## 5 Traffic Hazard Prediction Model
The input gate, \(i_{t}=\sigma(W_{i}\cdot[h_{t-1},X(t,s)]+b_{i})\), controls which new information to update, allowing the model to focus on current speed measurements. The candidate cell state, \(\widetilde{C}_{t}=\tanh(W_{C}\cdot[h_{t-1},X(t,s)]+b_{C})\), generates a candidate value for updating the cell state, reflecting potential changes in risk based on new inputs. The cell state itself is updated as \(C_{t}=f_{t}\cdot C_{t-1}+i_{t}\cdot\widetilde{C}_{t}\), combining the previous cell state \(C_{t-1}\) with the new candidate, modulated by the forget and input gates, to maintain a memory of traffic patterns over time. The output gate, \(o_{t}=\sigma(W_{o}\cdot[h_{t-1},X(t,s)]+b_{o})\), filters the cell state to produce the hidden state, \(h_{t}=o_{t}\cdot\tanh(C_{t})\), which captures the short-term memory of the network and encodes temporal dependencies in the data. Finally, the output layer predicts the threat level using a softmax function, defined as \(y(t,s)=softmax(W_{y}h_{t}+b_{y})\), where \(W_{y}\) and by are the weight matrix and bias for the output layer, respectively. The softmax function transforms the hidden state \(h_{t}\) into a probability distribution over the risk classes (no risk, moderate risk, and high risk), ensuring that the output sums to 1 and provides a clear interpretation of the predicted danger level. This approach, though conceptual, leverages machine learning techniques, particularly logistic regression or deep neural networks like LSTM, to process speed sensor data and environmental variables, enabling the prediction of traffic safety hazards. Despite its elementary and theoretical nature, it allows us to determine the necessary data to train the model, which is summarized in Table 1, detailing the types of data, their specifics, sources, and acquisition difficulties. The above summary suggests that the most significant difficulty in data acquisition will be obtaining vehicle speed data when the LoRaWAN sensor network is not yet operational. This represents a fundamental challenge at the conceptual stage of implementing area-based speed control. Especially when one intends to expand it with elements of traffic safety risk prediction, in such a situation, for the initial training of the model, the only acceptable solution in practice is the use of synthetic data. A separate issue here, however, will be to produce them with a sufficiently high degree of fidelity, reflecting vehicle traffic and driver behavior as closely as possible to reality. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type of Data** & \multicolumn{2}{c}{**Data Details**} & **Data Source** & **Difficulty of Obtaining** \\ \hline \multirow{8}{*}{Measurement data from a network of speed sensors} & \(\bullet\) & Speed measurements in km/h & & \\  & \(\bullet\) & The time interval between measurements (e.g., every minute or a few seconds) & & \\  & & Geographic location of the sensor (GPS) & \(\bullet\) & Radar speed sensor & Low (if the network is in place) \\ \cline{1-1}  & & The number of vehicles that exceed the speed limit. & & \\  & & An accurate timestamp & & \\  & & (timestamp) of each & & \\  & & measurement & & \\ Time data & \(\bullet\) & Time of day (hour/minute) & & \\  & \(\bullet\) & Day of the week & & \\  & \(\bullet\) & Or weekday/weekend & Low \\ \cline{1-1}  & & holidays, non-working days & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Type of data needed to train the model.