A Review of Modeling Approaches in Multi-Modal Transportation Systems: Optimization, Travel Behaviour, and Network Resilience

Wang et al. [14] introduced a mathematical framework aimed at optimizing the integration of various public transportation modes, namely general on-demand services, local on-demand options, and fixed-schedule transit. Utilising Continuous Approximation (CA) methods, the authors develop a system-state equilibrium model that considers the dynamic interplay between travellers’ rational choices and agency service levels, resulting in a unique equilibrium state. Extensive numerical experiments are conducted to test the model's effectiveness, validate and to analyse the impact of various design variables under different demand scenarios. Through the simulations, the model demonstrates that such an integrated system can significantly reduce overall travel costs and improve service levels, particularly by emphasizing the role of local on-demand services in enhancing last-mile connectivity. The findings indicate that adjusting the distribution of transportation services based on demand intensity leads to optimal societal benefits, affirming the value of combining different mobility solutions to better meet traveller’s needs.

Compared to Wang’s system-state equilibrium model, the study by Ma et al. [15] presents a more economically detailed bi-level framework that incorporates multiple user classes and actual fare data, thereby enabling a deeper understanding of the strategic behaviour of both public and private operators in a competitive environment.

The study by Ma et al. [15] presents a comprehensive economic analysis of a multi-modal transportation system, integrating bus, metro, and ride-sourcing services through a tractable bi-level model represented as a network, as illustrated in Figure 2. The study specifies a sample size of 6000 travellers categorised into different user classes. These user classes were determined based on their values of time (VOT), which were uniformly and normally distributed as part of the analysis. The validity of the model in the study is reinforced by its calibration with real-world data like Uber and Google Maps, ensuring relevance to actual transportation scenarios. Furthermore, the model’s robustness is enhanced through comparative statics that assess the impact of changing system parameters and sensitivity analyses that evaluate the stability of results under different conditions.

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Figure 2. Network representation options

Key findings from the analysis indicate that the stochastic user equilibrium (SUE) model provides a more conservative estimate of the ride-sourcing operator's profit, and the total system travel cost compared to the deterministic user equilibrium (DUE) model. Sensitivity analysis reveals that travellers with longer total travel distances are more likely to utilize short-distance ride-sourcing services, suggesting that ride-sourcing operators should enhance service provision in suburban areas. The study also highlights the complex interplay between both operators, showing that optimal fare and frequency adjustments in public transit, prompted by the presence of ride-sourcing services, may lead to less traveller-friendly outcomes. Moreover, simultaneous optimization of operational strategies by both service providers can yield improved system performance, increase ride-sourcing profits while reduce total system costs.

While Ma’s work relies on synthetic distributions and demand-based modeling, Aravinthan and Deepak [2] adopt an empirically grounded approach, validated through real-world traffic conditions, time-delay studies, and walkability assessments. Their modeling method incorporates various empirical data, including traffic volume studies to estimate passenger car units (PCUs), walkability index assessments to evaluate pedestrian infrastructure, and time-delay studies to measure travel times across different transport modes (2-wheelers, 4-wheelers, para-transit, and buses/metro) during peak hours. Additionally, origin-destination surveys are used to analyze travel patterns, and cost analyses assess the cost-effectiveness of each mode. The use of quantitative data enhances the model’s credibility and validity.

Key findings show that time and speed delays are particularly pronounced during peak traffic hours, with an observed 30% increase in delays during the evening compared to morning times. The MMTS demonstrated that integrating modes such as two-wheelers, four-wheelers, paratransit, and buses/metro leads to significant time and cost savings compared to using single modes of transport. Specifically, while paratransit emerged as the most expensive mode with similar travel times to owned vehicles, the combination of multiple transportation modes provided a more efficient and cost-effective travel solution. Furthermore, the study highlights the importance of a well-designed schedule that optimizes the timing between connecting modes to mitigate wait times, thereby enhancing the overall usability and attractiveness of public transport options. Overall, the findings support the adoption of multimodal networks to facilitate more efficient urban transit systems, reduce road congestion, and improve commuter satisfaction.

