# TSCH and RPL Joining Time Model for Industrial Wireless Sensor Networks
## 1 Introduction  
The concept of Industry 4.0 has revolutionized industry as we know it today, adding new degrees of digitalization to plant processes and providing greater knowledge of the different phases of the value chain. The new information obtained through digitalization, together with different technologies such as artificial intelligence, machine learning or analytical techniques based on big data, allow more precise optimization of the different processes involved in the value chain. It also allows the operator to perform low-level monitoring and even to carry out estimates, which allow predictive maintenance techniques to be carried out, to detect possible errors before they even occur [1]. However, this Industry 4.0 infrastructure requires a massive digitalization upgrade process from the current industry, so that the digitalization of new variables provides information that until now went unnoticed. Among all the technologies capable of carrying out this process, wireless sensor networks (WSNs) are positioned as one of the most relevant, thanks to their low consumption characteristics and their easy scalability when providing communication to a large number of sensors. This allows the deployment of large networks at a low cost. There are many technologies through which to carry out the deployment of a WSN, for example, Bluetooth and IEEE 802.15.4 for the personal area networks or LoRaWAN and SigFox for wide area networks, among others. However, industrial scenarios are characterized by a more aggressive means of communication in terms of multi-path fading, which means that not all technologies are capable of meeting the minimum operating requirements. The IEEE 802.15.4 [2] standard, together with the Time Slotted Channel Hopping (TSCH) mechanism, is specifically designed to work in industrial scenarios [3], whose requirements are characterized by high reliability, low latency and a maximum number of devices between 10 and 30 nodes, depending on the field of application. For these reasons, the TSCH mechanism is one of the most widely used solutions as a medium access control (MAC) mechanism in industrial environments. The main characteristics by which TSCH stands out against other access mechanisms defined in the IEEE 802.15.4 standard are the deterministic behavior of its scheduling in time slots and the technique of frequency hopping, which allows it to mitigate the possible interference or fading that occurr in a radio channel. Regarding the formation of ad hoc mesh networks and the creation of routes between the different nodes that form the network, the IPv6 Routing Protocol for Low-Power and Lossy Networks (RPL) [4] has become one of the most common solution [5], Ref. [6] for the creation of dynamic routes in WSN networks with few resources. Together with the IEEE 802.15.4e standard, they allow the deployment of robust WSNs, creating multi-hop mesh networks with support for IPv6-based networks. Although the use of both protocols together allows deployment of robust networks with a deterministic behavior during the stationary state, the deployment and synchronization phase may present some difficulties. This is mainly due to the operation of the TSCH mechanism. The nodes already synchronized will be sending the necessary messages to establish synchronization with the new nodes using different frequency channels depending on the instant in which the message is being sent. This behavior makes it more complex for the new nodes to receive the information needed to synchronize with the TSCH network, and later join the RPL network, since they do not know the instant of time or on which channel the synchronization message will be transmitted. This particular drawback of TSCH-based networks has been researched over the past few years, and different approaches have been proposed to reduce synchronization and connection times, since the standard does not propose any optimized configuration for certain application domains.