Model of Sustainable Household Mobility in Multi-Modal Transportation Networks

Abstract

Nowadays, urban and suburban areas face increasing environmental pressures, and encouraging sustainable transportation behaviors at the household level has become crucial. This paper presents a model of a decision support system (DSS) for promoting sustainable household mobility choices in multi-modal transport networks. The system was modeled using an enhanced Petri Net approach, allowing for the dynamic representation of complex transport networks and multi-modal journey options. The model incorporated various sustainability factors. These were combined into a single environmental impact score, which was considered alongside travel time and cost in the route optimization process. Simulation results demonstrated the DSS’s capability to guide users toward more sustainable mobility choices. The model also showed potential as a tool for policymakers to assess the impact of various sustainable transportation initiatives and infrastructure investments. This paper discussed the versatile applications of the system. It also addressed the limitations of Petri Net models in transportation systems and suggested future research directions.

1. Introduction

Sustainable household mobility has emerged as a critical factor in addressing global environmental challenges and improving the quality of life in urban areas [1]. The transport sector is one of the largest contributors to greenhouse gas emissions and noise pollution, with a substantial portion coming from personal vehicle use [2].

Despite the recognized importance of sustainable household mobility, achieving widespread adoption of sustainable transportation choices remains a challenge. Factors such as convenience, habits, infrastructure limitations, and lack of information often hinder individuals from making more sustainable mobility decisions [3]. This underscores the need for innovative approaches that can guide and support households in adopting more sustainable transportation behaviors.

The systematic review [4] evaluates synthetic data models for urban mobility, which generate artificial data resembling original datasets in structure and statistics while omitting sensitive information. The review offers a structured comparative overview of this diverse and active research area, with a special focus on the practical applicability of these models for household mobility purposes.

The four-step model is a traditional framework used in mobility estimation. This method employs various regression and utility models to consider factors like population and trip attributes affecting travel demand [5]. However, this model has notable shortcomings, such as not accounting for land use density and socioeconomic dynamics [6], prompting researchers to explore alternative traffic forecasting methods.

One such alternative is the Markov Chain model, which has gained popularity. For example, in the paper [7], a hidden Markov Chain model for individual users, achieving accuracy levels comparable to those of recurrent neural networks is developed. The two-step Markov Chain model that effectively replicates the spatiotemporal patterns of daily movements is proposed in [8].

Activity-based models have emerged to address the limitations of the four-step model by focusing on travel behaviors driven by specific activities. These models predict urban traffic flows by estimating the activities people will engage in, including the timing, location, and duration [9]. Within activity-based models, utility-based and rule-based models are two predominant types. In utility-based models, individuals are assumed to choose the travel option that maximizes their utility, incorporating utility equations to explore the interaction between activity-travel patterns and various influences, like land use and policy measures [10,11,12,13].

Nowadays, machine learning methods are very actively used for mobility modeling. The paper [14] utilized regression and decision tree models to forecast the mobility of individuals, determining activity locations based on characteristics of both activities and individuals. Methods such as support vector machines and random forest models have become popular in predicting activity-travel patterns [15,16,17].

Deep learning, a subset of machine learning, excels in identifying complex relationships between variables. Huang et al. [18] integrated a recurrent neural network model to create synthetic data for mobility. Sakuma et al. [19], for dimension reduction, developed another model instead of a variational encoder. The paper [20] utilized a bidirectional long short-term memory model to generate mobility data, which was validated by several metrics at the aggregate level. The paper [21] described the same tools for data generation and assessed the results based on various distributions, such as user trip length and location.

Badu-Marfo et al. [22] applied a generative adversarial network to synthesize people’s demographics and trajectories. The integration of long short-term memory into the modeling framework to generate mobility data incorporating spatial and temporal trajectory information is discussed in [23]. Jiang et al. [24] introduced an approach for generating “continuous” trajectories, evaluated using metrics like travel distance and location frequency. The generation of images on the base of location points with their subsequent processing by image-generation algorithms for mobility synthesis is discussed in [25].

The transformer model for generating household mobility was studied in [26], and its comparative effectiveness for the prediction of individuals’ next locations is discussed in [27].

To address the gaps in understanding residential relocation behavior, the study [28] developed a joint model analyzing the reasons for moving and duration of stay, providing essential insights into household mobility dynamics and predicting land use patterns. The study [29] employed a geographically localized interpretable model-agnostic explanation with a two-layered long short-term memory model, offering state-level interpretations of deep neural networks. The study [30] investigated the impact of transport infrastructure connectivity on conflict resolution using machine learning and natural experiment methodologies. The paper [31] introduced a blockchain-based smart contract mechanism for vehicular traffic sensing using a two-stage game approach. The paper [32] explored an adaptive agent decision model in uncertain transportation environments. The paper [33] introduced a spatio-temporal approach using a transformer model to enhance traffic prediction accuracy in metro and access networks, which are complicated by user behavior and geographical characteristics. The model employs a multi-head attention mechanism to grasp long-term temporal correlations and a graph convolutional layer for capturing short-term spatial correlations between users.

While existing research has made significant strides in modeling and optimizing urban mobility, several critical gaps remain, which this paper aims to address. Most current models focus primarily on time and cost optimization, with limited consideration of comprehensive environmental impacts.

While some models consider multiple transportation modes, few offer a truly integrated multi-modal route optimization that accounts for transfers and mode-specific characteristics. Existing systems often fail to adequately balance system-wide optimization with individual user preferences. Another significant gap is the lack of comprehensive decision support. Most existing tools focus on either individual route planning or system-wide analysis, but rarely both. Few current models adequately incorporate new mobility paradigms such as shared mobility and Mobility as a Service (MaaS).

