Analysis of the Activities of Fire Protection Units in Response to a Traffic Accident with a Cyclohexylamine Leak Using Petri Nets and Markov Chains

Abstract

Chemical emergencies in transport are rare but operationally demanding. This study presents a framework that converts the timeline of a real intervention involving a cyclohexylamine leak after a tanker truck overturned into a Petri net and subsequently into an absorbing Markov model. This provides decision-oriented indicators for the intervention phases and enables what-if analysis. Application to a case study shows that the capacity of the decontamination line has a significant impact on the duration of the incident resolution, while introducing a small probability of returning from technical measures to decontamination slightly prolongs the course while leaving the certainty of successful completion unchanged. Mapping between activities, Petri net locations, and aggregated states promotes transparency and the repeatability of procedures and highlights activities with a high number of repeat visits. The outputs are useful for decision making related to personnel and material resources, post-review analyses, and exercise planning. The limitations lie in calibration to a single incident, the partial use of expertly estimated parameters, and the approximate conversion of “steps” to time. Future work will focus on multiple cases, finer-grained time handling, and explicit capacity modelling.

1. Introduction

Serious chemical accidents and incidents involving the transport of hazardous substances constantly test the prevention and operational readiness of emergency services. Historical events have shown that a small failure in technology or logistics can trigger a chain of failures with significant impacts on human health, the environment, and infrastructure.

One of the most significant chemical accidents before 2020 was undoubtedly Seveso (1976, Italy). A massive leak of a substance known as TCDD (2, 3, 7, 8-tetrachlorodibenzodioxin, belonging to the dioxin group) following an uncontrolled exothermic reaction led to widespread contamination and was the catalyst for the creation of European Seveso legislation for the prevention of major industrial accidents. Among the largest chemical accidents ever recorded, the incident in Bhopal (1984, India) must also be mentioned. A massive leak of methyl isocyanate (MIC) from a pesticide plant caused thousands of deaths and long-term health consequences for tens of thousands of people. It was the most tragic industrial accident in modern history. From a historical perspective of more recent events, the AZF Toulouse incident (2001, France) can be mentioned. Here, an explosion of ammonium nitrate occurred at a fertiliser plant with the effect of tens of tonnes of TNT. The consequences of this accident were very tragic. Thirty-one people died and thousands were injured. This case had a fundamental impact on European risk management practices in the chemical industry [1,2,3].

In recent years (after 2020), there have been a number of events with global repercussions. One of the largest chemical incidents was the 2020 Beirut explosion, a devastating explosion of ~2750 tonnes of ammonium nitrate in the port, with massive consequences for the city. Other notable incidents include Tarragona IQOXE (Chemical Industries of Ethylene Oxide) 2020—an accident at an ethylene oxide facility (reactor + domino effects) that resulted in three fatalities and extensive damage outside the site—and Leverkusen Chempark 2021—an explosion in a chemical waste handling area that among other activities resulted in a large-scale evacuation and left a huge environmental burden in its wake. In rail transport, we can mention the incident in East Palestine (Ohio, 2023) where a train derailed, resulting in a massive leak of hazardous substances and a subsequent “controlled burn” [4,5,6,7,8,9].

In response to the accidents that have occurred and the international investigations that have been conducted, regulators are tightening the rules. One example is the US Environmental Protection Agency (EPA), which in 2024 finalised extensive amendments to their Risk Management Program (RMP) to prevent accidents and strengthen community preparedness [4,5,6,7,8,9].

When examining the most serious accidents in recent times, we should not overlook a recent event in Czechia. This involved the derailment of a train carrying benzene (more than 1000 tonnes) in Hustopeče nad Bečvou (February 2025). This unprecedented event led to the declaration of a state of emergency lasting several months, long-term groundwater remediation, and extensive media and official coverage. Estimates suggest that hundreds of tonnes of benzene (estimated at 400 tonnes) were leaked or burned, with the incident being described by the authorities and international media as the largest benzene contamination of its kind in the world [10,11].

When modelling emergency response, Petri nets (PNs) are a natural formalism for concurrency, priorities, and resource constraints. Recent work uses timed/coloured Petri nets (CPNs) to analyse cooperation, arrival times, and resource allocation in industrial accidents and firefighting interventions. At the same time, decision makers need interpretable metrics in a closed form, not just simulation traces [12].

In simplified terms, we can say that Petri nets represent a flowchart that defines which states are active and when, or which ones must be “waited for” in the process. A Markov chain then represents a probability map of jumps between key states. When we “wrap” a PN in layman’s terms into a smaller set of understandable states and supplement them with transition probabilities, we can calculate how often each state is visited and how long it typically takes to reach the goal (end of the intervention). This gives commanders measurable arguments for choosing reinforcements, equipment, and priorities [12].

2. Materials

2.1. Incident Description

This study contributes an analysis at the process level of a real-world event involving cyclohexylamine: we model the response workflow using Petri nets and map it to an absorbing Markov chain to obtain decision-oriented metrics and perform what-if experiments (e.g., staffing/equipment policies that reduce response times while maintaining certainty of termination). This approach complements recent Petri net studies by linking the operational command workflow in incidents with closed Markov analysis that is directly applicable to planning and training [13].

This study analyses the response to an emergency in the form of a tanker accident involving a large-scale uncontrolled leak of cyclohexylamine, examines the intervention carried out by the integrated rescue system, and highlights key operational challenges, decision points, and implications for emergency command practice. The serious incident in question took place in June 2017 in the Olomouc region and was one of the largest and most significant chemical emergencies in the Czech Republic that year, reflected in the length of the intervention, which lasted almost 21 h. During this time, a total of five firefighting units, both professional and volunteer, took turns at the scene of the accident. It is important to mention the very high personnel demands that this intervention required due to the rotation of firefighters and the use of special equipment for the disposal of hazardous substances [14,15].

