# Study of Mobility Enhancements for RPL in Convergecast Scenarios
## 4 The RSSI, Rank, and Dynamic+ (RRD+) Mechanism
### Loop Avoidance and Rank Update
Each performance metric is averaged over 10 iterations for each network size. #### 5.3.1 Packet Delivery Ratio

Figure 2 shows packet delivery ratio of different RPL variants based on different degrees of mobility. RRD+ outperforms other RPL and its enhancement protocols when the degree of mobility is above 25%. When the ratio of static nodes reaches 75%, RRD+ no longer has an advantage and is even outperformed by MR-RPL and RT-RPL in 60-node scenarios as shown in Figure 2d. This is mainly due to the fact that MR-RPL and RT-RPL have a mechanism to broadcast mobile nodes to other nodes in order to avoid being selected as next-hop nodes. Compared with mobile nodes, static nodes can offer more stable transmission paths. Therefore, MR-RPL and RT-RPL perform better when there are enough static nodes in the network to offer routes for the sink. On the other hand, MR-RPL and RT-RPL perform worse when there are not enough static nodes to chose from. Results also show that CO-RPL has limited contribution in mobility. This is mainly due to the fact that CO-RPL does not offer a method to update the C_ID value, which we already discussed in Section 3. \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Parameters** \\ \hline Mobility model & Random waypoint model \\ Minimum speed & 1 m/s \\ Maximum speed & 3 m/s \\ Speed changing interval & 5 s \\ New location rest time & 5 s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mobility model parameters. Figure 2: _Cont_. #### 5.3.2 Number of Dropped Packets

According to the IEEE 802.15.4 MAC (Medium Access Control) layer, nodes keep retransmitting frames until the number of retransmission attempts reaches a fixed maximum value after which the frame is dropped. The number of maximum retransmissions is three according to the standard. The number of dropped packets is the number of packets that are dropped after exceeding the maximum number of retransmission attempts. This evaluation metric shows how efficient the routing protocol is in finding a new parent when the link with the current parent is lost. Figure 3 shows the number of dropped packets of different RPL variants based on different degrees of mobility. Results show that RRD+ outperforms all other RPL variants in all scenarios. This is mainly due to the fact that RRD+ helps RPL to adapt quickly to mobility and efficient rank updating can pro-actively help nodes avoiding selecting a next-hop with a bad link quality. Therefore, RRD+ reduces retransmission attempts and the number of dropped packets is reduced as well. CO-RPL does not have proactive features, thus it suffers from a high number of dropped packets. With the increasing of the number of static nodes, ME-RPL and RT-RPL begin to show their performance for the reason discussed previously in packet delivery ratio results. Figure 3: _Cont._

Figure 2: Packet delivery ratio. (**a**) Packet delivery ratio (all nodes are mobile); (**b**) Packet delivery ratio (75% of nodes are mobile); (**c**) Packet delivery ratio (50% of nodes are mobile); (**d**) Packet delivery ratio (25% of nodes are mobile). OR-RPL: ORiginal RPL; CO-RPL: COrona RPL; ME-RPL: Mobility-Enhanced RPL; RT-RPL: Reverse Trickle timer algorithm. #### 5.3.3 Average End-To-End Delay

Figure 4 shows the average end-to-end delay of different RPL variants based on different degrees of mobility. The delay is computed on the delivered packets, lost packets do not appear in these results. The average end-to-end delay is computed according to the following equations. \[Total\ Delay=\sum_{i=1}^{n}\left(RecvTime(i)-SentTime(i)\right) \tag{5}\]

\[Average\ end\ to\ end\ Delay=Total\ Delay/n \tag{6}\]

where \(n\) refers to the number of successfully received packets. Results show that RRD+ suffers from high average end-to-end delay compared to OR-RPL, ME-RPL, and RT-RPL. The reason is that RRD+ does not have the mechanism to distinguish static nodes and mobile nodes. Therefore, compared with ME-RPL and RT-RP, RRD+ will select more mobile nodes as next-hops. Mobile nodes will indeed increase the delivery delay.