## 1 Introduction  
Wireless Sensor Networks (WSNs) are experiencing significant momentum in academic, industrial and standardization circles. WSNs comprise sensor and actuator nodes that enable intelligent monitoring and control applications in a wide spectrum of environments including smart cities, home automation, remote health and precision agriculture, to mention but a few [1]. A plethora of communication protocols for WSNs have emerged [2]. Among these, the contribution of the IETF is of outstanding importance, since this organization is producing IP-based protocol specifications that allow the connection of WSNs to the Internet, and thus enable the Internet of Things (IoT) [3]. Because many WSNs are multihop, and thus require a routing protocol, the IETF Routing over Low-Power and Lossy Networks (ROLL) working group [4] recently developed the IPv6 Routing Protocol for Low-power and Lossy Networks (RPL) [5]. RPL was specifically designed to meet the requirements of WSNs [6, 7, 8, 9] and is a central component of the IETF protocol suite for the IoT. Therefore, since RPL is expected to be widely deployed, it is fundamental to characterize its properties, and evaluate the influence of its main parameters and options on network performance. Despite its novelty, RPL has already been a subject of study [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. Most of the literature focuses mainly on evaluating RPL behavior in steady state [16, 17, 18, 19, 20, 21]. However, performance of RPL during network convergence may be critical, since it may significantly affect user experience (e.g., when a user expects fast network creation to fulfill a certain action) and it is fundamental to global network recovery due to topology changes. Nevertheless, RPL network convergence has received limited attention. The studies that consider RPL performance in transient state do not provide a deep analysis, since they do not focus on the joint influence of RPL parameters and mechanisms, and network characteristics (such as network size and density), on network convergence performance [10, 11, 12, 13, 14, 15, 16, 17, 21]. In this paper we investigate by simulation the influence of the main RPL parameters on the network convergence process, and we also propose and evaluate a mechanism that leverages an option available in RPL for spurring the network convergence process. The performance parameters we consider are network convergence time, network join time and message overhead. In order to assist the derivation of conclusions, we also evaluate the number of collisions during network convergence. With the aim of obtaining comprehensive results, we carry out extensive simulations for a wide range of conditions in terms of network size and density. We consider multihop networks whereby the nodes use IEEE 802.15.4, _i.e._, the most prevalent radio interface for WSNs. In order to achieve realistic results, we have tuned the simulation environment in order to accurately model the link behavior observed in real experiments. However, the results presented should be confirmed on a real testbed in a future work. Results show that RPL network convergence performance depends dramatically on the use and adequate configuration of key parameters and mechanisms. The findings and contributions of this work provide a guideline for configuring and selecting adequately crucial RPL parameters and mechanisms for achieving high network convergence performance, on the basis of network characteristics such as size and density, as well as a characterization of the related performance trade-offs. The remainder of this paper is organized as follows: Section 2 reviews the main characteristics of IEEE 802.15.4. Section 3 gives an overview of RPL, with special focus on the procedures for network creation. Section 4 describes the simulation environment and methodology used in the paper. Section 5 studies the impact of the main RPL parameters on performance of the network convergence process.