At 6:30 a.m., a tanker truck carrying hazardous material overturned on its side and blocked traffic on a busy motorway. The driver of the tanker, a Romanian national, was injured in the accident. Due to the early hour, a member of the fire and rescue service and a paramedic were passing through the area at the time. Both correctly assessed the seriousness of the situation and reported the accident, including the KEMLER and UN codes. This sped up the entire response process, as there was no doubt about the seriousness of the situation or the urgency of the response. Paramedics then provided first aid to the injured driver. Upon arrival of the first firefighting units at the scene, a check was carried out to determine the presence of cyclohexylamine. Due to the nature of the chemical, it was necessary to observe maximum protection practices and define dangerous and external zones. These established procedures required the closure of the motorway in both directions and the diversion of traffic to alternative routes. The initial response was carried out with maximum protection for the firefighters, i.e., using breathing apparatus and chemical protective clothing with subsequent decontamination. During the initial measures, an analysis of cyclohexylamine was carried out to confirm the accuracy of the information provided by the driver and the transport documents. The analysis was performed using Raman and FTIR spectrometers to confirm the accuracy of the result. An initial investigation found that cyclohexylamine was leaking through the upper inspection hatch. The leaking substance was collected in chemically resistant containment equipment, and the total leakage of cyclohexylamine was estimated at 200 litres. Due to possible public speculation, the authorities issued press releases and published only general information on their official social networks. Based on its properties, the leaked substance was flammable, potentially explosive, and highly toxic. As part of the assistance provided by the transport information and emergency response system, a replacement tanker was requested to pump out the contents of the damaged tanker. Once the replacement tanker arrived, a procedure was established for pumping the cyclohexylamine out of the damaged tanker as the standard procedure with a drain valve was not possible because the tanker was in a position where the valve was inaccessible. It was therefore necessary to improvise and pump the substance through the filling valve. It is important to note that the entire process of pumping cyclohexylamine from the crashed tanker was very problematic and time-consuming. After about 90% of the contents had been removed, it was no longer possible to pump out the remainder in that position, and it was necessary to put the tanker back on its wheels. Once the immediate risk (risk of explosion, exclusion of ignition sources) had been reduced, the Czech police also launched an investigation. The police officers had to be equipped with appropriate protective equipment because they were still entering the danger zone together with the firefighters. It should be noted here that the police are not directly responsible for managing chemical emergencies in the Czech Republic; their primary task is to investigate and clarify the incident. The responsible authority is the Fire and Rescue Service (FRS), and the police perform partial tasks (closing off the site of the incident, evacuating civilians). Before the rescue operation itself, it was decided to spray a layer of special foam for polar liquids onto the tanker to eliminate sources of ignition. Rescue work then began, which lasted several hours. After the tanker was put back on its wheels, the remaining cyclohexylamine was removed using a peristaltic pump. Following these operations, it was possible to clean the spill from the surface of the motorway by sufficient dilution. All technical equipment used was also decontaminated, including washing the crashed tanker before it was towed away by a specialised company [15].

The difficulty of the entire operation was influenced by several negative factors, one of the main being the high heat load, as the temperature during the day reached 30 °C. At such temperatures, working in chemical suits is very uncomfortable, which significantly reduces the time this protective equipment can be used. This factor was compounded by several subordinate problems. In particular, the greater the number of firefighters taking turns, the greater the amount of protective equipment, the greater the amount of decontamination agent used, the greater the amount of contaminated water, etc. From this negative factor, it is already apparent that the process of dealing with a chemical accident can be significantly affected even by such a trivial parameter as the daily temperature.

Another unfavourable factor was the unstable position of the overturned tanker, which made it impossible to use standard operating procedures for pumping. Although firefighters are trained for such incidents, conditions on site often require improvisation, which can complicate the response. The response to a chemical transport accident is strongly influenced by the severity of the accident, the amount of contaminant released, and the physical and chemical properties of the hazardous substance [15,16].

Negative factors also include the impact of the emergency on the civilian population. In this type of emergency, many restrictions are imposed that affect the entire adjacent area. When a motorway is closed, diversions are put in place, but these are unable to accommodate all traffic. This leads to a complicated traffic situation in the wider area. A huge increase in traffic is evident in neighbouring towns and villages, where significant traffic complications can have a major impact on the daily lives of the civilian population. Public transport is also restricted and there are significant delays. For these reasons, it is essential to keep the public adequately informed about the emergency through available communication or social networks. The security forces cooperating at the scene of the incident decide jointly what information will be provided to the media and within what time frame. It is important not to cause unnecessary panic if the emergency is under control and there is no immediate risk of a sudden deterioration in the situation. Despite the extensive closure of the site, some people want to watch the incident closely, which makes the work of the responding security forces more difficult. Very often, the media also do this, as they are eager to obtain the best footage from the scene in their pursuit of sensationalism [15,16].

2.2. Timeline of Events

Table 1. Emergency timeline.

Time Flow	Action	Time Flow	Action
06:32	Event occurs	06:54	Securing access routes, securing the surrounding area
06:33	Emergency call	07:35	Establishment of a parking area
06:33	Notification from the Regional Operational and Information Centre (ROIC)	07:38	Use of chemical protective clothing
06:33	Description and transmission of information about the emergency	07:44	Verification of the fire–technical properties of the substance leaking from the tanker
06:34	Availability of units according to the fire alarm plan	07:46	Use of support software, including transport and information systems
06:34	Availability of a support point for firefighting units	08:22	Provision of the necessary resources for accident response, replacement tanker
06:34	Firefighting equipment and gear	12:41–17:09	Clean-up work, pumping out leaked liquid
06:35	Departure of the unit	15:26	Injury to a member of the fire and rescue service
06:36	Journey to the scene	17:09–17:58	Decontamination of personnel and equipment used in the accident response
06:44	Determination of weather conditions	18:10–02:34	Rescue and recovery work, final rinsing of the road surface
06:46	Arrival of firefighting units at the scene	02:45	Withdrawal of units
06:50	Initial information about the accident is reported	03:01	Return of units to base
06:50	Provision of emergency medical services to injured persons	03:03	End of emergency

shows the timeline of the emergency in detail. It should be noted that some “actions” can be precisely determined, e.g., the occurrence of the event, the departure of the fire brigade and their arrival at the scene of the emergency, the injury of a firefighter, but some actions may overlap or take place in the background during the response to the emergency, e.g., securing the necessary resources for dealing with the accident, pumping out spilled liquids, decontaminating the responders, etc. It should also be noted that only essential “actions” during the response process are shown [15,16].

2.3. Physical and Chemical Properties of Cyclohexylamine

Cyclohexylamine (CHA; C₆H₁₁NH₂) is a primary aliphatic amine. In aqueous media it acts as a weak Brønsted base (conjugate-acid pK_a ≈ 10.6). CHA with strongly irritating to corrosive effects on the skin and mucous membranes. Its vapours can form explosive mixtures with air. CHA has a wide range of industrial applications, particularly in the agricultural, pharmaceutical, and chemical sectors. It is also widely used in the rubber industry, e.g., in the preparation of the vulcanisation accelerator CBS (N-cyclohexyl-2-benzothiazolesulfenamide) for the manufacture of tyres. Fire–technical and physical–chemical properties are key to tactical decisions during an intervention (leak from a stationary or mobile source): temperature (affects volatility), miscibility with water, neutralisation behaviour, and compatibility of extinguishing agents. The vapours released require the use of personal protective equipment (PPE) for chemical protection and subsequent decontamination of exposed surfaces and persons. A simplified formula for cyclohexylamine is shown in Figure 1. An overview of the basic fire–technical characteristics is shown in

Table 2. Fire–technical characteristics of cyclohexylamine.