In contrast to Aravinthan’s data-intensive approach, Jafari et al. [12] employed an agent-based simulation calibrated with regional travel behaviour data to model complex system interactions at the individual level. Next, this research implements an activity-based and agent-based transport model for Greater Melbourne, utilizing the MATSim simulation toolkit to achieve a comprehensive representation of multi-modal transportation. The model incorporates a range of travel modes, including active transport like walking and cycling, and is calibrated against real-world data to ensure accuracy. The sample size of 15,038 commute trips was selected from a total of 92,725 trips in the 2012-2016 VISTA dataset to estimate utility function parameters in the agent-based model.

The data focused on mandatory trips within Greater Melbourne using one of four modes: driving, public transport, walking, or cycling, to minimize the influence of non-commute factors. The outcomes indicate that the calibrated model successfully mirrors observed travel behaviours, such as mode share percentages and traffic volumes, demonstrating its effectiveness for evaluating transportation interventions. Specifically, the model outputs reflect realistic travel times, road usage patterns, and passenger flows, thus providing a valuable tool for examining the effects of potential changes in urban transport infrastructure and policies.

While Jafari simulated travel behaviour, Gu et al. [16] advanced this approach by introducing a Weibit-based model that explicitly accounted for mode and route similarity—an improvement over traditional logit models commonly used in agent-based frameworks. The paper models the vulnerability of multi-modal transportation networks using the Weibit-based combined modal split and traffic assignment (CMSTA) model that captures travel behaviour across various modes and routes. It employs advanced Weibit choice models to account for the complexity of travel behaviours that involve both mode choice (e.g., choosing between metro, bus, or private car) and route choice (e.g., selecting specific paths within the chosen mode). Key findings indicate that the proposed Weibit-based accessibility measures provide a more accurate assessment of network vulnerability by considering the similarities between routes and modes, which traditional logit-based models often overlook. The model demonstrates superior performance in vulnerability analysis, particularly under scenarios with heterogeneous travel times, and highlights the importance of encompassing both mode and route choices to avoid overestimating vulnerability. Numerical experiments based on a simplified multi-modal network in Hong Kong substantiate the effectiveness of the proposed approach, showcasing its applicability in real-world contexts.

Building on this, Gu and Chen [17] extended the Weibit framework to customized bus (CB) services, incorporating user loyalty dynamics through the Dogit model, which marked a significant shift from standard utility-based models. Specifically, a nested Weibit model is used to evaluate passenger choice, incorporating perceived disutility across multiple transport modes while accounting for both mode similarity and heterogeneity. Additionally, the study integrates a Dogit model to capture the behaviour of loyal CB passengers, who, due to their subscription-based commitment, tend to disregard alternative transport modes when making travel decisions.

The findings emphasise the critical role of passenger loyalty in shaping mode choice behaviour, revealing that loyal CB subscribers are significantly less likely to shift to other transport options. This insight leads to distinct demand patterns for CB services. Moreover, the study highlights that integrating loyalty schemes into transit models can enhance service design, improve network performance, and optimize pricing strategies for CB operations. These results emphasize the importance of understanding traveller loyalty and mode characteristics in the development of efficient and sustainable urban transit solutions.

Whereas Gu focused on mode-level behavioural nuances, Nourmohammadi et al. [18] turned toward macro-level dynamic traffic modeling, integrating structural data such as the General Modeling Network Specification (GMNS) to simulate congestion and support operations across the Melbourne network, which ensured ease of data sharing and interpretation. The model incorporates 2077 nodes and 4223 links, along with a time-dependent origin-destination demand matrix reflecting 330,000 commuting trips during morning peak hours. It effectively captures the dynamics of traffic congestion and includes various data inputs such as network geometry, traffic control information, and traveller behaviour models. It illustrates the effectiveness of simulation-based dynamic traffic assignment methodologies in understanding and predicting traffic patterns in urban environments.

The study highlights the significance of integrating diverse data sources—including publicly available datasets (e.g., Google Maps and OpenStreetMap)—to accurately reflect the characteristics of the transportation network. This integration aids in validating the model's structure and performance. The developed model has the potential to be utilised in various applications within transportation network design and traffic operational management, such as corridor management, pricing strategies, and emergency management scenarios.