This paper lays the groundwork for integrating these concepts into a unified modeling framework. By addressing these gaps, this study aimed to propose a more effective and sustainable approach to urban mobility modeling and decision support. This paper presents a novel approach to addressing this challenge through a heuristic-based decision support system designed to promote sustainable household mobility choices in transport networks. The proposed Petri Net-based heuristic DSS offers a novel solution that balances individual needs, system efficiency, and environmental considerations in a way that existing models have yet to achieve.

The structure of this paper has five sections. Section 2 presents the description of the household mobility system model, the heuristic approach for decision-making, and the methodology for transforming the transport system graph into a Petri Net model. Section 3 presents the application of the proposed model through a simulation example and analyzes the outcomes. Section 4 follows, exploring the versatile applications of the Petri Net-based decision support system, methods for integrating user feedback, and strategies for optimizing real-time data integration. It also addresses the limitations of Petri Nets in transportation systems and suggests future research directions. Section 5 accumulates contributions of this research, emphasizing its potential impact on sustainable urban mobility.

2. Materials and Methods

Household mobility models are essential for regional development and the enhancement of transportation systems. They enable policymakers and urban planners to identify improvement areas, optimize resource allocation, and implement targeted interventions that support regional growth and livability by aligning transportation systems with residents’ needs while advancing economic and environmental goals.

2.1. Description of the Household Mobility System Model

In this paper, the household mobility model was designed to represent complex urban and inter-urban public transport networks, incorporating various modes of transportation and their interconnections. The model was based on a directed finite graph structure, which allows for a comprehensive representation of the transit network’s topology and characteristics.

The transit system is formally defined as pair $D=(V,A)$, where $V=\left\{v_i\right\}, i=\overline{1,n}$ is a finite set of vertices representing transportation nodes, such as bus stops, train stations, airports, and other passenger terminals. $A=\left\{a_j\right\}, j=\overline{1,m}$ is a finite set of arcs representing the transportation links between different terminals.

Each arc $a_j$ in the set $A$ is associated with multiple attributes, including travel time $t_j$, travel cost $c_j$, environmental impact factor $e_j$, mode of transportation ${\mu }_j$, and frequency of service $f_j$.

The environmental impact factor $e_j$ is an attribute that quantifies the ecological footprint of each transportation segment: energy consumption per passenger-kilometer, greenhouse gas emissions, land use impact, noise pollution and others.

To account for the multi-modal nature of urban transit systems, our model incorporates various transportation modes, including:

• Walking;
• Cycling (private and public bike-sharing systems);
• Bus (local and inter-city);
• Tram;
• Metro/Subway;
• Train (light rail and heavy rail);
• Taxi and ride-sharing services;
• Private car.

The model also includes transfer points where passengers can switch between different modes of transportation. These transfer points are represented as special vertices in the graph, with associated transfer times and costs.

The household mobility model serves as the foundation for our heuristic-based decision support system. It provides a comprehensive representation of the transit network, enabling the evaluation of multiple route alternatives based on various criteria, including travel time, cost, and environmental impact. This model structure allows for the incorporation of real-world complexities and constraints, making it suitable for analyzing and optimizing sustainable mobility choices in diverse urban environments.

2.2. Explanation of the Heuristic Approach for Decision-Making

The decision-making process for selecting optimal routes in the household mobility system is based on a heuristic approach. This method was designed to balance computational efficiency with the ability to find high-quality solutions, making it suitable for real-time applications in complex transit networks.

The heuristic approach follows these key steps:

Generation of alternative routes:

Based on the origin and destination points provided by the user, the system generates a set of feasible route alternatives $R=\left\{r_{ij}\right\}$, where $i=\overline{1,n}$ represents different route options, and $j=\overline{1,m}$ represents the transport levels within each route.

For example, in Figure 1, some hypothetical alternatives for travel from origin point X to destination point Y in the regional transportation system are shown. The figure shows five distinct route alternatives, each represented by a horizontal line with different segments indicating various modes of transportation and transfer points:

• Alternative 1. This is the simplest route, consisting of a single segment representing travel by private car directly from X to Y.
• Alternative 2. This route involves five levels of transit: walking from point X, taking a local bus, transferring to an intercity bus, transferring back to a local bus, and walking to destination Y.
• Alternative 3. This route has four levels of transit: walking from point X, taking a local bus, transferring to a train, and taking a taxi to destination Y.
• Alternative 4. This route consists of five levels of transit: walking from point X, taking a local bus, transferring to a train, transferring to a tram, and walking to destination Y.
• Alternative 5. This route involves six levels of transit: walking from point X, taking a local bus, transferring to a train, walking to a bike-sharing station, using a public bicycle, and walking to destination Y.

2.3. Decision-Making Process

The decision-making process in the transportation system has been enhanced by incorporating environmental factors alongside traditional criteria such as travel time and cost. Users can now select their primary preference: minimizing travel time, minimizing cost, or minimizing environmental impact.

The process begins with the input of travel demand, specifying the origin point $X$ and the destination point $Y$. This establishes the basis for generating potential routes between the two points.

The decision support system generates a comprehensive matrix of alternative routes $R=\left\{r_{ij}\right\}$, where each route consists of various levels of transit and different transport modes. This step considers all possible combinations of transportation options available within the system.

The next step involves defining the criterion of preference $CP$, which includes three potential factors:

• Cost of travel $c_{ij}$;
• Travel time $t_{ij}$;
• Environmental impact $e_{ij}$.

Users can select their primary preference among these factors based on their individual priorities for the journey.

For each alternative route $i=\overline{1,n}$, the total value of the $CP$ is calculated based on the user’s selected preference. The calculations involve summing up the individual values for each segment $j$ of the route:

$${CP}_i=\left\{\begin{array}{c}{\sum }_{j=1}^m{c}_{ij}, if cost is selected\hfill \\ {\sum }_{j=1}^m{t}_{ij}, if time is selected\hfill \\ {\sum }_{j=1}^m{e}_{ij}, if environmental impact is selected\hfill \end{array}\right.,$$

where $c_{ij}, { t}_{ij}$, and $e_{ij}$ represent the cost, travel time, and environmental impact for segment $j$ of route $i$, respectively.