Parameter	Value	Units and Clarifications
CAS/EC/INDEX	108-91-8/203-629-0/612-050-00-6
UN	UN 2357	Clear identification of the substance according to the UN code.
ADR	83	8—Corrosive, 3—Flammable
Flash point	27	°C
Ignition temperature	293	°C
Explosive limits	LEL 1.6–UEL 9.4	% vol.
Initial boiling point (1.013 bar)	134–135	°C
Melting point	−17	°C
Vapour pressure	13.33 hPa (22 °C); 30.66 hPa (37.7 °C)	(≈10 and 23 mmHg)
Density (20 °C)/Rel. Density (25 °C)	0.866 g·cm−3/0.86
Relative vapour density	3.42	air = 1
Solubility in water (20 °C)	completely miscible
pH (100 g·L−1; 20 °C)	11.5	alkaline
GHS pictograms/H statements	GHS02, GHS05, GHS08/H226, H302 + H312, H314, H361fd	GHS02—Flammable, GHS05—Corrosive, GHS08—Serious Health hazard
Suitable extinguishing media	CO2, foam, powder
Special hazards in case of fire	NOx, COx; vapours heavier than air; forms explosive mixtures with air when heated
PEL/NPK-P (Czech Republic)	20 → 40 mg·m−3 (≈4.85/9.7 ppm)

[17,18,19].

2.4. Data Collection

Data for this study was collected from multiple sources. The author responsible participated in the intervention as head of the chemical and technical services of the Fire and Rescue Service of the Czech Republic (FRS CR), but this experience was only used to reconstruct the events. The numerical input data is primarily based on documentation and was subsequently verified by experts.

The following were used in particular:

• The incident report (standard FRS CR protocol prepared after each emergency);
• A record of operational communication between the incident commander and the Regional Operational and Information Centre (ROIC);
• After-action review (structured SWOT recapitulation);
• Semi-structured interviews with members of the command staff (incident commander, territorial department commanding officer, Olomouc Regional Fire Protection commanding officer) [15].

The materials contain non-public internal information of the Fire and Rescue Service of the Czech Republic and were used with the consent of the relevant management bodies. The published data does not contain personal data or facts subject to investigation. Only aggregated and technical information relevant to modelling is presented in the work [15].

Documentary sources (reports, logs) took precedence over memory reconstruction. Discrepancies were resolved by triangulation with the testimony of members of the command and by reaching a professional consensus. The timeline (Table 1) serves as the main data source for mapping events into the model [15].

3. Methods

3.1. Definition of the Process

The term “process” is often mentioned in the introduction. To properly set up and understand the whole issue, it is important to describe its meaning. In general, a process is an activity or a set of several activities that serve to transform inputs into outputs. If we transfer this simple definition to the field of chemical accident management, it is a set of several hazardous processes that have occurred and that need to be brought to a state where they are no longer hazardous, i.e., where there is no further potential danger (fire, explosion, effects of chemical substances, etc.) or when the danger is reduced to a safe level (extinguishing, neutralising chemical substances, etc.).

The characteristics of the process set further divide the processes into priority phases (not into “subordinate” or “superior” processes). An important part of the process is so-called feedback, which can support the correct execution of the process. This additional part of the definition can be reimplemented in the chemical accident response process, where the individual steps of the response process are more important and thus become priority phases. For example, rescue operations take precedence over measures to prevent further leakage of hazardous substances [16,20].

3.2. Definition of Petri Nets

In general, Petri nets represent a wide range of mathematical models that enable a very accurate graphical description of the concurrent information dependencies and conflicts of modern distribution systems. Currently, Petri nets are most often associated with applications in the design, analysis, and modelling of various parallel systems, particularly in the fields of automation, telecommunications, and various database systems. The comprehensibility and analytical capabilities of Petri nets are primarily due to their simplicity [21,22].

In general, they are a precisely defined mathematical structure whose properties can be proven by formal methods. The existence of different variants of Petri nets is related to the effort to increase modelling capabilities and the level of models while maintaining the simplicity that is characteristic of Petri nets [21,22,23].

A Petri net model is described by places that contain information about the current state in the form of tokens and transitions that represent possible state changes, i.e., they describe actions that can occur and thus change the current state of the system. Places are connected to the corresponding transitions by arcs. An important advantage of this modelling tool is the ability to graphically represent and simulate the dynamic behaviour of the model. Currently, there are several programmes that support working with Petri nets. These programmes usually include a graphical editor and a simulator for network analysis. Their use significantly increases the efficiency of Petri nets in specific applications and is also very useful for practical teaching [21,22,23].

3.3. Modelling Using Petri Nets

A Petri net is a triplet N = (P, T, F), where P is a finite set of places, t is a finite set of transitions, P ∩ T = ∅, and F ⊆ (P × T) ∪ (T × P) is a set of directed arcs with multiplicities.

W: F  → N₀

(1)

The function W is a weight (multiplicity) function of arcs: W (P, t) specifies the number of tokens required to enter transition t, and W (t,p) specifies the number of tokens produced at place p; for existing arcs, W ≥ 1.

Let N = (P, T, F) be a Petri net. For each transition t ∈ T and for each place p ∈ P, we define sets.

t∙ = {p ϵ P|W (t, p) > 0}
 t = {p ϵ P|W (p, t) > 0}
 p∙ = {t ϵ T|W (p, t) > 0}
 ∙p = {t ϵ T|W (t, p) > 0}

(2)

This notation applies to places and transitions. For a place $p$, ∙p denotes the set of input transitions to $p$ (from which $p$ can receive a token) and p∙ the set of output transitions from $p$ (to which $p$ can pass a token). Analogously, for a transition $t$, ∙t is the set of input places of $t$ and t∙ the set of output places of $t$ [21,22,23].

3.4. Petri Net-Based Procedure for Reaction Process Analysis

The application of a Petri net to the analysis of the chemical accident response process involves the following basic steps.

• Selection of a representative significant chemical incident suitable for reaction process analysis.
• Setting up a Petri net model for a specific response process to the selected emergency.
• Definition of tokens (states) and transitions [21,22,23].

3.5. Markov Chains

Markov chains are discrete-time stochastic processes used to describe systems that evolve step-by-step over time. They are memoryless: the next state depends only on the current state, not on the past. This property allows the behaviour of the system to be characterised by transition probabilities between states and makes the evolution of state probabilities analytically tractable.

