## 7 Related Work  
Despite the novelty of RPL, it has already been a subject of study in the literature [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. However, only a few research works focus on or consider RPL network convergence. This section reviews related work, highlighting the differences of such work with the contributions and findings from this paper. Authors of [12] present a simulation study of RPL based on the COOJA/ContikiRPL simulator. The main goal of this work is to investigate the impact of network parameters including number of nodes, number of DODAG roots, and packet loss on the performance of the network convergence process. The authors evaluate a range of network size values. Two different network topologies are considered: regular topologies, whereby nodes are quasi-uniformly distributed, and random topologies. A single value is tested for \(I_{min}\), which was set to 1 s. On the other hand, the redundancy constant value is not specified in the paper. Periodical transmission of DIS messages is evaluated in this work, based on a mechanism used in the COOJA/ContikiRPL [28] simulator. An initial delay is applied before the first DIS message transmission. The values used for the initial delay and for the length of the periodic intervals are 5 s and 60 s, respectively. Figure 21: _Cont._  
A survey about the most relevant RPL research efforts, along with an experimental performance evaluation of RPL, is presented in [13]. The performance evaluation of RPL provided by the authors includes network convergence time as a performance parameter, based on a single network size of 30 TelosB motes running ContikiRPL [28]. \(I_{min}\) is set to a single value, equal to 4.096 s, which is the default value used in ContikiRPL. However, authors neither indicate which is the value of the redundancy constant nor whether DIS messages are used or not. Another performance analysis of RPL that is also based on the COOJA/ContikiRPL simulator is presented in [21]. The authors evaluate control message overhead, network throughput and end-to-end packet delay in RPL for fixed values of \(I_{min}\) and \(k\) set to 4.1 s and 10, respectively. This work considers a single area size and two different numbers of nodes: 20 and 100 nodes. However, the authors do not study the network convergence time. DIS messages are used in this work, but the parameter settings and further details on DIS message scheduling are not given. A simulation-based performance evaluation of RPL for a single, medium size network is carried out by [PERSON] _et al._ in [16]. Results include that global repair (_i.e._, a mechanism that allows the root node to form a new DODAG when bad performance is detected) has a significant effect on the control message overhead. However, network convergence time is not studied in this work. \(I_{min}\) is set to a single value (equal to 1 s), but the redundancy constant value used is not indicated. DIS-based mechanisms are not used in this work. [PERSON] _et al._ investigate the efficiency of broadcast mechanisms in WSNs using RPL in [10, 17]. The authors use two mechanisms for DIO transmission: (i) the Trickle algorithm, in which \(I_{min}\) is set to a single value (equal to 2 s), and (ii) periodic DIO transmission. In both schemes the redundancy constant is set to infinity, _i.e._, the suppression mechanism is disabled. The authors evaluate the network convergence time and message overhead parameters, based on a fixed node density (50 nodes/km\({}^{2}\)), for different network sizes in [10]. Results show that convergence time grows logarithmically with the number of nodes in the network. DIS-based mechanisms are not considered in the paper. An experimental evaluation of RPL in TinyOS devices is provided in [11]. Regarding RPL parameters, a single value of \(I_{min}\) is considered (\(I_{min}\) = 128 ms), whereas the paper does not mention the redundancy constant setting.