The DSS compares the calculated $CP$ values for all alternative routes based on the user’s primary preference. This comparison is crucial for identifying the most efficient, cost-effective, or environmentally friendly route.

The DSS selects the optimal route ${CP}_{opt}$, which is the route that minimizes the $CP$ value based on the selected preference:

$${CP}_{opt}=\mathrm{m}\mathrm{i}\mathrm{n}\left({CP}_i\right|i=\overline{1,n})$$

(1)

This route is considered the best option for the traveler, balancing cost, time, and environmental impact according to the specified preference. The selected optimal route is then outputted as the final decision, providing the traveler with a recommended path from $X$ to $Y$.

The system can also consider secondary criteria to ensure balanced solutions by calculation of total values:

$${CP}_i={\sum }_{j=1}^m{{(w}_{c}c}_{ij}+{w_{t}t}_{ij}+{w_{e}e}_{ij}),$$

where $w_c$, $w_t$, and $w_e$ indicate weights for cost, time and environmental impact, respectively.

The route with the minimum ${CP}_i$ value that satisfies all criteria thresholds is determined by expression (1).

Figure 2 illustrates the heuristic decision-making process for selecting optimal routes in a household mobility system. The flowchart demonstrates a step-by-step approach to route selection, incorporating user preferences and system constraints.

The process begins with the generation of a matrix of alternative routes based on the origin and destination points provided by the user. This matrix represents various possible travel options, including different modes of transportation and transfer points.

Next, the user defines their criterion of preference for route selection, choosing between cost, time of travel, environmental impact, or balanced solution. This preference guides the subsequent evaluation of route alternatives.

The system then calculates the total value of the chosen criterion of preference for each alternative route, depending on the user’s preference.

Finally, the decision support system compares all transport alternatives and selects the optimal route. This is achieved by identifying the route with the minimum criterion of preference value, represented by Equation (1).

This heuristic approach allows for efficient decision-making in complex transport networks, balancing user preferences with the multitude of available route options. The process can be easily adapted to include additional criteria or constraints, making it a flexible tool for transportation planning and individual travel decisions.

The primary aim of the proposed decision support system model is to assist decision-makers in the planning and design phases of urban and regional mobility systems. This model is specifically tailored to support the initial development stages, where comprehensive analysis and strategic planning are crucial for optimizing transportation networks. By providing a robust framework that integrates key sustainability and efficiency metrics, the model enables decision-makers to make informed choices that align with long-term urban development goals.

While the model is designed with a focus on high-level decision-making, it also lays the groundwork for future enhancements that can incorporate real-time user feedback. Such feedback mechanisms, including route rating systems and adaptive sustainability weighting based on user inputs, can be integrated into the model in subsequent phases. These future developments will allow the DSS to evolve into a more interactive and user-centric tool capable of dynamically adjusting to changing user preferences and real-world conditions.

2.4. Detailing the Incorporation of Sustainability Factors into the Criteria of Preference

To promote sustainable mobility choices, we can include different environmental sustainability factors alongside the conventional metrics of travel time and cost.

The main sustainability factors incorporated into the $CP$ are as follows:

• Greenhouse gas emissions ($GGEs$) are calculated as the estimated CO₂ equivalent emissions for each transportation segment based on the mode of transport and distance traveled. This factor is expressed in grams of CO₂e per passenger-kilometer.
• Energy efficiency ($EE$) represents the energy consumption of each transportation mode, measured in megajoules per passenger-kilometer.
• Land use impact ($LUI$) is considered to be the land area required for each transportation mode, including infrastructure such as roads, parking spaces, and stations. This factor is normalized to a scale of 1–10, with lower values indicating more efficient land use.
• Noise pollution impact ($NPI$) of each transportation mode is quantified using a scale of 1–10 based on average decibel levels and duration of exposure.
• Air quality impact ($AQI$) accounts for local air pollutants such as particulate matter, nitrogen oxides, and volatile organic compounds. It is normalized to a scale of 1–10, with lower values indicating less pollution.

These sustainability factors are combined into a single environmental impact score $e_{ij}$ for each route segment $j=\overline{1,m}$ of $i=\overline{1,n}$ transport alternatives:

$$e_{ij}=w_{1}GGE+w_{2}EE+w_{3}LUI+w_{4}NPI+w_{5}AQI,$$

where $w_l, l=\overline{\mathrm{1,5}}$ are weights assigned to each factor, which can be adjusted based on local environmental priorities or user preferences.

In accordance with the goals and objectives of those making decisions, any set of core indicators for sustainability [34,35] can similarly be set as parameter $e_{ij}$.

Users can customize the weights to reflect their personal preferences and constraints. This approach aims to strike a balance between individual needs and broader environmental goals, promoting sustainable household mobility in a user-friendly and adaptable manner.

2.5. Methodology for Transforming the Transport System Graph into a Petri Net Model

To effectively model the dynamic and concurrent nature of household mobility, we employed a transformation methodology that converted our initial graph-based representation into a Petri Net model [36]. This transformation allows for a more nuanced representation of the system’s behavior, including time-dependent aspects and the synchronization of different transportation modes.

The Petri Net is formally defined as follows:

$$PN=(P,T,I,O,M,\tau ),$$

where $P=\left\{p_s\right\}$ is a set of $s$ places, $T=\left\{t_z\right\}$ is a set of $z$ transitions, $I:T\to P$ is the input function, $O:P\to T$ is the output function, $M$ is the marking (token distribution), and $\tau$ is the set of time delays associated with transitions $\left\{t_z\right\}$.