A Markov chain is a discrete-time, time-homogeneous stochastic process $\{X_k{\}}_{k\ge 0}$ on a finite state space $S=\{1,\dots ,m\}$ that satisfies the Markov property (memorylessness):

$$Pr(X_{k+1}=j\mid X_k=i,X_{k-1},\dots \hspace{0.17em})=Pr(X_{k+1}=j\mid X_k=i)=p_{ij}$$

(3)

The probabilities $p_{ij}$ form a transition matrix $P=\left[p_{ij}\right]$ with $p_{ij}\ge 0$ and each row summing to one (row-stochastic). The chain’s evolution is conveniently expressed in linear-algebraic terms: if $s$ is an initial distribution on $S$ (a row vector), then the distribution after $n$steps is $s{P}^{\hspace{0.17em}n}$. The $n$-step transition probabilities are the entries of $P^{\hspace{0.17em}n}$. The probability of a specific finite path $i_0\to i_1\to \cdots \to i_n$ equals ${\prod }_{k=0}^{n-1} p_{i_k{i}_{k+1}}$ [24,25].

A step denotes one transition between states in $S$ (discrete event), not a unit of physical time. When modelling waiting or persistence in a state, this is represented by a self-transition $p_{ii}>0$. Fundamental qualitative notions include communicating classes, transient vs. recurrent states, and periodicity; for finite chains these properties determine long-run behaviour and the existence of limiting distributions. Standard quantitative questions involve $n$-step transitions, hitting probabilities, and expected numbers of steps to reach specified sets of states, all computable from $P$ by linear-algebraic methods [24,25].

The management of chemical emergencies can be effectively represented using Markov chains because they model random processes where state transitions depend solely on the current state, which allows them to be expressed through systems of linear equations. Each linear equation then expresses the state process in the solution of a chemical emergency [24,25].

3.6. Modelling Software

To model the response to a chemical accident, it is necessary to select a suitable software tool that can create Petri nets and model and graphically represent the resulting process. When solving the process of responding to a chemical accident using Petri nets in common text editors, the modelling process is disproportionately time-consuming. This method can only be used for initial interpretation, i.e., an introduction to the problem. These tools are also unsuitable because they cannot display the course of the process. For these reasons, modelling must be performed using tools designed for this specific purpose [26].

Mathematica software 13.3 from Wolfram Research was selected to solve the problem of modelling using Petri nets. This tool was originally designed to perform mathematical, scientific, and technical calculations. Today, it is a comprehensive development environment that offers a wide range of functions and calculations, including numerical simulation, visualisation, graph generation, etc. The Python 3.12 programming language was used to visualise Markov chains and related graphs, as visualisation and some calculations were relatively complex in the Mathematica software. After several simulations, the Python programming language became a proven tool capable of visualising Markov chains [26,27].

3.7. Analysis of the Chemical Accident Response Process

The chemical accident response process can be considered a very complex dynamic process consisting of a series of stochastic subevents. According to established standards and procedures for responding to chemical accidents, the entire process can be theoretically simplified and divided into three basic phases:

• The information reception and confirmation phase;
• The chemical accident response phase;
• The decontamination phase.

1.

The information reception and confirmation phase is divided into the following basic parts: correctly obtained information about the emergency, correctly transmitted information about the emergency, correct determination of the location of the emergency, operability of the warning and dispatch system, and dispatch of fire protection units.

2.

The chemical accident response phase is divided into the following main parts: initial intervention by service personnel, investigation of the extent of the accident, investigation from the perspective of the affected persons, establishment of safety zones, evacuation, identification of hazardous substances, prevention of further leakage, handling of hazardous substances, and provision of replacement packaging.

3.

The decontamination phase is divided into the following essential parts: securing contaminated assets, removal of contaminated water, decontamination techniques, and remediating affected areas [16,28].

Although the individual emergency response activities are presented in a specific order, it is clear that some activities take place simultaneously, for example, the investigation at the accident site, where all the circumstances are ascertained. This depends on the extent of the accident and whether more than one unit has been dispatched to the site, which may result in more than one investigation team, for example, a support point is immediately connected to the standard centre point [16,28].

When modelling the response to a chemical accident using the selected method, it is necessary to break down the response into clearly defined steps and express the links between defined locations and transitions. As already described, locations and transitions are connected by so-called edges. Correct notation is essential so that the modelling tool can graphically represent the overall process of responding to a chemical accident. The first step is to define the individual places (set P), which represent the substeps in the response process, and the transitions (set t), which represent the main milestones without which the process could not proceed to the next substep or phase. At each point, there are so-called tokens, i.e., imaginary information (status information) that enters the emergency response process and permeates the entire proposed system. The correctness of the proposed system is then evaluated based on the throughput of the entire process [23,28].

We analysed a case study of a chemical accident using Wolfram Mathematica software for accident response modelling. In the context of a gradual examination of interventions already carried out, transition sets were identified that represent the emergency response process for a selected chemical accident [23,28].

(1)

Final set of locations: P.

P1: emergency call;

P2: notification of the Regional Operational and Information Centre (ROIC);

P3: description and transmission of information about the emergency;

P4: availability of units according to the fire alarm plan;

P5: availability of support point for fire protection units;

P6: firefighting equipment and gear;

P7: departure of the unit;

P8: route to the incident;

P9: determination of weather conditions;

P10: arrival of firefighting units at the scene;

P11: provision of initial information about the accident;

P12: provision of emergency medical services to injured persons;

P13: securing access routes and the surrounding area;

P14: setting up a parking area;

P15: use of chemical protective clothing;

P16: verification of the fire–technical properties of the substance leaking from the tanker;

P17: use of support software, including transport and information systems;

P18: securing the necessary resources for accident disposal, replacement tanker;

P19: clean-up work, pumping out of leaked liquid;

P20: injury to a member of the fire and rescue service;

P21: decontamination of personnel and equipment used in accident response;

P22: rescue work;

P23: restoration of road traffic at the accident site;

P24: withdrawal of units;

P25: return of units to base.

(2)

Final set of transitions: t.

t1: receiving information;

t2: assessment of the severity of the emergency;

t3: preliminary determination of responding units;

t4: raising the alarm and passing on information to firefighting units;

t5: directing fire engines to the scene;

t6: obtaining information about the hazardous substance from available sources and passing this information on to the responding units;

t7: survey of the site;

t8: cordoning off the scene;

t9: definition of safety zones;

t10: detection of chemical substances;

t11: forwarding information about the leak to the regional operations and information centre;

t12: prevention of further leakage of hazardous substances from the tanker;

t13: emergency location;

t14: accident clean-up;

t15: emergency response;

t16: handover of the site;

t17: end of intervention [15,23,28].