While Nourmohammadi modeled the full network, the study conducted by Wang et al. [19] focused on identifying critical nodes in MMT networks using a modified weighted k-shell (MWKS) method. MWKS model integrates both the network topology and traffic demand, considering the differential contributions of multi-order neighbour nodes represented by passenger volume and the concept of transportation corridors. The MWKS model aims to reflect the interactions between nodes in a transportation corridor, which traditional methods may overlook. Validation through a real transportation system in Zhejiang Province, China, showed that MWKS outperformed traditional methods and other k-shell-based approaches, accurately predicting crucial nodes that could lead to significant disruptions if compromised. The proposed contribution attenuation coefficient enhanced the assessment of node importance by reflecting the varying influences of multi-order neighbour nodes based on passenger volume and traffic dynamics. Additionally, the model exhibited a higher potential for cascading failures, demonstrating its robustness and reliability in practical applications.

On the other hand, Dixit et al. [20] developed a multi-modal transit route choice model using smart card data from Amsterdam to analyse the impact of a new metro line introduced in July 2018. By comparing pre- and post-introduction data, the research assesses changes in travel behaviour and validates the model through external testing of parameters. Despite discrepancies in parameter values between the two timeframes, the transferred model demonstrated satisfactory predictive performance, achieving a First Preference Recovery rate of 71.5% and a Mean Absolute Percentage Error (MAPE) of 0.3% for mode shares compared to observed choices. Overall predictive accuracy remained comparable to the locally estimated model, with less than a 10% increase in error for route and link-level predictions. The findings indicate that excluding important variables hinders predictive performance, while the inclusion of different modes of transit like bus and trams in model specifications did not improve transferability, suggesting context-specific considerations for overlaps in transit modelling.

Lastly, research conducted by Othman et al. [13] explained about the SUMMIT (Singapore Urban Multi-Modal Integrated Transport Simulator) which employs an agent-based simulation model to replicate the behaviours and interactions of commuters during unplanned disruptions in Singapore's Mass Rapid Transit (MRT) system. Each commuter is modelled as an autonomous agent, making decisions based on real-time data and environmental factors, which allows for an accurate representation of commuter responses to service interruptions.

4.1 Strength

The reviewed studies demonstrate significant methodological advancements in MMTS modelling, particularly in optimization, travel behaviour analysis, and network resilience. Mathematical optimization models (e.g., Wang et al. [14]; Ma et al. [15]) have played a crucial role in enhancing service integration, reducing congestion, and optimizing public transit operations. These models allow transportation planners to balance demand and supply efficiently, improving travel time reliability and cost-effectiveness. Additionally, agent-based and activity-based models (e.g., Jafari et al. [12]; Othman et al. [13]) have been instrumental in simulating real-world commuter behaviour under different scenarios, providing valuable insights for policy interventions and transit planning.

A key strength observed in many studies is the integration of real-world data for model validation. For instance, Dixit et al. [20] employ smart card transaction data to evaluate the accuracy of transit route choice models, demonstrating high predictive validity. Similarly, Nourmohammadi et al. [18] utilize General Modelling Network Specification (GMNS) to create a comprehensive, open-source MMTS dataset, enabling cross-comparison and replication of results. These data-driven approaches enhance the credibility and applicability of MMTS models, making them more relevant for real-world deployment. Additionally, several studies focus on network resilience and vulnerability analysis, addressing critical infrastructure weaknesses in MMTS. Gu et al. [16] and Wang et al. [19] introduce advanced computational models to identify critical nodes and potential failure points, providing a foundation for disaster preparedness and risk mitigation strategies. These studies highlight the need for robust, adaptive transportation networks capable of withstanding disruptions such as natural disasters, technical failures, or sudden demand shifts.

4.2 Limitations

Despite these strengths, several limitations persist across the studies.

4.2.1 Limited geographic generalizability

A recurring issue is limited geographic generalizability, where models are calibrated for specific urban contexts (e.g., Othman et al. [13] focus on Singapore’s public transport system). This restricts their applicability to other cities with different transport infrastructures and commuter behaviours. This challenge is also highlighted in research by Waddell [31], which discusses the difficulties in adapting academic models like UrbanSim for practical use in various U.S. cities. His study emphasizes the need to balance theoretical validity with operational requirements, reinforcing the argument that location-specific transport models often require significant adjustments before they can be applied to different urban environments.

The challenge of applying models developed for specific urban contexts to other cities necessitates a shift towards more flexible and adaptable modeling frameworks. Instead of building monolithic models, future research should focus on developing modular components that represent fundamental aspects of transport systems and commuter behaviour. These modules could be designed with adaptable parameters that can be calibrated using local data. For instance, a mode choice module could incorporate socio-economic factors and travel preferences that can be adjusted based on city-specific surveys and census data which had been done in the City of Warsaw [32]. Recent work in transfer learning within transportation science could offer methodologies to adapt models trained on one city's data to another with minimal retraining. This involves identifying shared representations across different urban environments.

