# Study of Mobility Enhancements for RPL in Convergecast Scenarios
## 4 The RSSI, Rank, and Dynamic+ (RRD+) Mechanism
### Loop Avoidance and Rank Update
In order to make it more suitable for urban and unstable environments, we included a random behaviour to its path loss calculation. Indeed, we added a Gaussian random variable in the path loss formula of MRM in order to simulate instability of the radio links. We calibrated the randomness in order to make transmission range randomly fluctuate between 30 m and 50 m independently for each transmission. The path loss formula in decibels is shown in (4). \[Path\_loss(dB)=min\big{(}-20,-30\log_{10}d-30\log_{10}f-32.45+Shadow\big{)} \tag{4}\]

where \(d\) is the distance in kilometres between the antennas, and \(f\) is the frequency in megahertz. Shadow stands for the Gaussian random variable in the interval \([-2,2]\) with mean value of 0 and a standard deviation of 1. With this random behaviour, we fixed the hysteresis value to \(-1\). This means that if the difference between the old RSSI and the new RSSI is \(1 dB\), we consider that it is most probably the effect of the randomness of the propagation model and not the effect of mobility (Note that the randomness of the propagation model is related to the nature of the environment and that the value of hysteresis is closely related to the randomness of the propagation model). Table 1 summarizes the rest of the simulation parameters we used. ### Mobility Model

We used a random waypoint model as a mobility model. At the beginning, all nodes are randomly deployed in a 200 m \(\times\) 200 m area. We make sure that at the start of the simulation there are no isolated nodes. The sink is always located at the centre of the area for the duration of the simulation. When the simulation starts, each node makes a random choice to select a location within the area as a destination. Then, it moves towards this destination. The velocity is randomly chosen from 1 to 3 m/s every 5 s. We introduce rest time for each node. Whenever a node reaches its destination position, it will rest in new location for 5 s and then select a new destination for the next movement. All nodes, except the sink, repeat these steps until the simulation stops. Table 2 summarizes mobility model \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Parameters** \\ \hline Network simulator & Cooja under contiki OS (3.0) \\ Radio propagation model & MRM with random behaviour \\ Medium access control & CSMA/CA (Carrier-Sense Multiple Access with Collision Avoidance) \\ Simulation time & 5 min \\ Emulated platform & Z1 starter platform \\ Sensor node deployment & Random deployment \\ Data size & 30 Bytes \\ Transmission rate & 1 pkt/s \\ Transmission power & \(-20\) dBm \\ Transmission range & [30 m, 50 m] \\ Number of nodes & 20, 40, 60 \\ Area of deployment & 200 m \(\times\) 200 m \\ Frequency range & 2.4 GHz \\ Reception threshold & \(-95\) dBm \\ RRD+ RSSI \(THRESHOLD\_2\) & \(-92\) dBm \\ RRD+ RSSI \(THRESHOLD\_1\) & \(-89\) dBm \\ RRD+ RSSI \(HYSTERESIS\) & \(-1\) dB \\ Long lifetime timer & 30 s \\ Short lifetime timer & 15 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation setup. parameters. In addition, we considered different mobility scenarios where the ratio of mobile nodes to fixed nodes in the network varies from 100 to 25%; we call this degree of mobility. The rationale behind using random mobility scenarios is to put protocols under pessimistic mobility scenarios where the trajectory of nodes cannot be predicted. Thus, performance evaluation would show worst case scenario results. ### Simulation Results

In order to assess the efficiency of RRD+ in dealing with mobility we compared it to other existing methods studied in the related work section. These protocols are the original RPL (OR-RPL), Co-RPL [10], ME-RPL [12], and the reverse trickle timer algorithm (RT-RPL) [11]. We used four performance metrics to evaluate the efficiency of these protocols: (1) packet delivery ratio; (2) number of dropped packets; (3) average end-to-end delay; and (4) number of control packets. For each network size, we generated 10 different random mobility scenarios.