Dynamic headway control for capacity optimization: a critical review

1 Introduction

The continuous growth of passenger and freight transportation demand has turned railway capacity into a key performance indicator of modern transport systems and a central challenge for infrastructure managers and operators. Unlike other transport modes, the expansion of railway capacity through the construction of new lines is associated with high investment costs, long implementation periods, and significant environmental constraints. Consequently, increasing the throughput of existing infrastructure by improving operational control and signalling technologies has become a priority research direction. In this context, train headway is the temporal or spatial separation between consecutive trains is widely recognised as one of the dominant factors limiting line capacity and operational efficiency (He et al., 2022).

Traditionally, railway traffic has been governed by fixed-block signalling principles, where the infrastructure is divided into discrete track sections and safe train separation is ensured by conservative braking distance assumptions. In this context, fixed-block signalling refers to a system in which the railway line is divided into discrete track sections, and a train is allowed to enter a section only if it is completely unoccupied, resulting in conservative and spatially rigid separation rules. Moving-block signalling removes this discretisation by continuously calculating a safe braking distance based on real-time train position, speed, and performance characteristics, allowing trains to operate with dynamically updated separation. Such concepts are implemented in modern communication-based train control (CBTC) systems and are partially reflected in advanced European Train Control System (ETCS Level 3) and Chinese Train Control System (CTCS-3) architectures. Virtual coupling represents a further evolution of moving-block principles, in which trains operate in a coordinated manner based on relative motion and train-to-train communication, effectively forming dynamically controlled platoons with reduced separation while maintaining safety through cooperative control strategies.

Although such systems provide a high level of safety and operational robustness, they inherently impose static headway margins that lead to underutilisation of infrastructure capacity (Spunei et al., 2014). The transition toward moving-block and communication-based train control (CBTC) systems has introduced the possibility of continuously updated movement authority and dynamically calculated train separation, enabling a substantial reduction in operational headways and a corresponding increase in traffic density (Felez and Vaquero-Serrano, 2023). Recent studies demonstrate that dynamic headway models based on real-time trajectory prediction and iterative control strategies can significantly decrease train spacing while maintaining safety constraints, thus improving network throughput and service reliability (He et al., 2022; Usama and Koutsopoulos, 2025).

Despite these technological advances, the relationship between headway control and railway capacity remains insufficiently understood from a system-level perspective. One of the fundamental problems is the lack of a unified and universally accepted definition of railway capacity. In this study, this limitation is addressed by adopting a control-oriented perspective on capacity, in which different modelling approaches are compared not only in terms of absolute throughput values but also with respect to their underlying assumptions, ability to represent real-time control, and sensitivity to disturbances. Rather than relying on a single definition, the analysis focuses on relative performance, scalability, and robustness across modelling frameworks, allowing a consistent comparison despite the absence of a universally accepted capacity metric. Existing approaches distinguish between theoretical capacity, representing idealised maximum throughput under deterministic conditions, and operational (or effective) capacity, which accounts for real-world constraints such as traffic heterogeneity, timetable structure, and disturbance propagation. In this paper, the terms operational capacity and effective capacity are used interchangeably to describe achievable performance under realistic operating conditions, while the term practical capacity is not treated as a separate category in order to avoid ambiguity. However, most capacity assessment methodologies are still based on static or quasi-static formulations, where system conditions are assumed to change slowly and control decisions are based on aggregated or time-averaged parameters rather than continuous real-time updates, do not adequately account for real-time control actions, stochastic delays, or dynamic interactions between trains (Ramdas and Chapman, 2017). As a result, conventional capacity metrics often overestimate achievable performance and fail to capture the stability of traffic flow under disturbed conditions.

Another limitation of the current research landscape is that existing modelling approaches, although diverse and well-developed, do not capture the full system-level dynamics of railway operations. Analytical formulations, traffic-flow models, discrete-event simulations, and optimisation-based methods are frequently developed in isolation and applied to specific operational scenarios. For instance, simulation studies incorporating stochastic dispatching delays have shown that the consideration of operational variability leads to more realistic capacity estimates, particularly in partially automated railway systems (Shukamanov et al., 2025). However, these models are rarely integrated with control-oriented formulations capable of describing adaptive headway regulation in real time. Similarly, emerging intelligent control techniques, including predictive control, machine-learning-based trajectory estimation, and cooperative train control, are typically evaluated in terms of local performance indicators rather than system-wide capacity effects.