Figure 2 shows the input of parameters into the Mathematica software input used to declare the Petri net: the list of places P = {P1,…,P25}, the list of transitions t = {t1,…,t17}, the directed arc set F ⊆ (P × T) ∪ (T × P) with integer weights W: F → N₀, and initial marking M0. As described above, it is necessary to precisely define individual places and transitions and then accurately describe individual relationships. When entering individual places that independently enter our traversal process, we create an initial set.

Initial Petri-net marking (indicator over places $P_1\dots P_{25}$). The following 0/1 vector specifies tokens at the start of the process; it is not a Markov transition row.

This initial Petri-net marking M0 lies in the region associated with macrostate M1. Consequently, the Markov chain starts in M1, i.e., the initial macrostate distribution is $s=[1,0,\dots ,0]$.

M0 (1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0)

This set represents the entry of a token into the process and the state of the process or system. Modelling thus provides us with the final state of individual processes, which depends on the movement of tokens in the system. Simply put, modelling gives us the final number of individual states (possibilities). This is the number of steps needed to complete the process or reach the absorption state.

Figure 3 thus represents a bipartite Petri-net graph produced from the input in Figure 2. Places P = {P1,…,P25}, are shown as circles. Transitions t = {t1,…,t17}, as rectangles. directed arcs follow the set $F$ with weights $W$. This figure conveys the causal/structural relations (sequence, concurrency and synchronisation) that underpin the model. It is a structural view—no probabilities are shown here [24,28].

For a complete graphical representation of the entire process, it would be necessary to show all achievable states. In order to “save space”, this step was not taken, as it would have led to an unreasonable increase in the length of the article. However, the result does contain 11 different system states. Each individual result state represents a set of the system, so we can define individual sets (the movement of tokens in the response process). From these sets, we construct the transition-probability matrix and compute the absorption probability to confirm that the process terminates. This provides a simple consistency check before scenario analysis. Alternatively, a control calculation can be used to determine the probability of completing the process. This is very important because this calculation proves the correctness of the procedure for performing the intervention without repeating the process, that is, the given passage of the system [24,28].

The displayed matrix defines individual rows that represent individual states (M1–M11), while the columns indicate where the state transitions to:

$$\begin{gathered} M1 \left(1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0\right) \\ M2 \left(0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0\right) \\ M3 \left(0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0\right) \\ M4 \left(0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0\right) \\ M5 \left(0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0\right) \\ M6 \left(0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0\right) \\ M7 \left(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0\right) \\ M8 \left(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0\right) \\ M9 \left(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0\right) \\ M10 \left(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0\right) \\ M11 \left(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0\right) \end{gathered}$$

Once we have determined the sets of individual system states in this way, we can draw a Markov chain graph. As described in the previous paragraphs, the rows of the set represent a certain state of the system (M1–M11), and the columns represent certain properties (the movement of tokens in Petri nets). In order to draw a Markov chain graph, we must determine the transitions between states. For better orientation, we can also name the individual states; an overview of these named states is given in

Table 3. Definition of M states (aggregation of reachable marks).

Markov State	Phase
M1	Alert and dispatch
M2	Mobilisation and travel
M3	Information before arrival
M4	Arrival and initial assessment of the situation
M5	Site inspection and establishment of zones
M6	Chemical detection/decision gate
M7	Preparation of necessary equipment
M8	Decontamination operations
M9	Technical measures and rescue
M10	Handover and stand-down
M11	Safe termination (absorption)

. A transition between two states Mi and Mj exists only if

• Mj contains 1 where Mi has 0;
• Mi contains 1 at the point where Mj has 0.

There is a direct transition between $M_i$ and ${ M}_j$ only if their binary state vectors differ in exactly one position (Hamming distance = 1).

If the distance is 0 or ≥2, no direct transition is defined. After implementing the above conditions, we obtain a Markov chain graph (see Figure 4; unweighted, topology only), while edge probabilities are added in Figure 4 (transition probabilities at the edges). Python numerical software was used to visualise the graph [28,29].

3.8. Aggregation of the Detailed Petri Net into Markov Chain Macrostates

For the analytical part, we aggregated the detailed Petri net (P1–P25, T*) into eleven macrostates, M1–M11, which represent operational steps and decision nodes. The aggregation was governed by two rules:

• Places that are co-active in a single operational step were merged into the same M state;
• Purely source/guard locations do not form a separate Markov state.

The mapping of reality to the model is shown in

Table 4. Mapping table—connection of the Petri net to Markov chains.

Event Timeline	Corresponding Places P	Markov State M	Phase
6:31–6:33	P1, P2, P3, P4, P5, P6	M1	Alert and dispatch
6:35	P7	M2	Mobilisation and travel
6:36–6:42	P8, P9	M3	Information before arrival
6:46	P10, P11, P12	M4	Arrival and initial assessment of the situation
6:47–7:15	P13, P14	M5	Inspection of the site and establishment of zones
7:16–7:38	P15, P16, P17	M6	Chemical detection/decision gate
7:39–8:31	P18	M7	Preparation of necessary equipment
8:31–22:00	P20, P21	M8	Decontamination operation
22:01–1:06	P19, P22	M9	Technical measures and rescue
1:06–2:18	P23, P24	M10	Handover and stand-down
03:09	P25	M11	Safe termination (absorption)

(timeline → P → M).

4. Results

The next step in analysing the intervention is to determine the Markov chain and calculate the probability of transition between states. To create a Markov chain, it is necessary to convert the specified binary transition matrix (M1 to M11) into a probability transition matrix by summing the number of outgoing transitions from each state Si (the sum of ones in each row) and then dividing the resulting number by the total number S of transitions from that state. This gives us the transition matrix P [29,30,31].

Each element of the matrix P_ij corresponds to the probability of transition from state M_i to state M_j.

$$P_{ij}={\displaystyle \frac{A_{ij}}{{\sum }_j{A}_{ij}}}$$

(4)

where A is the original binary matrix (with a value of 0 or 1), and ${\sum }_j{A}_{ij}$ is the number of outgoing edges from state M_i.

This condition is used to calculate the probability transition matrix P, which has the following form:

$$P= \left[\begin{array}{ccc}{p}_{1,1} & \dots & p_{1,11}\\ ⋮& \ddots & ⋮\\ p_{11,1}& \dots & p_{11,11}\end{array}\right]$$

(5)

4.1. Derivation of Markov Chain Transition Probabilities

This step is crucial for the work because it determines the transition matrix $P$, on which all further calculations and results are directly based. Therefore, the probabilities $p_{ij}$ were designed to be as transparent as possible, supported by the timeline and operational logic of the intervention.

The transition probabilities ${ p}_{ij}$ were determined in three steps.

