## 4 Partition Aware-RPL Protocol Overview
### Parent Selection Algorithm
To evaluate the performance of PA-RPL in comparison with RPL, we use simulation. For that, we use the simulation parameters of Section 4.3. Moreover, we assume that the nodes transmit their sensed data periodically every 30 s. The evaluation of the PA-RPL consists of exploring the evolution of some metrics as a function of time. In the simulation, these metrics are evaluated for a variable number of parcels in the farmland. Four key performance metrics are considered in this evaluation:

* Convergence time: This is the time required for the algorithm to build the DODAG and reach a stable state, i.e., after that time, the DODAG remains almost unchangeable. This convergence time can be measured by monitoring the number of preferred parents switching along then simulation. When the permanent regime is reached, this number becomes almost constant. * Communication overhead: this parameter represents the communication load used for the DODAG maintenance messages (i.e., control packets used to establish and maintain the DODAG). In LLN, a good performance routing algorithm must generate the lowest number of maintenance messages in order to leave most of the communication bandwidth for the data packets. * Packet delivery ratio (PDR): this parameter helps to evaluate the reliability of the LLN. In fact, the PDR represents the percentage of the received messages out of the transmitted messages. This parameter reflects the reliability of the protocol and determines the usefulness of any network. * Global energy consumption: through this parameter we study the evolution of the energy consumption of the network as a function of time, and the relation between this energy and the number of parcels. In the LLN, it is well known that most of the energy consumption is related to communication. Hence, instead of energy, it is commonly accepted to exploit the percentage of time, in which communication transceiver is active. The simulation results in terms of the four defined metrics are presented in Figure 5:1 The Figure 13a shows that the number of best parent switching starts very high in the first simulation minutes, then rapidly decreases to finally reach a negligible value after 1500 s to be considered as the convergence time. Practically, after that point of time the DODAG becomes almost stable and conserves essentially the same shape. From the figure, it is clear that the convergence time does not depend on the number of considered parcels. In addition, we can see that both protocols have similar permanent regime. However, and even if both transient regimes last for the same duration, we can see that PA-RPL induces more parent switching before converging in comparison with the RPL. This can be explained by the additional constraint in our best parent selection process, in order to have one bridge from every parcel. In a smart farm, where an LLN is used to operate for months and years, the convergence duration of 1500 s is a very acceptable value for both protocols, as once permanent regime is reached, almost all the available bandwidth (and energy) will be used to transfer data. In fact, Figure 12(b), confirms that most of the exchanged DIO messages (i.e., the overhead) are generated before the network convergence (during the transient time) then they become negligible. In addition, we can see that during the transient time, the number of DIO messages generated by the PA-RPL is higher than the one generated by RPL, before both overheads decay towards zero in the permanent regime. Another important remark is that the number of DIO messages is not directly related to the number of parcels. As expected, the energy curves, depicted in Figure 12(d), present similar shapes as those of parent switches and sent DIOs. We can easily identify the transient and permanent regimes.