From a control-systems perspective, headway should not be treated merely as a safety constraint but as a dynamic and controllable variable that directly determines traffic flow stability, energy efficiency, and infrastructure utilisation. Real-time regulation of train motion and dwell times has already been shown to reduce headway variance and stabilise metro operations through feedback control mechanisms formulated as stochastic optimal control problems (Schanzenbacher et al., 2018). Moreover, recent research on virtual coupling and cooperative train operation demonstrates the potential for distributed and consensus-based control architectures to further minimise train separation and enable flexible, high-density traffic management (Wu et al., 2023). These developments indicate a paradigm shift from infrastructure-based capacity enhancement to control-driven performance optimisation.

However, the practical realisation of dynamic headway control faces several unresolved challenges. Communication latency, positioning uncertainty, safety certification requirements, and the trade-off between robustness and maximum throughput limit the achievable capacity gains in real networks. Even in moving-block systems, theoretical reductions in train separation are often constrained by station dwell times, mixed traffic operations, and the need for operational buffers (Versluis et al., 2024). Therefore, a critical reassessment of existing modelling paradigms and control architectures is required in order to identify the actual performance limits and research gaps.

In light of these considerations, this paper provides a critical review of dynamic headway control as a system-level mechanism for capacity optimisation. Unlike conventional railway-oriented surveys, the study adopts a control- and performance-driven perspective that links headway regulation, traffic dynamics, and infrastructure utilisation within a unified analytical framework. The review systematically compares modelling approaches in terms of their ability to represent real-time control, scalability, and sensitivity to disturbances, and analyses the effectiveness of modern control architectures for increasing network throughput. Based on this analysis, key limitations of current methodologies are identified and future research directions toward intelligent, adaptive, and distributed railway traffic control are outlined.

2 Methodology

This study adopts a control-oriented analytical review methodology to investigate the role of dynamic headway control in railway capacity optimization. While the review does not strictly follow a formal systematic review protocol (e.g., PRISMA), it applies a structured and transparent literature selection and analysis process.

The literature selection focused on peer-reviewed journal articles and recent conference proceedings published primarily within the last 10–15 years, with emphasis on studies addressing railway signalling systems, headway control, traffic-flow modelling, and real-time control architectures. Key databases and sources included Scopus-indexed journals and major transportation and control-systems venues. Priority was given to works that explicitly analyse real-time control mechanisms, system-level performance, and scalability aspects.

The review is guided by the following research questions:

• How do existing modelling approaches represent train headway under real-time operational conditions?
• To what extent do current control frameworks capture disturbance propagation and traffic stability at the network level?
• What are the limitations of existing approaches in terms of scalability, robustness, and integration with modern signalling systems?

Different modelling paradigms, including analytical formulations, traffic-flow models, simulation-based approaches, and optimization-based control methods, were comparatively analysed in terms of their ability to represent real-time headway regulation, disturbance propagation, and system scalability. Particular attention was given to modern control architectures such as moving-block systems, predictive control, and cooperative train operation.

The comparative synthesis of these approaches enabled the identification of key methodological limitations and the formulation of a system-level framework linking headway control, traffic stability, and infrastructure utilisation.

3 Dynamic headway as a control variable

3.1 From static safety margins to dynamic control

In this study, the term dynamic headway control is used to denote the general framework in which train separation is continuously updated based on real-time information, trajectory prediction, and system state. Adaptive headway control is considered a specific implementation within this framework, in which control parameters such as speed, dwell time, and braking profiles are actively adjusted through feedback mechanisms to maintain system stability and optimise performance under varying operational conditions.

The traditional determination of train separation has historically been rooted in the concept of fixed safety envelopes derived from worst-case braking scenarios and predefined signalling logic. In these approaches, the minimum permissible headway is calculated using conservative assumptions regarding train deceleration, driver reaction, track conditions, and communication delays. While such formulations guarantee fail-safe operation, they implicitly transform headway into a static constraint rather than a controllable system variable. As a consequence, infrastructure utilisation is limited not by the physical performance of rolling stock or real traffic conditions, but by predefined safety buffers that remain unchanged during operation. This paradigm is still embedded in many capacity assessment methodologies and dispatching practices, particularly in networks operating with legacy signalling or semi-automatic block systems (Versluis et al., 2024).