The transformation process followed these steps:

• Vertex transformation. Each vertex $v_i$ in the original graph $D=(V, A)$ was transformed into a place $p_i$ in the Petri Net. These places represent the states or conditions in the transit system, such as the presence of a passenger at a particular station or stop;
• Arc transformation. Each arc $a_j$ in the original graph was transformed into a transition $t_j$ in the Petri Net. These transitions represent the events or actions in the system, such as a passenger moving from one station to another using a specific mode of transport;
• Token definition. Tokens in the Petri Net represent passengers or transportation units moving through the system. The initial marking $M_0$ defines the initial state of the system;
• Input and output functions. We defined input function $I:T\to P$ and output function $O:P\to T$ to describe the relationships between transitions and places in the Petri Net.
• Time association. To model the temporal aspects of the transit system, we associated each transition $t_j$ with a time delay ${\tau }_j$, representing the travel time for the corresponding arc in the original graph;
• Scheduling integration. To incorporate timetabled services, we introduced special transitions controlled by time-based activation rules, representing the arrival and departure of scheduled transportation services;
• Multi-modal connections. Transfer points between different modes were modeled using special places and transitions that represent the process of changing between transportation modes;
• Environmental impact integration. We associated each transition with an environmental impact factor $e_j$, corresponding to the sustainability metrics of the original graph arcs.

The transformation from a graph to a Petri Net model enhanced our ability to analyze and optimize route choices, considering both the structural aspects of the transit network and its dynamic behavior. This approach provided a more robust foundation for our heuristic-based decision support system, enabling more accurate and realistic modeling of sustainable mobility options in complex urban environments.

2.6. Set of Basic Components for the PN Model

Based on [37], we can describe a set of basic components for the PN model used in this transportation system. These elementary networks serve as the building blocks for constructing more complex models of large-scale transportation systems. The class of elementary networks includes the following:

• Simple transition ${PN}_T$ is represented by a single transition with one input place and one output place (Figure 3a). This is the most basic element, representing a simple action or event in the system;
• Multiplier ${PN}_M$ consists of a transition with one input place and two or more output places (Figure 3b). When a token enters this transition, it is duplicated, resulting in two tokens in the output. This can represent processes where a single input leads to multiple outcomes or paths;
• Integrator ${PN}_I$ with multiple input places and one output place (Figure 3c). A token appears in the output place if there is at least one token in any of the input places. This network is particularly useful for modeling in transportation systems the merge points in transportation networks where multiple routes converge;
• Generator ${PN}_G$ represented by a transition with no input place and one output place (Figure 3d). This element can generate tokens without requiring input. It is useful for modeling sources of passengers, vehicles, or other entities entering the system;
• Absorber ${PN}_A$ consists of a transition with one input place and no output place (Figure 3e). This can represent endpoints in the system where tokens are removed, such as final destinations;
• Generator of schedules ${PN}_{GS}$ is a specialized network for modeling public transport with fixed schedules (Figure 3f). It consists of three places, $p_0,p_1,p_2$, and two transitions, $t_1,t_2$. Place $p_0$ generates tokens according to a schedule (representing vehicle arrivals). Place $p_1$ represents transportation requests. Transition $t_1$ is triggered when there are tokens in both $p_1$ and $p_2$ positions, representing the synchronization of a transport request with a scheduled vehicle arrival.

This set of basic components for the PN provides a flexible tool for modeling various aspects of a transportation system:

• Simple transitions for basic movements or actions;
• Duplication for representing branching paths or multiple outcomes
• Generators for modeling entry points of passengers or vehicles;
• Absorbers for modeling exit points or final destinations;
• Schedule generators for incorporating timetabled public transport services.

By combining these elementary networks, it is possible to construct complex models that accurately represent the dynamics of large-scale transportation transit systems, including multi-modal transfers, scheduled services, and passenger flows.

The modular nature of the proposed Petri Net model is fundamental to its design and functionality. By breaking down the complex transportation network into smaller, manageable modules, each representing a specific mode of transport or a segment of the transit system, we could effectively manage the potential issue of state space explosion. These modules could be independently analyzed and optimized before being integrated into the overall network, ensuring both scalability and flexibility in the model’s application. This modular structure also allows for easier updates and modifications, as individual components can be adjusted without affecting the entire system.

2.7. Transition Delay Generation in the Petri Net Model

In the Petri Net model for transportation systems, transition delays play a crucial role in representing the dynamic aspects of travel times and other time-dependent factors. While this paper primarily focused on deterministic delays calculated from travel times, costs, and environmental impacts, it is important to note that in more complex implementations, these delays can be stochastic in nature. Transition delays can be generated using various probability distribution laws, such as normal, exponential, or Weibull distributions, to more accurately reflect the inherent variability and uncertainty in transportation systems. For instance, travel times on a particular route segment could follow a normal distribution with parameters based on historical data. Alternatively, delays can be determined by functions that describe the dependencies of changing quantities represented by these transitions. For example, a function could model how travel time changes based on traffic density, time of day, or weather conditions. This functional approach allows for a more dynamic and context-sensitive modeling of transition delays, capturing the complex interrelationships between various factors in the transportation network. The flexibility to incorporate both stochastic and functionally determined delays enhances the Petri Net model’s capability to represent real-world transportation scenarios more accurately, thereby improving the decision support system’s recommendations.

2.8. Description of the Simulation Tools and Software Used

To implement and evaluate a heuristic-based decision support system for sustainable household mobility choices, specialized software tools can be used [38]. This comprehensive suite of tools and software can be used for the creation of a robust simulation environment for our decision support system, allowing for detailed modeling of transit networks, accurate representation of system dynamics, and effective integration of sustainability factors in route optimization.

3. Results

In this section, we demonstrate the application of the modular approach through a case study that illustrates how larger modules of the Petri Net model architecture can be formed for each mode of transport within a multi-modal system. By leveraging the modular structure, we can construct a comprehensive model that retains clarity and manageability, even as it encompasses the diverse elements of urban/rural transportation. This modular design not only simplifies the modeling process but also enhances the model’s adaptability to various scenarios and transportation environments.

