# TSCH and RPL Joining Time Model for Industrial Wireless Sensor Networks
## 3 Related Work  
Over the past few years, since the TSCH media access mechanism was introduced in the 2012 IEEE 802.15.4 standard, research papers have been submitted, researching different ways to improve the synchronization processes for TSCH. The authors of [13; 14; 15; 16] propose different frameworks and configurations for scheduling in TSCH in order to mitigate the synchronization problem, so as to improve connection times based on enabling more radio resources for sending signaling messages. [PERSON] et al. [13] propose two different frameworks for TSCH scheduling, improving the network connection processes through the use of random slots for sending periodic EBs. [PERSON] et al. [14] propose a new framework by which to determine the optimal number of EBs needed to establish synchronization quickly. [PERSON] et al. [15] make a comparison with the state of the art of a new framework that allows the TSCH beacons to be sent through all channels of the network, ensuring that no collisions will occur, and thus improving on the results obtained in [13]. The authors of [16] define a different framework that allows the nodes to estimate the best channel through which to transmit the signaling messages, so their solution is focused on particularly noisy scenarios. [PERSON] et al. [17; 18] carried out two studies that led to an improvement in the synchronization times in TSCH networks, firstly, by proposing a schedule for the nodes to send beacons in slots that are free of collisions, also considering that these nodes can be mobile nodes, and secondly, increasing the traffic of EB messages without adding new slots, sending several EB messages in different channels using a single timeslot. [PERSON] et al. [19] conducted a study on how to improve the synchronization process in situations where a beacon sending mechanism with a random period is used, showing how synchronization times improve with the influence of other parameters such as the number of channels used by the WSN network. [PERSON] et al. [20] conducted a study similar to those previously mentioned, in which they performed different simulations modifying the density of nodes in the network and the period of transmission of EB messages, showing that, as in the article [19], a random transmission period improves the synchronization process in TSCH. In [21], the authors propose a mechanism that allows modification of the beacon transmission period according to the number of nodes in the network, thus reducing congestion in networks with higher node density. The above studies focus on analyzing only the TSCH synchronization process. However, in [22] the authors consider the complete communications stack, and compare its dynamic resource management algorithm for 6 TiSCH networks with the state of the art, demonstrating that it improves the synchronization processes in TSCH networks. In [23] a complete protocol stack is proposed, using both TSCH and RPL in order to achieve high reliability and robustness for industrial scenarios. To reduce the network formation times, the authors propose a simple mechanism that reduces the slotframe size during the network formation period. However, no information is given on how long the network formation takes or the energy impact cased by the increase in EB messages. The authors of [24; 25] carried out a study in which they validate how the synchronization time improves in TSCH-RPL networks by using a dynamic EB transmission period, proposing a cyclic algorithm that they call Bell-X, with windows of opportunity in which the probability of a node connecting rapidly increases. However, although these studies propose mechanisms that improve the synchronization processes, they are rarely supported by an analytical model that allows characterization of the synchronization and RPL joining processes, which can help to determine the most optimal configuration for a parameterizable algorithm. [PERSON] et al.