• Informed estimate based on complexity: Based on direct participation in the intervention and knowledge of tactical and technical procedures, possible departures $i\to j$ were ranked for each node according to operational complexity (requirements for personnel and resources, coordination burden, risk and expected waiting time). Simpler departures were given higher weight, and more demanding ones lower. From these weights $w_{ij}$, an initial distribution was created as

$$p_{ij}^{\left(0\right)}={\displaystyle \frac{w_{ij}}{{\sum }_k{w}_{ik}}}.$$

(6)

which, in nodes with comparable alternatives, leads to equal shares

$$(\mathrm{e}.\mathrm{g}., {\displaystyle \frac{1}{2}},{\displaystyle \frac{1}{3}}=>0.5;0.33).$$

• Check against the timeline: From the documentary records (intervention timeline), the number of transitions from $n_{ij}$ to successors $j$ was calculated for each state $i$. Where sufficient records were available, a frequency estimate was used:

$${\widehat{p}}_{ij}={\displaystyle \frac{n_{ij}}{{\sum }_k{n}_{ik}}}$$

(7)

and the initial distribution was adjusted towards ${\widehat{p}}_{ij}$. In nodes with few records, the original weights $w_{ij}$ were given greater weight.

• Verification with direct participants: The resulting values $p_{ij}$ were validated via analysis with key participants in the intervention (intervention commander, territorial department control officer, regional control officer). They confirmed that the proposed proportions correspond to the actual difficulty of the individual branches and the course of the event. Each row of the probability matrix was normalised to 1 and checked against the Petri net topology and the timeline. In case of discrepancy, documentary sources (timeline, intervention protocol) took precedence over memory reconstruction. For key branches, we provide uncertainty intervals (min–max) used in the sensitivity analysis of scenarios [29,30,31].

In practice, this implies that more operationally demanding transitions are assigned lower $p_{ij}$ values than simpler ones, unless the incident timeline data indicate otherwise. Uniform values (0.50; 0.33) are used only when the available alternatives are operationally comparable and the number of records is limited. For clarity, the terminal state M11 can be interpreted as a return to the initial “ready” condition M1, i.e., the state in which the rescue system is prepared to respond to another chemical emergency.

Here, the calculated probability transition matrix P is obtained by normalising the binary transition matrix:

$$P=\left[\begin{array}{cccccccccccc}& M1& M2& M3& M4& M5& M6& M7& M8& M9& M10& M11\\ M1& 0.00& 0.3\left(3\right)& 0.00& 0.00& 0.3\left(3\right)& 0.00& 0.00& 0.00& 0.3\left(3\right)& 0.00& 0.00\\ M2& 0.00& 0.00& 0.3\left(3\right)& 0.00& 0.3\left(3\right)& 0.00& 0.00& 0.00& 0.3\left(3\right)& 0.00& 0.00\\ M3& 0.00& 0.00& 0.00& 0.3\left(3\right)& 0.3\left(3\right)& 0.00& 0.00& 0.00& 0.3\left(3\right)& 0.00& 0.00\\ M4& 0.00& 0.00& 0.00& 0.00& 0.00& 0.50& 0.00& 0.00& 0.50& 0.00& 0.00\\ M5& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.50& 0.00& 0.50& 0.00& 0.00\\ M6& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.50& 0.50& 0.00& 0.00\\ M7& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 1.00& 0.00\\ M8& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 1.00\\ M9& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.50& 0.50\\ M10& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 1.00\\ M11& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 1.00\end{array}\right]$$

Each row corresponds to the probability of transition from state M_i to other states M_j. The values in each row sum to 1 (printed values are rounded) if there are outgoing transitions, which represents the validity of the probability interpretation. Once the probability matrix P is determined, we can visualise the Markov chain with transition probabilities; see Figure 5 (an edge-weighted directed graph with transition probabilities on the edges) [29,30,31].

Now we can determine the probability of completing the entire process in the Markov chain based on the absorption analysis of the transition matrix [29,30,31].

First, it is important to divide the transition matrix P into a block structure.

$$P=\left[\begin{array}{c}Q R\\ 0 I\end{array}\right]$$

(8)

where

Q is the submatrix of transitions between transient states;

R is the submatrix of transitions from transient states to absorption states;

I is the identity matrix for absorption states.

For each transient state ${ M}_i$, the row stochastic transition matrix is

$$P_{ij}={\displaystyle \frac{A_{ij}}{{\sum }_k{A}_{ik}}} \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r} {\sum }_k{A}_{ik}>0$$

(9)

where $A$ is the binary adjacency matrix of Markov states.

The absorbing state M_j must satisfy the condition ${ P}_{ii}=1$ and $P_{ij}=0$ for all $i\ne j$.

State j is absorbing if P_jj = 1 and P_jk = 0 for all k ≠ j.

If absorption states exist, we can determine the fundamental matrix N:

$$N={\left(I-Q\right)}^{-1}$$

(10)

Definition of Q and the fundamental matrix. Here Q denotes the t x t submatrix of P restricted to transient states (M1, …, M10), I is the identity, and $N={\left(I-Q\right)}^{-1}$ is the fundamental matrix. Element N_ij is the expected number of visits to transient state j when starting from transient state I. We order states as transient first and absorbing afterwards (here t = 10, a = 1).

$$N=\left[\begin{array}{c}1.511 2.089 4.000 3.333\\ 0.400 3.200 4.000 3.333\\ 0.178 1.422 4.000 3.333\\ 0.089 0.711 2.000 3.333\end{array}\right]$$

The result is the expected number of steps to the absorbing state.

From M1, the expected number of steps to absorption is 3.931.

This matrix determines the expected number of steps that the system will take in each state before reaching the absorbing (final) state [29,30,31].

The expected steps represent discrete shifts between macrostates (e.g., in the preparation of a decontamination site after decontamination itself), not a state expressing time dependence. To make the scenarios and individual steps more understandable, the number of steps is converted into approximate time using average times that can be derived from the intervention timeline shown in Table 1.

If we express the simplified description of the expected steps mathematically, it is a transient part of the transition matrix and the fundamental matrix.

Initial distribution $s$ and visit counts. Let $s$ be the $1\times t$ initial distribution over transient states (baseline $s=e_1$, i.e., start in M1). The row vector of expected visits to transient states is $v=sN$, and the expected number of steps to absorption equals $v 1$.

For a given initial state distribution S (typically starting in M1), we define

$$v=sN$$

(11)

v is the vector of expected visits to transient states.

We consider two approximations of time:

From the time axis, we estimate the average holding time d_j (min) for each transient state j. Then, the estimate of the time to absorption is

$$T_{approx}={\sum }_j{v}_j{d}_j=vd$$

(12)

In practice, d_j is estimated from the intervals between events (actions) that map the entry/exit to state M_j.