The Petri Net model has proven to be a powerful tool for realizing the proposed decision-making approach in transport networks.

The PN model’s strength lies in its ability to represent both the structural and behavioral aspects of transportation systems. It captures the static network layout through its places and transitions while also modeling the dynamic flow of passengers, vehicles, and information through the system. This dual capability is crucial for implementing our decision support system (DSS), as it allows for the simultaneous consideration of network topology and real-time system states.

The Petri Net model serves several key functions:

• The PN structure allows for a comprehensive representation of all possible routes, including multi-modal options, transfers, and scheduling constraints;
• Transitions in the PN model represent decision points where the DSS can evaluate and choose between different path options based on the current system state and user preferences;
• By associating time delays and costs with transitions, the PN model accurately captures the temporal and economic aspects of different route segments, which is essential for calculating the criterion of preference;
• The inclusion of schedule generators in the PN model enables the accurate representation of timetabled services, which is crucial for the realistic modeling of public transportation options;
• The token distribution in the PN provides a real-time representation of the system state, allowing the DSS to make decisions based on current conditions;
• The structure of the PN facilitates the implementation of heuristic algorithms for route selection, allowing for efficient processing even in large-scale systems.

The following results demonstrate how this PN-based approach effectively realizes our proposed decision-making methodology, providing a robust foundation for the DSS in complex transportation environments.

Let’s construct a directed graph for the previously discussed hypothetical case (Figure 2) with five mobility alternatives in a multi-modal transport network. Figure 4 illustrates such a directed finite graph. The vertices represent transportation nodes such as bus stops, train stations, and airports, while the arcs represent the transportation links between these nodes. Each arc is associated with attributes such as travel time, cost, and environmental impact, providing a comprehensive view of the transit network’s topology and characteristics.

The transport network graph presented in Figure 4 can be converted, using the previously described basic components (Figure 3), into a PN shown in Figure 5.

Figure 5 depicts the PN model derived from the transportation graph. The PN consists of basic components, like simple transitions, multipliers, integrators, generators, absorbers, and schedule generators. These components serve as the building blocks for constructing a more complex Petri Net model, accurately representing the dynamics of large-scale transportation systems, including multi-modal transfers, scheduled services, and passenger flows.

We can formulate the following rules for transforming the transport network graph into the Petri net:

• Node transformation. Each node (vertex) in the transport network graph is transformed into a place in the Petri net. These places represent locations or states in the transportation system, such as bus stops, train stations, or transfer points;
• Edge transformation. Each edge (arc) in the transport network graph is transformed into a transition in the Petri net. These transitions represent the movement or action of traveling between two locations;
• Direction preservation. The direction of the edges in the graph is preserved in the Petri net. Input places connect to transitions, which then connect to output places, maintaining the flow direction of the original graph;
• Multi-modal connections. Where multiple edges connect in the graph (representing different transportation modes or routes), the Petri net uses multiplier or integrator structures (as described in Figure 3c of this paper) to represent these connections;
• Start and end points. The start point of the network is represented by a generator transition in the Petri net (no input place, one output place). The end point of the network is represented by an absorber transition in the Petri net (one input place, no output place);
• Transfer points. Nodes in the graph where transfers between different modes are possible are represented by more complex structures in the Petri net, potentially using multiple places and transitions to model the transfer process;
• Scheduled services. For parts of the network with scheduled services (like trains or buses), the Petri net incorporates schedule generator structures (as shown in Figure 3f of this paper);
• Attribute association. The attributes associated with edges in the graph (such as travel time, cost, and environmental impact) are associated with the corresponding transitions in the Petri net;
• Tokens. While not visible in the static representation, the Petri net model would use tokens to represent passengers or vehicles moving through the system.

These rules provide a framework for translating the structural and behavioral aspects of the transport network from a simple graph representation to a more complex and dynamic Petri net model.

In line with standard practices in modeling, calibration and validation are crucial steps that ensure the accuracy and reliability of the proposed model. For Petri nets, these processes have been well-documented in numerous studies, such as [39,40,41,42]. Given the extensive literature on this subject, the calibration and validation of Petri net models were not elaborated on in this article. However, it is important to note that these processes were conducted following established methodologies [39].

To calculate the delay of transitions in the Petri Net model using different criteria of preference (cost, time, environmental impact, or a balanced solution), we followed specific steps tailored to each criterion.

When cost is the primary criterion of preference, the delay of transitions can be calculated based on the travel cost associated with each transportation segment ${\tau }_j=c_j, \forall j$. When time is the primary criterion, the delay of transitions is directly calculated from the travel time of each transportation segment ${\tau }_j=t_j, \forall j$. When environmental impact is the primary criterion, the delay of transitions is calculated based on the environmental impact factor associated with each transportation segment ${\tau }_j=e_j, \forall j$. When a balanced solution is preferred, a weighted sum of cost, time, and environmental impact is used to calculate the delay of transitions. We assigned weights to each factor to reflect their relative importance:

$${\tau }_j=w_1{c}_j+w_2{t}_j+w_3{e}_j \forall j$$

(2)

Normalization is the process of scaling different metric values to a common range, typically from 0 to 100, to allow for easier comparison. This process ensures that metrics with different units and ranges can be compared directly. Below is a detailed explanation of the step-by-step normalization process for each metric:

For each metric, identify the minimum and maximum values across all routes. These values will be used to scale the data.

Apply the normalization formula for metrics where a lower value is better (travel time, cost, environmental impact, balanced solution):

$$Nomalized Value=\left(1-{\displaystyle \frac{Actual Value-Min Value}{MaxValur-Min Value}}\right)\times 100$$

Example of Modeling

For the graph of alternative mobilities depicted in Figure 2, a simulation is performed using the Petri net depicted in Figure 5.

The simulation results for all transportation alternatives are shown in

Table 1. Results of simulation.