A fundamental limitation of static headway modelling lies in the use of fixed braking distance assumptions. In this context, braking distance refers to a scalar estimate of the minimum safe separation required to prevent collision under predefined conditions, whereas the braking curve represents the dynamic deceleration profile of a train as a function of speed, distance, or time. Static formulations typically approximate safety constraints using simplified or deterministic braking curves for both leading and following trains, thereby reducing the problem to fixed separation distances. Such representations neglect variations in adhesion, train mass, traction control strategies, and real-time speed profiles, which influence the actual braking behaviour under operational conditions. As shown in recent modelling studies, braking distance is frequently treated as a constant parameter, while longitudinal train dynamics, gradients, and energy-efficient driving modes are neglected, leading to an overestimation of the required separation distance (Sofroniou, 2021). This simplification introduces structural rigidity into the control process and prevents the system from exploiting the actual performance envelope of modern rolling stock. In high-density operations, such conservative assumptions translate directly into reduced throughput and increased sensitivity to perturbations, since recovery margins must also be embedded in the timetable.

The transition toward moving-block and communication-based train control systems has challenged this static safety paradigm by enabling continuous train positioning and real-time exchange of motion authority. In these architectures, headway is no longer determined by the occupancy of discrete track sections but by the dynamically computed safe braking distance relative to the preceding train. However, even in advanced implementations, many operational models still rely on quasi-static formulations in which the separation distance is updated periodically but not optimised as a function of predicted train trajectories (Basile et al., 2019). This reveals a conceptual gap between the technological capability of modern signalling systems and the control strategies used to manage traffic flow.

Recent research demonstrates that the incorporation of trajectory prediction into headway computation fundamentally changes the nature of train separation control (He et al., 2022; Kunimatsu et al., 2019). Hybrid approaches combining model-based estimation with machine-learning techniques allow the future motion of the leading train to be forecast within the braking horizon of the following train. This enables iterative control algorithms to continuously adapt the separation distance to actual operating conditions rather than worst-case scenarios. Simulation results for communication-based train control environments indicate that such dynamic headway formulations can reduce inter-train distance by more than 60% while maintaining safety constraints, thereby significantly increasing traffic density without infrastructure expansion (Usama and Koutsopoulos, 2025).

These results are not contradictory but reflect different modelling assumptions. The reported reduction in inter-train distance represents a theoretical potential achieved under controlled conditions, where accurate trajectory prediction and coordinated control allow the system to operate close to safety limits. In contrast, the observed capacity overestimation arises from stochastic operational effects such as dwell-time variability, heterogeneous rolling stock, and disturbance propagation, which are not fully captured in deterministic formulations. Consequently, while dynamic headway control can significantly reduce nominal train separation, the effective capacity gain in real railway systems is moderated by variability and stability constraints. This highlights the importance of integrating stochastic dynamics and disturbance sensitivity into control-oriented headway models.

Despite these advances, the shift from static safety margins to dynamic control is far from complete. One of the key unresolved issues is the limited integration of stochastic operational effects into headway models. Real railway traffic is characterised by dwell-time variability, heterogeneous rolling stock, temporary speed restrictions, and dispatching interventions. When these factors are ignored, capacity calculations based on deterministic headway values systematically overestimate achievable throughput. Discrete-event simulation studies that explicitly incorporate random delays have shown that neglecting stochastic variability can lead to capacity overestimations of up to 30%, highlighting the need for adaptive control strategies capable of responding to real-time disturbances (Shukamanov et al., 2025).

Another critical aspect concerns the control architecture required to support dynamic headway regulation. Static formulations assume a unidirectional safety logic in which the following train passively reacts to the behaviour of the leader. In contrast, dynamic control frameworks treat train motion as a coupled system in which speed commands, braking profiles, and dwell times are coordinated through continuous feedback. This shift transforms headway from a geometric spacing parameter into an emergent property of the traffic flow dynamics. Such a perspective is consistent with system-level traffic management approaches, where capacity is determined not only by minimum separation but also by the stability of train sequences under varying demand and disturbance conditions (Pachl, 2022).