Edge times:

If average transition times T_jk (min) for edges j → k can also be assigned from the timeline, we use

$$T_{approx}={\sum }_j{v}_{j }{\sum }_k{p}_{jk}{T}_{jk}={\sum }_{j,k}{v}_j{p}_{jk}{T}_{jk}$$

(13)

Equation (12) then corresponds to the “expected number of transitions” j → k multiplied by the number of transitions [28,29,30,31].

In scenario analysis, we recalculate v = s N under the changed P_jk, while the per-state dwell times d (or edge times T_jk) and leave the timeline unchanged, as the scenarios change the capacity, not the times of individual operations. The resulting times can be considered indicative and are used to compare scenarios, not to set fixed limits [28,29,30,31].

Once we have determined the fundamental matrix N, we can calculate the absorption probability (the probability of completing the response process). To do this, we use the following relationship:

$$B=NR$$

(14)

where B contains the probability that a process starting in a certain transient state will end in a final state, i.e., an absorption state.

It is also essential to define R. Let $R$ denote the $t\times a$ transient-to-absorbing block of $P$ (with $a$ absorbing states; here $a=1$ with M11). The absorption matrix is $B=NR$; the probability of eventual termination in M11 from start $s$ is $sB$ [29,30,31].

Absorption into M11 is certain for all initial transition states (B = 1.00). The expected steps to absorption vary depending on the initial states. The calculation results for each step are shown in

Table 5. Expected steps for absorption (transitional states M1–M11).

Individual States	Expected Steps
M1	3.931
M2	3.542
M3	3.375
M4	2.875
M5	2.750
M6	2.250
M7	2.000
M8	1.000
M9	1.500
M10	1.000
M11	0

[29,30,31].

The results show where time is lost (feedback/bottlenecks) and how tactical choices affect duration.

4.2. Analysis and Verification of What-If Scenarios

Responding to emergencies involves uncertainty and time pressure, so decision options should be tested without real risk. What-if analysis provides a transparent way to see how targeted operational changes propagate through the workflow and affect performance metrics. In our model, we change the routing at decision gate M6 between decontamination (M8) and technical measures (M9) to mimic different decontamination line capacities. Since the network topology does not change, the certainty of safe completion (absorption into M11) remains 1.00 as designed, while the expected number of steps may increase or decrease depending on the M6 distribution [31,32,33,34].

Therefore, we change the distribution M6 → {M8, M9} to represent capacity levels. Increasing the proportion of M8 (higher capacity) should reduce the expected steps for initial states that reach M6 with non-negligible probability. A decrease in the share should lengthen them. To make the effect sizes visible even when global averages change only slightly, we report Δ = scenario − baseline (a negative Δ value indicates improvement) for a set of frequently reached initial states (including M6 itself). We evaluate three settings: baseline, scenario A (0.4 → M8/0.6 → M9), and scenario B (0.7 → M8/0.3 → M9). This formulation isolates the operational contribution of decontamination capacity and supports prioritisation in terms of staffing/equipment and pre-incident planning. The numerical results are summarised in

Table 6. Expected absorption steps within scenarios (selected starts).

	Base	Scenario A	ΔA	Scenario B	ΔB	Scenario C	ΔC
M1	3.931	3.931	+0.001	3.929	−0.002	3.949	+0.019
M3	3.375	3.383	+0.008	3.358	−0.017	3.394	+0.019
M5	2.750	2.750	+0.000	2.750	+0.000	2.763	+0.013
M6	2.250	2.300	+0.050	2.150	−0.100	2.263	+0.013
M8	1.000	1.000	+0.000	1.000	+0.000	1.000	+0.000
M9	1.500	1.500	+0.000	1.500	+0.000	1.525	+0.025

[31,32,33,34].

In order to provide a more realistic picture of the intervention (testing the case of a firefighter injury during an event where decontamination had to be repeated), we expand the analysis to include scenario C (re-work), in which we allow for a small probability of returning from the later state M9 → M8 (repeated decontamination after measuring the effectiveness of the decontamination agent). We parameterise it as p (M9 → M8) = 0.05, with the original departures from M9 being proportionally recalculated so that the row of the transition matrix remains stochastic [31,32,33,34].

The topology of the chain does not change otherwise, so the certainty of absorption into M11 remains 1.00, but the expected steps increase by an amount corresponding to the added feedback loop. With this scenario, we test how a minor “disruption of continuity” in work (re-work) extends the passage through the critical phases M8–M10 and whether the effect “carries over” to earlier starts via M6. The numerical results, including Δ against the baseline, are shown in Table 6 (scenarios A–C) [31,32,33,34].

Increasing the proportion of M6 → M8 (greater decontamination line capacity) reduces the estimated number of steps (−0.10 from M6 in scenario B), while reducing it increases the number of steps (+0.05 in scenario A). The certainty of completion (absorption into M11) remains at 1.00 in all scenarios [31,32,33,34].

Scenario C (re-work M9 → M8) was introduced with ε = 0.05 and a proportional adjustment of the remaining departures from M9. Expected steps from the main start M1 increased from 3.931 to 3.949 (+0.0188; +0.48%), with absorption remaining certain (B = 1.00). Expected visits to M8 will increase (re-work after technical intervention), while visits to M9 will not change significantly, as the new branch will only take effect after reaching M9. Operationally, this supports the maintenance of the backup capacity of the decontamination variant and ongoing quality control after technical operations. The result also shows that any minor intervention in the process will affect the overall management of the emergency [31,32,33,34].

5. Discussion

Validation of results: We validated the transition probabilities and resulting metrics in three steps. The first step is so-called documentation compliance. This involves a proposal for transitions and branching, that we compared with the intervention timeline (KOPIS extract and intervention report), which fixes the sequence of key events and decisions. This allowed us to verify that the proposed branches and their relative importance correspond to the actual course of events. The second step was expert review. The specified parameters were then consulted with key participants (intervention commander, territorial department control officer, regional control officer, chemical service manager). They confirmed that the relative “difficulty” of the branches (e.g., higher demands of technical measures for smooth decontamination) corresponds to real experience from the intervention. The final step was to ensure the consistency of the metrics. For scenarios A–C, we verified that the metrics behaved as expected: an increase in the proportion of M6 → M8 shortens the expected steps for starts often passing through M6 (B), while a decrease prolongs them (A), and the introduction of a small M9 → M8 feedback loop slightly increases the expected steps without changing the certainty of absorption into M11. These effects correspond to the numerical summary in Table 6. For conversion to indicative time, we interpret a “step” as a discrete shift between macrostates and use the relationship $E\left[\mathrm{kroky}\right]\times \bar{\tau }$, where $\bar{\tau }$ is the average time of one step estimated from the timeline for the M6–M9 section. This is an approximation for comparing scenarios, not an SLA.

