# TSCH and RPL Joining Time Model for Industrial Wireless Sensor Networks
## 2 TSCH and RPL Network Deployment
### RPL Tree Network Topology Construction  
Once the nodes have managed to synchronize with the TSCH network, they have the necessary information to be able to establish communication with the rest of the nodes in the network. However, they do not know which nodes already belong to the network, nor how to reach those nodes that are not within their coverage area. For this reason, it is necessary to build a network topology in order to be able to establish communication in the multi-hop network. Wireless sensor networks are made up of devices with reduced computing capabilities and low power consumption. The RPL protocol calls these types of networks low-power lossy networks. This protocol is designed to be a lightweight routing protocol with low computing requirements, making it ideal for deployment in WSNs. For this reason, the RPL protocol is widely used in network deployments based on the IEEE 802.15.4 standard, including those using TSCH, thus allowing routes to be established between devices and maintaining a meshed network topology. To maintain the network topology in situations where wireless links can vary continuously, the RPL protocol uses a series of objective functions, which allow the nodes to update their routes dynamically and autonomously. These objective functions are based on monitoring the connection quality through different metrics, allowing the nodes to change  
Figure 1: Example of beacon advertising process using four channels. their routes if the current connection quality is degraded [10]. For the formation of the RPL tree, known as DODAG (Destination Oriented Directed Acyclic Graph), different control messages of the type ICMPv6 are used. The DODAG Information Object (DIO) messages are sent by the nodes that are already part of the network, in order to keep the routes updated and allow new nodes to obtain the RPL topology information. DIO messages can be sent either by multi-cast, triggered by the Trickle Timer, or unicast methods in response to an explicit request. DODAG Information Solicitation (DIS) messages are sent to request nodes that already belong to the network to send a DIO message with the RPL tree information. Finally, DAO (Destination Advertisement Object) messages allow paths to the RPL root node to be created. This DAO message is sent through all nodes in the path between the node that originates the DAO message and the root. The RPL protocol uses a timer to mark the sending of signaling traffic. This is a timer that increases its period over time, and its operation is based on a Trickle Timer, whose operation is described in RFC6206 [11]. The use of this type of timer to send DIO messages allows this traffic to be reduced once the network is deployed and stable, reducing the congestion that signaling traffic can produce. The algorithm allows the value of the DIO Trickle Timer to be increased as long as the information exchanged by the different nodes in the topology does not indicate that any change has occurred that requires an update. This timer will restart whenever any inconsistency is detected in the RPL topology, such as in the case of a parent change, the loss of a network node or also due to the reception of a DIS message. Figure 2 shows the evolution of the RPL Trickle Timer. Every time the configured timer expires (starting with an initial value of \(I_{min}=4\) s), the algorithm doubles its value and plans a new transmission of a DIO message, repeating this process until the timer reaches the maximum configured value. In the specific case shown in the graph, the Trickle Timer reaches its maximum value in a few minutes, causing a DIO message to be sent once every few minutes thereafter. The authors of [12] carry out a detailed analysis showing the evolution of the RPL Trickle Timer.