# Multihop Latency Model for Industrial Wireless Sensor Networks Based on Interfering Nodes
## 1 Introduction and Related Work  
We are currently in a transition stage, in which the digitization of production processes is becoming more widespread, with large areas of new technologies such as Big Data, Machine Learning or Artificial Intelligence depending on it. These new technologies will improve and optimize the configuration and maintenance of industrial processes, even leading to the proposal of a Digital Twin of an industrial scenario, with the ability to test new configurations in controlled virtual environments or to predict the behaviour of systems in order to anticipate unexpected behaviours such as the deterioration of a tool. Personal area Wireless Sensor Networks (WSNs) allow for an increase in this level of digitization, enriching the systems already deployed in the plant with greater flexibility, which allows deployment of a large number of sensors, without strict limitations in range, location or power consumption. The Time-Slotted Channel Hopping (TSCH) mechanism proposed in the IEEE 802.15.4e standard [1] has positioned itself as one of the benchmarks for WSN deployment in industry, since its deterministic behaviour and the use of frequencyhopping techniques are designed to work in the type of scenario where there is a high probability of interference. The combination of the IEEE 802.15.4e standard with the IPv6 Routing Protocol for Low-Power and Lossy Networks (RPL) protocol [2] allows the construction of meshed networks whose routes are dynamically updated autonomously, which facilitates the unattended use of this type of network. One of the weaknesses of these systems based on TSCH and RPL is the network formation process, which can be extensive in terms of time without a correct configuration of the parameters involved in the process. For applications such as home automation or smart cities, the network formation times may not be as relevant. However, in industrial applications, the network commissioning time and the energy efficiency associated to this process are key performance factors to consider when deploying this kind of WSNs. On the TSCH side, this is due to the fact that the nodes do not know in advance at what instant of time or on what frequency the necessary messages will be transmitted in order to synchronize. This process is not detailed in the standard, so different alternatives have been proposed to speed up this stage of the formation of a WSN. Some authors, such as [3; 4; 5], propose different alternatives and schemes to improve synchronization processes, such as TSCH schedules dedicated to beacon transmission or modifications of the beacon transmission period to use optimal traffic to speed synchronization. However, all these approaches do not cover the entire network formation process, since they do not consider the creation of the RPL routing tables. On the RPL side, the formation of both upstream and downstream routes is carried out once TSCH synchronization has been obtained, exchanging control messages with the rest of the neighbouring nodes to establish the optimal route to the root node. The formation of these routes can be compromised without proper use of radio resources, as interference can cause these control messages to collide, delaying the network formation process. Other works have addressed the problem of the whole WSN formation process. The authors of [6] propose a dynamic algorithm to manage the resources in IPv6 over the TSCH mode of IEEE 802.15.4e (6 TiSCH) [7] and RPL networks, improving the behaviour of previous state-of-the-art solutions. A network based on TSCH and RPL is also used in [8], reducing the network formation time by reducing the slot frame size during the network deployment phase. The authors of [9; 10] conducted a study in which they observed how the synchronization and network formation time are affected by different configuration parameters, highlighting the beacon transmission period.