# TSCH and RPL Joining Time Model for Industrial Wireless Sensor Networks
## 2 TSCH and RPL Network Deployment
### TSCH Beacon Advertising  
In the first revisions of the standard, different access mechanisms were proposed to improve the performance of networks based on IEEE 802.15.4, such as DSME (Deterministic and Synchronous Multi-channel Extension), LLDN (Low Latency Deterministic Network) and TSCH (Time Slotted Channel Hopping). Among these mechanisms, TSCH stands out, as it focuses on the deployment of networks in industrial scenarios, allowing a high degree of reliability and robustness to be achieved thanks to its time synchronization and techniques to mitigate interference and fading. The access mechanism to the TSCH medium allows the temporal plane to be structured in such a way that a certain number of slots are repeated periodically over time. This subset of slots is called a slotframe, and its length determines how often the same slot is repeated. In addition to time synchronization, the TSCH mechanism uses a frequency hopping technique to mitigate interference, which allows the use of a different transmission channel for each time slot in which communication is established between two nodes. The use of a different channel to send the information between two nodes allows us to compensate for any interference or fading that may be occurring in a certain channel, which improves the robustness and reliability of communications. The following equation is used to calculate the channel used in each timeslot:  
\[f=F\{(ASN+ch_{offset})\cdot mod(C)\} \tag{1}\]  
where \(f\) is the physical transmission channel; \(ASN\) is the absolute slot number, which corresponds to the number of slots that have passed since the network was deployed; the \(ch_{offset}\) parameter allows for different channels to be used in the same time slot; and, \(C\) corresponds to the total number of channels that are used. Therefore, the function \(F\{-\}\) consists of selecting a channel of a predefined sequence according to the index that is obtained after calculating the module. The scheduling of these radio resources (timeslot and frequency channels) allows the exchange of information between the network nodes to be optimized. This is because it is possible to configure a contention free scheduling, with high immunity to interferences, thanks to frequency hopping, and with high energy savings due to the fact that slots that are not used are totally disabled. The method to define this scheduling is not described by the standard, but some recommendations have been proposed to allocate minimum resources to carry out this exchange of messages between nodes, known as minimal 6 TiSCH configuration [7; 8]. Different scheduling mechanisms focused on TSCH have also been previously proposed, such as the autonomous planning mechanism Orchestra [9]. This mechanism allows the nodes to build the TSCH schedule autonomously, without the need for additional signaling traffic, and allows the schedule to be separated into different traffic planes. Since the time plane is structured in timeslots, it is necessary that the nodes belonging to the same TSCH network are synchronized so that the exchange of messages occurs simultaneously between two nodes. To achieve this, it is necessary to perform a previous phase of synchronization, in which the new nodes that join the network must obtain the information on the scheduling used, as well as adjust the time base to a reference of the nodes that already belong to the network. The nodes that already belong to the network and are correctly synchronized send periodic signaling messages with information about the schedule used and the current value of the ASN parameter. This is necessary to carry out the synchronization process. These signaling messages are known as Enhanced Beacons, an improved version of the traditional beacons proposed by the IEEE 802.15.4 standard, which allow additional information to be added in the fields known as Information Elements. On the other hand, the nodes that want to join the network start a scanning process.