Key findings: This study combines a process-level Petri net with an absorbing Markov chain to obtain decision-oriented indicators: certainty of absorption into a safe termination state and expected steps to termination. In the case of the cyclohexylamine incident from 2017, the analysis highlights a small set of intermediate activities with a high number of repeat visits and shows that the capacity of the decontamination line is a significant factor affecting duration. Scenario (C) also verified that even a slight influence in the form of repeated decontamination has an impact on the number of steps in the remediation process.

Relationship to previous work: Our approach complements discrete event simulation by providing closed-form summary metrics (expected steps, expected visits) and contrasts at the scenario level without the need to rerun full simulations. Similar response models based on Petri nets exist in safety-critical domains, but their application to road accidents involving hazardous materials remains sporadic. Our results extend this line by quantifying operational trade-offs in the area of decontamination.

Operational implications: Increasing the proportion of the M6 → M8 route (greater decontamination capacity) consistently reduces the expected steps for starts reaching M6, while the certainty of completion remains unchanged. In practice, this supports the prioritisation of personnel and equipment for the decontamination line and maintaining continuity in situations with a high expected number of visits. This model can also be used to verify the importance of repeated decontamination. Specifically, how the repetition of certain substeps affects us. In reality, this supports the fact that safety in the form of repeated decontamination after control measurements does not have a significant impact on the overall response process. This underlines the general fact that safety takes precedence over the speed of response.

Limitations: This study is an analytical single-case application of a PN → MC workflow to a documented cyclohexylamine release. Its goal is to reconstruct the response process, make the place-to-macro aggregation explicit, and derive decision-oriented metrics. We therefore do not claim statistical generalisation; rather, we pursue analytic generalisation of the method. The case was selected because a complete timeline and command communications were available, enabling transparent reconstruction and verification. The results emphasise structural features—notably decision gates and bottlenecks—that are plausibly transferable to comparable incidents.

Transition probabilities were derived from the incident timeline and expert elicitation (after-action review and consultation with the command team). Small perturbations of these estimates do not change the qualitative conclusions, although they can shift fine-grained metrics by a few hundredths of a step; this is consistent with the sensitivity analyses and the additional Scenario C (introducing a realistic re-work loop). Throughout, a “step” denotes a macro-transition between aggregated states. Mapping steps to time uses an average dwell time $\bar{\tau }$ estimated for the M6–M9 segment; this conversion is indicative, intended for comparing scenarios, and not a binding operational target or service-level agreement (SLA). With multi-incident datasets, time mapping can be refined phase-by-phase.

Data sources include internal Fire Rescue Service/Regional Operations and Information Centre (FRS/ROIC) records, which cannot be released in full. This imposes practical limits on public reproducibility, especially regarding detailed timelines. External researchers without privileged access may need to rely on publicly available incident records. To support reuse, we document the aggregation rules, provide pseudocode and parameterised matrices, and describe the probability-elicitation procedure so that other teams can apply the same workflow to their own data while respecting legal and ethical constraints on operational records.

Practical applicability of the study: In the current practice of the Fire and Rescue Service of the Czech Republic, post-review analyses are based mainly on a simplified SWOT analysis. Although this analysis captures the strengths and weaknesses of the intervention well, it lacks a process step-by-step, data-based view of which specific activities and decision points significantly shaped the course and duration of the incident resolution. The proposed framework (timeline → Petri net → Markov model) extends this practice with a transparent, repeatable analysis of the phases of the intervention and a scenario comparison of different procedures or capacity settings, including the identification of bottlenecks and points with the greatest impact.

At the level of the General Directorate of the Fire and Rescue Service of the Czech Republic (analytical activities department), the method can be used as a standardised workflow for selected events: normalising time records, converting them into semantic states, evaluating step sequences, and comparing scenarios. The output is specific recommendations for the future management of similar types of emergencies or targeted adjustments to tactical and technical standards. In corporate fire protection units (chemical/petrochemical, automotive, and other industries), the framework is suitable for preliminary planning, exercises, and internal audits of procedures: it allows for the comparison of personnel and material options, the timely detection of coordination bottlenecks, and reduction in the risk of partial consequential damage.

Future work: Future work will focus on expanding the database and external validation across multiple incidents and substances to verify the transferability of conclusions. At the same time, the conversion of operational records to a timeline (including annotations) will be standardised, which will increase reproducibility and speed up mapping to the model. The next step is to work more finely with time and capacities (taking into account dwell times, queues, and blockages) in order to assess bottlenecks and reinforcement effects more accurately. The model will be supplemented with the quantification of uncertainties and systematic sensitivity analysis, and a decision layer will be created above it to compare tactical options and allocate resources. On a practical level, we plan to prototype a tool for quick what-if comparisons and support for post-audit analyses and exercises. In parallel, the methodology will be generalised to other industrial and transport environments, and anonymised materials with scripts will be published in a repository to ensure transparency and repeatability.

6. Conclusions

This study presents a comprehensive framework for analysing interventions in chemical emergencies based on the conversion of a timeline into a Petri net and subsequently into a Markov model. The procedure was applied to a traffic accident involving a cyclohexylamine leak. The mapping between real activities, Petri net locations, and aggregated states is shown in a separate table, which increases transparency and repeatability. The transition rates are based on documented records and expert verification by direct participants in the intervention.

The results provide comprehensible metrics for passing through the intervention phases and allow for the testing of practically relevant variants. Strengthening the capacity of the decontamination line shortens the expected course of the intervention by units of hundredths of a step at frequently reached starting points. The opposite setting slightly prolongs the passage. The introduction of a small probability of returning from technical measures back to decontamination adds only a small delay and at the same time increases the decontamination load after technical operations. The certainty of the successful completion of the intervention remains unchanged. These effects are consistent with operational experience and show which parts of the process have the greatest leverage on the overall duration of the intervention.

From a practical point of view, the framework complements existing post-review approaches with quantitative, step-by-step evidence. It supports capacity planning, the setting of controls after technical operations, and targeted adjustments to tactical and technical procedures. The methodology can be used to analyse other events and substances, as well as for internal training and exercises, as it allows for the safe comparison of what-if scenarios without operational risk.

This study also has its limitations. It is based on a single case, and some of the parameters are derived from an informed estimate, which was subsequently verified. The conversion of steps to time is approximate and serves to compare scenarios. These limitations do not diminish the main benefit: the framework provides a reproducible and transparent method to derive decision-making information for intervention management from real data and operational knowledge. Future work will focus on expanding the database, refining the handling of time and capacities, and deploying the tool for routine post-review analyses and unit preparation.