Besides that, emphasize the use of extensive local data for calibrating and validating models. This includes not just traditional travel surveys but also leveraging emerging data sources like smart card data, mobile phone location data, and social media data (while respecting privacy concerns). Advanced statistical and machine learning techniques can be employed to extract meaningful insights from these diverse datasets and fine-tune model parameters for specific urban environments. Research on federated learning (FL) could also be explored, allowing models to be trained on decentralized data from multiple cities without directly sharing sensitive information. Research conducted by Betul et al has proven that FL strategies can solve privacy and confidentiality concerns, particularly for high-risk applications [33].

4.2.2 Computational complexity

Additionally, according to Bastarianto et al. [34] computational complexity is a major issue since it poses a challenge for large-scale implementation, particularly for agent-based and activity-based models such as the model developed by Jafari et al. [12], which requires substantial processing power. Besides that, Jafari et al. [12] and Othman et al. [13] models also require high computational resources, making them difficult to implement in cities with complex, multimodal transit systems. To address this, future research should focus on developing scalable MMTS models that maintain high accuracy while reducing computational demands. One of the solutions is to explore methods to simplify model structures and aggregate individual behaviours where appropriate, without significant loss of accuracy. This could involve using representative agent groups instead of simulating every individual or employing coarser spatial and temporal resolutions for certain analyses. Research in macroscopic traffic flow modelling and system dynamics offers techniques for representing aggregate behaviour efficiently.

On the other hand, advancements in HPC and parallel processing techniques to handle the computational load of complex models also a solution to the computational complexity which had been highlighted in previous section. Cloud computing platforms offer scalable resources that can be utilized for large-scale simulations. Recent developments in GPU-accelerated computing can significantly speed up simulations, particularly for agent-based models [35].

4.2.3 Incorporating behavioural realism

Many studies also assume static demand elasticity or rational traveller behaviour, which may not accurately reflect real-world commuter decisions. For instance, Ma et al. [15] does not account for behavioural uncertainties in user preferences, which could affect mode choice predictions. Incorporate insights from behavioural economics and psychology to model more realistic traveller preferences and decision-making processes. This includes accounting for factors like bounded rationality, cognitive biases, habits, and the influence of social networks. Recent research in behavioural travel modeling is exploring the use of concepts like prospect theory and regret minimization to better understand mode choice and route selection [36].

4.2.4 Emerging transport trends

Furthermore, most studies do not fully incorporate emerging transport trends such as autonomous vehicles, e-bikes, or Mobility-as-a-Service (MaaS), limiting their relevance for future transport planning. This is particularly evident in the case of MaaS, where its integration with public and private transport modes remains an emerging field of research, with most relevant studies only recently published [37].

Recent research promotes integrating these trends through platform-based modeling and multi-actor digital ecosystems, which simulate collaboration between public and private stakeholders. The digital twin’s (DT) paradigm supports this by creating a virtual sandbox where new technologies (like AVs or MaaS platforms) can be stress-tested under different policy or market conditions before real-world deployment. One of example implementing DT is in research conducted by Yu et al. [38], who presented real-world applications of digital twin technology as an effective approach for developing autonomous driving (AD) systems, enabling the creation of comprehensive, accurate, and reliable virtual models of the physical environment.

4.2.5 Policy and governance

Lastly, policy and governance considerations are underrepresented in MMTS research. While some studies analyse economic impacts and fare optimization, few integrate policy-driven regulations, urban transport policies, or government intervention strategies [39]. For instance, Aravinthan and Deepak [2] focus on MMTS design for congestion reduction but does not account for regulatory frameworks or sustainable transport incentives. Future research should incorporate multi-level policy analysis, including pricing policies, public transit subsidies, land use and infrastructure investments, to develop more comprehensive MMTS planning frameworks.

To illustrate the potential of a more integrated approach, Pozoukidou’s research [40] offers a valuable example. While the study makes significant steps in linking transport planning with urban development, it also highlights a key prerequisite for successful implementation: the essential need for comprehensive data availability, well-structured data management, and strict standardization across all stages of the modelling process.

Figure 4. MCDA flowchart