# Advancing Digital Twin-Based Collision Avoidance:
## 4 Functional Safety for Wireless Systems
### Background
#### 4.1.2 Reliability of Wireless Networks  
For communication networks, loss of packages or messages is the main reason for failure. Therefore, it plays a critical role for the calculation of the performance level of a chain of tools which contain signal transmissions. The Simple Gilbert Model (SGM) [20] is the first important model to describe the burstiness of packet loss and models it as a Markov chain with two states: the GOOD state never produces packet loss; the BAD state always produces packet loss. The transition diagram for the SGM is depicted in Figure 8a. An extension to the SGM as a two-state hidden Markov model (2 HMM) is proposed in [21], which is why the SGM and the 2 HMM are often referred to as the Gilbert-Elliot model. In this extension, GOOD and BAD have a low/high probability to produce packet loss instead of 0 and 1. However, deriving the hidden state probabilities from measurements is not easy. Furthermore, it performs much worse than the SGM at estimating the max loss burst length and the mean loss burst length [22], which are critical for safety functions. This is why we focus on the SGM in this paper instead. The Extended Gilbert Model (EGM) [23] extends it to \(n+1\) states, where \(n\) is the number of remembered loss eventsto describe loss more accurately. In [22], the authors discuss these models for packet loss and argue that they do model packet loss in terms of some metrics for nonbursty traces, but they fail to model packet loss patterns for bursty traces accurately, including SGM and EGM. They propose a complex model that introduces an outer layer to the SGM that consists of three states and that describes the location in the network where the loss event was caused: ACCESS LINK, EDGE, and CORE. The transition probabilities are dependent on the current outer layer state. Furthermore, an SGM may be replaced by above 2 HMM in EDGE and CORE for increased accuracy. The transition diagram of the SGM/SGM/SGM variant of their model is depicted in Figure 8b. For the application of safety systems, we would therefore consider using the SGM model for traffic that is only transmitted over the link level and the SGM/SGM/SGM to model packet loss in systems that transmit traffic over the internet. The study conducted by the authors in [24] investigates the distribution of burst errors and latency in LTE and Wi-Fi. Employing the SGM, they compare the reliability of ultra-reliable channels and redundant LTE and Wi-Fi interfaces. The incorporation of redundant safety channels, as mandated by [18], is crucial for achieving enhanced performance. In a separate work, the authors of [25] examine packet loss in real-time internet services using the SGM. Their analysis encompasses UDP and TCP streams. A noteworthy contribution of their research lies in proposing a method that extends the SGM to better align with the second-order statistics, thereby improving its applicability to real-world outcomes. A Kalman filter can also be used to model the packet loss, as shown in in [26]. The authors demonstrate that such a model performs better than the SGM for their real trace, which had 30% packet loss. The authors of [27] explore strategies aimed at preventing collisions in LoRaWAN channels and assess the impact of unavoidable random access cross-traffic on such strategies. They provide guidelines on how to implement these strategies, introducing a time-scheduled channel access approach. Through simulations, they evaluate the performance of this time-scheduled approach in the presence of access cross-traffic. While LoRaWAN may not be well suited for real-time applications, it finds effective applications in various industrial IoT scenarios. The authors highlight ongoing efforts to enhance its reliability, potentially making it suitable for safety-critical applications where low latency is not a  
Figure 8: Transition diagrams for Markov chains that model packet loss. (**a**) Simple Gilbert Model (SGM). (**b**) Two-layer SGM/SGM/SGM model. Each outer state contains an SGM (**a**). primary concern.