However, the implementation of fully adaptive headway control introduces new trade-offs between performance, robustness, and computational complexity. Real-time optimisation requires reliable communication, high-precision positioning, and fast decision-making algorithms. In the presence of communication latency or temporary data loss, the control system must revert to more conservative separation rules, effectively reintroducing static safety margins. This hybrid operational mode remains insufficiently explored in the literature and represents a major barrier to the practical deployment of dynamic headway strategies in mixed-traffic and long-distance railway networks.

From a capacity perspective, the persistence of static modelling assumptions reflects a deeper methodological issue: the separation between safety verification and performance optimisation. In conventional approaches, safety constraints are imposed a priori and capacity is evaluated within these limits. In dynamic control frameworks, safety and performance become interdependent variables that must be managed simultaneously through predictive and feedback control. The absence of integrated models capable of capturing this interaction explains why many existing studies report theoretical headway reductions that cannot be realised in real operation.

In summary, the evolution from fixed safety margins to dynamic headway control represents a transition from infrastructure-based to control-driven capacity enhancement. Static braking assumptions, deterministic separation rules, and the lack of adaptation to stochastic traffic conditions remain the primary factors limiting infrastructure utilisation. Although modern signalling technologies provide the data and communication capabilities required for real-time control, the modelling paradigms used for capacity assessment are still largely based on conservative and decoupled formulations. Bridging this gap requires the development of control-oriented headway models that integrate trajectory prediction, disturbance propagation, and system stability into a unified framework.

3.2 Control parameters shaping headway dynamics

In a dynamic traffic management environment, train separation is no longer determined solely by infrastructure constraints but emerges from the interaction of multiple controllable variables that govern the longitudinal motion of trains and the temporal structure of operations. From a control-systems perspective, headway becomes a state-dependent output influenced by speed regulation, braking behaviour, dwell time management, communication latency, and inter-train coupling mechanisms. Understanding how these parameters shape headway dynamics is essential for transitioning from static safety envelopes to performance-oriented railway control.

Speed constitutes the primary control input in real-time headway regulation. Modern automatic train operation systems continuously adjust traction commands in order to maintain stability of train sequences and prevent the amplification of disturbances. Unlike timetable-based regulation, where speed profiles are predefined, model-based control allows the velocity of each train to be modified as a function of the predicted motion of neighbouring trains and downstream constraints. Recent optimal control formulations demonstrate that speed modulation can be used to reshape headway without invoking full braking cycles, thereby reducing energy consumption while preserving throughput. In dense metro operations, feedback-based speed harmonisation has been shown to decrease headway variance and improve service regularity by actively damping traffic waves (Polinder et al., 2021).

Closely related to speed control is the treatment of braking curves as adjustable rather than invariant safety functions. In classical signalling logic, braking distance is derived from worst-case deceleration and remains fixed throughout operation. In contrast, dynamic control frameworks treat the braking profile as a function of real-time adhesion estimates, train mass, and control system response time. Moving-block implementations with continuous supervision enable the computation of a moving safe-braking envelope that evolves with the instantaneous state of the train. This approach not only reduces the required separation distance but also allows smoother control actions by replacing discrete braking commands with continuous deceleration trajectories. Recent studies on adaptive braking supervision show that incorporating real-time estimation of braking performance can significantly improve the utilisation of line capacity while maintaining certified safety margins (Goverde et al., 2013).

Communication latency introduces an additional dynamic constraint that directly affects the achievable minimum headway. In communication-based train control systems, the movement authority of the following train depends on the timely reception of position and speed information from the leading train and the control center. Even small delays in data transmission lead to an increase in the uncertainty of the predicted stopping point, which must be compensated by enlarging the safety buffer. Control-theoretic analyses show that this effect can be interpreted as a time-delay system in which stability and performance are strongly dependent on the update frequency of the communication channel. When latency exceeds a critical threshold, the control system must switch to more conservative operating modes, effectively reverting to quasi-static separation logic (Gong et al., 2023). Consequently, headway optimisation cannot be considered independently of communication performance, and joint design of control algorithms and data-exchange architectures becomes necessary.