Metric	Route 1	Route 2	Route 3	Route 4	Route 5
Travel time (minutes)	49	64	51	61	91
Travel cost (USD)	26	34	81	51	46
Environmental impact (units)	61	64	55	48	36
Balanced solution	71.4	48.7	44.1	62.2	54.5

. The balanced solution is defined in the clause of equal weighting coefficients in Formula (2)

The radar chart of normalized values for all alternative analysis criteria (cost, time, environmental impact, and balanced solution) is shown in Figure 6.

Analysis of normalized values for a balanced solution shows the following:

• Route 3. Highest normalized balanced solution score of 100, indicating the best overall performance across most metrics;
• Route 2. A normalized balanced solution score of 82.74, performing well in travel cost but weaker in environmental impact;
• Route 5. A normalized balanced solution score of 61.65, with strengths in cost and environmental impact;
• Route 4. A normalized balanced solution score of 33.63, showing balanced performance in travel time, cost, and environmental impact;
• Route 1. A normalized balanced solution score of 0, indicating the lowest overall performance across most metrics when compared to other routes.

4. Discussion

4.1. Applications of the PN-Based DSS in Urban Mobility

The Petri Net model integrated into a DSS for sustainable household mobility choices offers a versatile and powerful tool for addressing various challenges in the transportation domain. This subsection explores several key use cases where this system can be applied effectively.

One of the primary applications of this DSS is in optimizing daily urban commutes. As cities grow increasingly complex and congested, commuters face a multitude of transportation options with varying impacts on time, cost, and the environment. The PN-based DSS can analyze these factors comprehensively, suggesting optimal routes that balance efficiency with sustainability. For instance, it might recommend a combination of public transit and cycling that reduces both travel time and carbon emissions compared with driving, thereby promoting more sustainable urban mobility patterns.

Large-scale events, such as concerts, sports matches, or festivals, often create significant transportation challenges. The DSS can be employed by event organizers to develop efficient and sustainable transportation plans. By modeling the influx of attendees from various locations, the system can recommend the most effective combination of public transit services, shuttle buses, and pedestrian routes. This approach not only eases congestion but also minimizes the environmental impact of large gatherings.

For the tourism sector, the DSS can enhance visitors’ experiences while promoting sustainable travel. Tourists often wish to explore multiple attractions within a limited timeframe. The PN model can generate itineraries that optimize sightseeing opportunities while favoring eco-friendly transportation modes. This might include suggesting a mix of walking tours, bicycle rentals, and public transit options, thereby reducing the reliance on taxis or rental cars and decreasing the tourism industry’s carbon footprint.

In crisis situations such as natural disasters or large-scale accidents, efficient evacuation and emergency response are crucial. The PN-based DSS can model various evacuation scenarios, considering factors like road capacity, public transit availability, and potential bottlenecks. This allows emergency planners to develop more effective response strategies, potentially saving lives and reducing the impact of disasters.

City planners and policymakers can use the proposed model for analysis of efficiency of transport network and its ecological impact and its impact on householder mobility for proposed infrastructure projects or policy changes. By simulating different scenarios, such as the addition of new bus routes or the implementation of congestion charging, planners can predict the effects on traffic flow, public transit usage, and overall environmental impact. This data-driven approach can lead to more informed decision-making in urban development.

While the focus of the described system is on household mobility, the principles can be extended to freight transportation. Logistics companies can use a similar PN-based DSS to optimize delivery routes, considering factors like traffic patterns, vehicle capacity, and environmental impact. This could lead to more efficient supply chains and reduced emissions in the freight sector.

As Mobility as a Service (MaaS) platforms become more prevalent, the PN model can serve as a backend system for integrating various transportation services. It can help MaaS providers offer users optimal multi-modal journey plans that consider real-time data on service availability, costs, and environmental factors, thereby enhancing the overall efficiency of urban mobility systems.

In light of public health concerns, such as pandemics, the DSS can be adapted to include health risk factors in its decision-making process. It could suggest routes and modes of transport that minimize exposure risks while still maintaining efficiency and sustainability, helping to create resilient transportation systems in times of health crises.

4.2. Integrating User Feedback into the DSS

Integrating user feedback into the DSS with the described PN model can significantly enhance its effectiveness and adaptability. There are some directions on how user feedback can be incorporated into the DSS:

• Dynamic weight adjustment for different factors in calculating the balanced solution. User feedback can be used to dynamically adjust these weights. For example, if users consistently prefer routes with lower environmental impact despite longer travel times, the system could automatically increase the weight of the environmental factor;
• Route rating system implementation where users can score their journey after completion. This feedback can be associated with specific transitions in the PN model. Transitions with consistently high ratings could have their “cost” reduced in future route calculations, making them more likely to be selected;
• Real-time updates that users could provide as feedback on conditions not captured by the system’s sensors, such as unexpected congestion or service disruptions. This information can be used to temporarily adjust the delay times ${\tau }_j$ of affected transitions in the PN model;
• Personalized preferences (e.g., preference for cycling over bus travel) can be translated into personalized weights or additional place-transition pairs in their individual PN model instance;
• Incorporation of a machine learning algorithm that analyzes patterns in user feedback and journey choices. This could lead to refinements in the heuristic approach used for route selection;
• New route or connections suggestions by users. These could be modeled as new transitions or places in the PN and initially given a probationary status until validated by sufficient positive user feedback.
• Accessibility feedback by users could provide feedback on the accessibility of different route segments, which could be incorporated as an additional attribute of transitions in the PN model;
• Environmental impact verification by users could confirm or contest the environmental impact scores of different route segments based on their observations, helping to refine the accuracy of the $e_{ij}$ values in the model;
• Transfer point optimization on the base of user feedback on the ease of transfers between different modes of transport. This information could be used to adjust the modeling of transfer points in the PN;
• Seasonal variations from user feedback on how routes perform in different seasons or weather conditions. This could be used to create season-specific versions of the PN model.

