 m \\ Transmission range & 30 m \\ Data rate & 250 kB/s \\ Packet length & 100 B \\ Sloframe length & 200 slots \\ Time slot duration & 10 ms \\ No. of channels & 4 \\ Output buffer size & 10 packets \\ No. of retransmissions & 3 \\ \(I_{min}\) & 3s \\ \(\Delta\) & 0.25 \\ \(\theta\) & 0.5 \\ \(\delta\) & 0.5 \\ \(m\) & 4 \\ \(\alpha_{1}\) & 1/50 s \\ \(\alpha_{2}\) & 1/20 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. 23, and 25. The situation was even worse for Node 28, which had the responsibility to forward the traffic of almost 70% of the network. This imbalanced network was mainly due to the adopted parent selection mechanism in RPL-OF0, which was unaware of the congestion situation at parent nodes, and hence imposed significant degradation in the network performance in terms of delay and packet delivery. However, the proposed CCTD distributed the traffic load fairly among intermediate nodes, as shown in Figure 8b. The CCTD approach managed to reduce the standard deviation of the number of children per node from 1.6 to 0.73. This was due to the adopted congestion-aware parent selection mechanism in CCTD where a node selected its preferred parent according to its queue occupancy, which was updated efficiently through the improved Trickle timer algorithm. Next, we evaluated the impact of the design parameters \(\lambda\) and \(\Gamma\) on the performance of the proposed CCTD. Figure 9 shows the PDR at a packet generation rate of 90 packets per minute (ppm). The PDR was calculated by dividing the number of packets successfully received at the DODAG root by the total packets generated in the network. We first observed that the PDR improved as \(\lambda\) increased due to the fact that increasing \(\lambda\) in Equation (7) made the parent switching mechanism mainly based on the queue backlog factor to avoid congestion, hence improving the PDR. However, the PDR then decreased until it stayed almost constant as larger values of \(\lambda\) may cause the node to select parents with longer paths and/or unreliable links. Furthermore, we observed that the PDR performance almost followed the same trend with varying \(\Gamma\). For large values of \(\Gamma\), the nodes had a high tendency to change their parents as soon as a congestion was detected, which constituted the trade-off between fast load balance and the thundering herd effect as mentioned in Section 3. Therefore, the values of \(\lambda\) and \(\Gamma\) could be empirically adjusted by observing network performance. Based on Figure 9, we selected \(\lambda=4\) and \(\Gamma=0.5\) for the following results as these values gave the best PDR performance. Figure 8: DODAG created by: **(a)** RPL-Objective Function (OF) 0; **(b)** Congestion Control and Traffic Differentiation (CCTD). Figure 9: PDR performance under different values of \(\lambda\) and \(\Gamma\) at a traffic load of 90 ppm/node. Hereafter, we compare the proposed work with RPL-OF0 and CoAR [30] under different performance metrics. Figure 10 shows the Queue Loss Ratio (QLR) of the three schemes for different traffic rates.