# SPN-Based Dynamic Risk Modeling of Fire Incidents in a Smart City
## 3 Modeling Methodology and Analysis
### SPN Model and Isomorphic MC Chain  
Based on the specific process of natural fire accidents, this paper maps the complex accidents into intuitive BPMN diagrams through natural language processing methods, and then maps the evolution process into SPN models. According to the flowchart of the emergency natural fire preplan and the corresponding relationships among places, transitions, and arcs, an SPN model based on the urban natural fire preplan as shown in Figure 2 was designed. The BPMN model (Figure 2a) visually represents the sequence of events, decision points, and parallel processes in the fire rescue workflow. The SPN model (Figure 2b) translates this workflow into a formal structure using places, transitions, and arcs, enabling the quantification of key event nodes and dynamic system behavior. This model captures the key nodes at each stage of the accident and provides a quantitative basis for identifying potential risk points and formulating response strategies through simulation analysis. It consists of decisions made by three parties: the expert decision-making department, the emergency rescue department, and the rescue support department. Figure 1: Dynamic risk modelling. In practical situations, it is necessary to consider the impact of time on the system. In the model of this paper, a random delay time was added to each transition. Tables 1 and 4 explain the meanings of the place set and the transition set of the urban natural fire SPN model in Figure 2. During the initialization stage of the model, the initial marking set was set according to the actual situation to ensure that the model could truly reflect the initial state of natural fire accidents. In addition, regarding the conflict handling mechanism in the model, the conflicts between transition false alarm removal (t\({}_{2}\)) and expert decision (t\({}_{4}\)) and between the emergency plan upgrade (t\({}_{5}\)) and the upgraded plan rescue feedback (t\({}_{6}\)) were addressed by comprehensively considering the authenticity of alarms and the analytical judgments of experts. Flexible decision-making support is provided for the dynamic evolution of the model. \begin{table}
\begin{tabular}{c c c} \hline
**Place** & **Meaning** & **Transition** & **Meaning** \\ \hline p0 & Normal state & t0 & Fire event \\ p1 & Alarm information & t1 & Analyze alarm information \\ \hline \end{tabular}
\end{table} 
Table 4: The definition of the SPN model place set. Figure 2: (**a**) BPMN model for urban fires, (**b**) SPN model for urban fires. The concurrent processing mechanism: for place medical rescue support information (p\({}_{6}\)), emergency communication support information (p\({}_{7}\)), road condition isolation support information (p\({}_{8}\)), and emergency resource support information (p\({}_{9}\)), when medical rescue, emergency communication, road isolation, and emergency resource guarantee are sufficient, the corresponding transitions will be triggered, making place rescue end information (p\({}_{10}\)), communication restoration information (p\({}_{11}\)), road condition isolation end information (p\({}_{12}\)), emergency resource allocation end information (p\({}_{13}\)), and rescue information (p\({}_{14}\)) have tokens and enabling transition (emergency rescue start feedback, P\({}_{12}\)) to be implemented (that is, the emergency rescue operation is initiated). According to the SPN model of the accident, there is no information flow in the initial stage during the urban natural fire rescue process. Thus, in the initial state of the SPN model for the urban natural fire rescue process, there is exactly one token in each of p\({}_{1}\) and p\({}_{15}\). The initial marking set of the model is M\({}_{0}=(1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0)\), indicating that, among the 17 places in the model, they are marked as 1, with one token in each of these two places, while the remaining places are marked as 0. This configuration reflects the initial stage of the rescue process, where only alarm information and rescue feedback are active.