By integrating these forms of user feedback, the DSS can continuously improve its accuracy and relevance, making it more responsive to real-world conditions and user preferences. This adaptive approach would enhance the system’s ability to provide truly optimal and user-friendly sustainable mobility solutions.

4.3. Optimizing Real-Time Data Integration in a PN-Based DSS for Dynamic Transportation Management

In the rapidly evolving landscape of urban mobility, the ability to integrate real-time data into decision-making processes is paramount. By enhancing the system’s responsiveness to dynamic conditions, we can significantly improve the accuracy and relevance of sustainable mobility recommendations.

The foundation of this optimization lies in the inherent flexibility of the Petri Net model. PNs are well-suited for representing complex, concurrent systems, making them ideal for modeling the multifaceted nature of urban transportation networks. However, to fully use this potential, we must implement a robust framework for real-time data integration.

The implementation of a distributed sensor network across the transportation infrastructure can be proposed for this purpose. This network would include GPS trackers on public transit vehicles, traffic flow sensors, air quality monitors, and crowdsourced data from user smartphones. Each sensor would be associated with relevant places or transitions in the PN model, providing a continuous stream of real-time data.

To manage this influx of data, the deployment of edge computing nodes at key points in the transportation network can be recommended. These nodes would perform initial data processing and aggregation, reducing the burden on the central system and minimizing latency. The processed data would then be used to dynamically update the attributes of the PN model, such as the delay times associated with transitions.

A crucial aspect of this optimization is the implementation of a real-time token generation and consumption mechanism. In the context of our transportation PN, tokens represent travelers or vehicles moving through the system. By generating and consuming tokens based on real-time data, we can accurately model the current state of the transportation network. For instance, a sudden influx of passengers at a bus stop could be represented by an increase in tokens at the corresponding place in the PN.

To handle the complexity of real-time updates to the PN structure, the use of a layered model can be proposed. The base layer would represent the static infrastructure of the transportation network, while additional layers would model dynamic elements such as vehicle movements, passenger flows, and temporary disruptions. This layered approach allows for efficient updates to the model without constantly reconstructing the entire network.

Machine learning algorithms play a vital role in this optimized system. The implementation of predictive models that can anticipate near-future states of the transportation network based on historical data and current trends can be recommended. These predictions can be incorporated into the PN model as probabilistic transitions, allowing the DSS to make recommendations that account for likely future conditions.

To ensure the system can handle the computational demands of real-time data integration, the use of parallel processing techniques can be proposed. The PN model can be partitioned into subnetworks that can be processed simultaneously, with results aggregated to inform final decision-making. This approach significantly reduces computation time, allowing the DSS to provide timely recommendations even in large, complex transportation networks.

Data quality and reliability are critical concerns in real-time systems. The implementation of a data validation layer that uses statistical techniques and cross-referencing to identify and filter out anomalous or erroneous data can be recommended for this purpose. This ensures that only high-quality, reliable data are used to update the PN model.

To address the challenge of data gaps or temporary sensor failures, the use of data imputation techniques can be proposed. These methods would estimate missing values based on historical trends and data from nearby sensors, ensuring the continuity of the PN model even in the face of partial data loss.

User feedback remains a valuable source of real-time information. This feedback can be quickly incorporated into the PN model, providing an additional layer of real-time data that may not be captured by traditional sensors.

Optimizing real-time data integration in a PN-based DSS for transportation management requires a multifaceted approach. By combining advanced sensor networks, edge computing, machine learning, parallel processing, and adaptive modeling techniques, a system that provides highly accurate, timely, and relevant recommendations for sustainable urban mobility can be created. This optimized system would not only improve the efficiency of daily commutes but also contribute to broader goals of reducing environmental impact and enhancing urban livability. As cities continue to grow and evolve, such dynamic, data-driven approaches to transportation management will become increasingly crucial in creating smart, sustainable urban environments.

4.4. Limitations of PN in Transportation DSS

Petri Nets have emerged as a powerful modeling tool in the realm of DSS for transportation networks, offering a robust framework for representing complex, concurrent systems. However, like any modeling approach, Petri Nets come with their own set of limitations that must be carefully considered when applying them to real-world transportation scenarios.

One of the primary limitations of PNs in transportation modeling is their potential for state space explosion. As the complexity of a transportation network increases, the number of possible states in the PN model can grow exponentially. This is particularly problematic in large urban areas with multiple interconnected transportation modes. The state space explosion can lead to computational challenges, making it difficult to analyze and simulate the model in real time, which is crucial for providing timely recommendations in a DSS. While the risk of state space explosion is a recognized challenge in Petri Net modeling, the modular approach we propose effectively mitigates this issue. By structuring the model into distinct modules, each representing different transportation modes or network segments, we significantly reduce the complexity of the overall system. This modular architecture facilitates the integration of new components and allows for more efficient management of the model’s state space. Moreover, it provides a clear framework for analyzing and optimizing each part of the network independently, further contributing to the robustness and scalability of the decision support system.

Another significant limitation is the static nature of traditional Petri Net structures. While PNs excel at modeling the topology and basic dynamics of a system, they can struggle to represent the highly dynamic and often unpredictable nature of transportation networks. Factors such as sudden traffic congestion, weather-related disruptions, or spontaneous events that affect traveler behavior are not easily incorporated into the basic PN framework. This can lead to a gap between the model and real-world conditions, potentially reducing the accuracy of the DSS recommendations.

Petri Nets also face challenges in representing complex decision-making processes. While they can model the flow of tokens (representing vehicles or passengers) through a network, they are less adept at capturing the nuanced decision-making factors that influence traveler choices. Factors such as personal preferences, comfort, or dynamic pricing are not easily integrated into the basic PN structure.

Another limitation lies in the representation of continuous processes. Transportation systems often involve continuous variables, such as the gradual buildup of traffic or the continuous flow of passengers. Petri Nets, being inherently discrete event models, have limitations in accurately representing these continuous processes. While extensions like hybrid Petri Nets exist, they add complexity to the model and may still not fully capture the nuances of continuous processes in transportation systems.

Petri Nets also face challenges in incorporating real-time data updates efficiently. While it is possible to update PN models with new data, doing so in real time for a large, complex transportation network can be computationally intensive. This limitation can affect the DSS’s ability to provide up-to-the-minute recommendations based on current conditions.

Recognizing these limitations is crucial for transportation planners and modelers. It allows for the development of strategies to mitigate these challenges, such as using hybrid modeling approaches, implementing advanced computational techniques, or developing new extensions to the basic PN framework.

4.5. Future Research Directions in PN-Based Transportation DSS

As urban environments continue to evolve and the demands on transportation systems grow increasingly complex, the need for sophisticated DSS becomes ever more critical. PN models have proven to be valuable tools in this domain, yet there remains significant potential for advancement.

One of the most promising areas for future research lies in the integration of artificial intelligence and machine learning techniques with PN models. While PNs excel at representing system structures and basic dynamics, they can be enhanced by AI’s predictive and adaptive capabilities. Future research could focus on developing hybrid models that combine the structural clarity of PNs with the predictive power of machine learning algorithms. These hybrid models could potentially overcome limitations in representing complex decision-making processes and adapting to dynamic, real-world conditions.

Another crucial direction for future research is the development of more sophisticated methods for handling uncertainty and stochasticity within PN models. Transportation systems are inherently unpredictable, with numerous variables affecting travel times, route choices, and system performance. Advanced stochastic PNs that can better represent and analyze these uncertainties could significantly improve the accuracy and reliability of transportation DSS. This might involve developing new mathematical frameworks for incorporating probabilistic elements into PN structures or creating novel simulation techniques that can efficiently handle stochastic processes within large-scale PN models.

The scalability of PN models for large, complex transportation networks remains a challenge that future research must address. As cities grow and transportation systems become more intricate, there’s a pressing need for methods that can efficiently model and analyze vast networks without succumbing to computational limitations. Research into hierarchical or modular PN structures could provide solutions, allowing for the decomposition of large networks into manageable sub-networks while maintaining overall system coherence. Additionally, exploring parallel and distributed computing techniques specifically tailored for PN-based transportation models could significantly enhance their scalability and real-time performance.

Another exciting direction for future research is the application of PN models to emerging transportation technologies and paradigms. As concepts like autonomous vehicles, Mobility as a Service (MaaS), and shared mobility become more prevalent, there’s a need for PN models that can accurately represent these new systems and their interactions with traditional transportation modes. Research into how to model and optimize these complex, multi-modal systems using PNs could lead to significant advancements in urban mobility management.

The future of research in PN-based transportation DSS is rich with possibilities. These advancements have the potential not only to improve the efficiency of urban mobility but also to contribute significantly to the creation of more sustainable, livable cities and regions.

To contextualize the results of the study, it is crucial to compare them with those from previous research in the field of sustainable urban mobility modeling. Studies such as [43,44] focused on optimizing transportation networks primarily through cost and time efficiency, often overlooking the environmental impact. The proposed model, in contrast, integrates sustainability factors directly into the decision-making process, providing a more holistic approach to mobility optimization.

Previous research has also explored machine learning-based methods for mobility prediction, as discussed in [45,46]. While these methods offer high predictive accuracy, they often require extensive computational resources and large datasets for training. The proposed heuristic-based approach offers an alternative that is computationally efficient and interpretable, making it suitable for real-time applications even in data-constrained environments.

The obtained results align with recent findings in the literature that emphasize the need for integrated multi-modal transportation solutions [47,48]. By incorporating a wide range of transportation modes and considering user preferences, our model contributes to the growing body of work that advocates for more user-centric and environmentally sustainable urban mobility solutions.

5. Conclusions

This paper presented a model of DSS for promoting sustainable household mobility choices in transport networks, utilizing an enhanced Petri Net model approach. The proposed system integrates environmental impact factors alongside traditional considerations of time and cost in transportation route selection, offering a multifaceted solution to the complex challenge of urban mobility.

The PN model demonstrated its effectiveness in representing both the structural and dynamic aspects of transportation systems. Its ability to capture the static network layout while also modeling the flow of passengers and vehicles provides a robust foundation for the DSS. The integration of sustainability factors into the decision-making process, including greenhouse gas emissions, energy efficiency, land use impact, noise pollution, and air quality, allows for a more comprehensive evaluation of mobility options.

The heuristic approach developed for route selection balances computational efficiency with the ability to find high-quality solutions, making it suitable for real-time applications in complex transit networks. The system’s flexibility in accommodating user preferences, whether prioritizing cost, time, environmental impact, or a balanced solution, enhances its practical applicability to diverse user needs.

The simulation results demonstrate the system’s capability to guide users toward more sustainable mobility choices. The normalized analysis of different routes showcases how the DSS can effectively compare and rank various transportation alternatives based on multiple criteria.

However, this research also acknowledges the limitations of PN models in transportation systems, such as potential state space explosion in large networks and challenges in representing highly dynamic or continuous processes. These limitations point toward future research directions, including the integration of artificial intelligence and machine learning techniques with PN models and the development of advanced methods for handling uncertainty and stochasticity and improving scalability for large, complex networks.

The versatile applications of this PN-based DSS, ranging from daily commute optimization to emergency response planning and urban development assessment, highlight its potential impact across various aspects of urban mobility management.

The PN-based DSS, with its enhanced Petri Net model, offers a promising approach to promoting sustainable household mobility choices. By providing data-driven insights and recommendations that balance individual needs with broader societal and environmental considerations, it contributes to the ongoing efforts to create more efficient, sustainable, and livable urban transportation systems.