Dwell time at stations represents another major control variable that influences headway dynamics at the network level. While running time regulation primarily affects train pairs in open track sections, dwell time variability propagates through the timetable and creates secondary conflicts. Traditional capacity models treat dwell time as an exogenous random variable; however, recent research demonstrates that it can be actively controlled through passenger-flow management, platform-door coordination, and adaptive departure strategies. Real-time dwell time control allows the system to absorb small delays locally and prevent their amplification along the line. Model predictive control frameworks integrating dwell time and speed regulation have been shown to increase line throughput by stabilising train sequences rather than by simply reducing minimum separation (Buchunde, 2024). This finding highlights that headway is not only a function of longitudinal motion but also of station operation dynamics.

The coupling effect between consecutive trains further reinforces the need for a system-level interpretation of headway. When separation decreases, the behaviour of one train becomes increasingly dependent on the control actions of its neighbours, forming a coupled dynamic system. In this regime, local control strategies based on pairwise spacing are no longer sufficient, because disturbances propagate through the entire train sequence. Cooperative control concepts, including virtual coupling and distributed optimisation, address this issue by synchronising acceleration and braking phases of multiple trains. Such approaches enable the formation of dynamically coordinated train platoons that operate with reduced separation while maintaining traffic stability. Recent experimental and simulation studies indicate that cooperative train control can significantly increase corridor capacity and reduce energy consumption through coordinated motion profiles (Quaglietta et al., 2022).

A critical implication of these developments is that headway can no longer be interpreted as a purely geometric or temporal measure. Instead, it emerges from the closed-loop interaction between control inputs, communication infrastructure, vehicle dynamics, and passenger-induced operational variability. Existing capacity assessment methodologies rarely capture this interaction, because they treat speed, braking, dwell time, and communication performance as independent parameters. Such decoupled representations fail to describe the feedback mechanisms that determine traffic stability and lead to overly optimistic or overly conservative estimates of achievable throughput (Schanzenbächer, 2020).

Furthermore, the simultaneous optimisation of these control parameters introduces multi-objective trade-offs that are absent in static models. For example, aggressive speed control can reduce headway but increase energy consumption and reduce passenger comfort, while longer dwell times may stabilise traffic at the cost of local capacity. Recent multi-objective optimisation studies demonstrate that optimal headway regulation requires balancing capacity, energy efficiency, and punctuality within a unified control framework (Ning et al., 2015). This confirms that headway dynamics should be analysed as part of an integrated performance optimisation problem rather than as an isolated safety constraint.

The interaction of the described control parameters forms a closed-loop structure in which headway is no longer a predefined constraint but an emergent dynamic variable determined by train motion control and real-time traffic conditions. This system-level interpretation is illustrated in Figure 1.

The scheme illustrates the transformation of headway from a static safety constraint into a dynamically controlled system variable within a closed-loop control architecture. Real-time control inputs, including speed regulation, adaptive braking, dwell time management, communication performance, and cooperative train operation, directly influence train motion dynamics and trajectory evolution. The Train Motion Dynamics block represents the physical and operational behaviour of trains, including acceleration, braking processes, and interactions with infrastructure constraints. The resulting trajectory evolution determines the formation of time-space separation between consecutive trains, which defines the instantaneous headway. The Traffic Stability & Flow Homogenization block reflects the collective system response, including disturbance propagation, headway variance, and the emergence of stable or unstable traffic patterns. These factors directly affect system-level performance in terms of throughput, robustness, and energy-capacity interaction. The lower connection from Train Motion Dynamics to Traffic Stability & Flow Homogenization represents a feedback mechanism, in which traffic conditions influence subsequent control decisions. This feedback loop corresponds to predictive monitoring and continuous control adaptation, enabling real-time optimisation of headway and traffic flow. To ensure consistency, the terminology used in the figure (e.g., real-time control inputs) is aligned with the terminology used throughout the text.

In summary, dynamic headway is shaped by a set of interdependent control parameters that collectively determine the stability and throughput of railway traffic. Speed regulation provides the primary mechanism for real-time spacing control, adaptive braking transforms safety envelopes into continuously updated constraints, communication latency defines the feasible control horizon, dwell time management stabilises the temporal structure of operations, and cooperative train control introduces system-level coupling effects. The absence of integrated models capable of representing these interactions remains a major research gap and explains why many advanced signalling technologies have not yet achieved their full capacity potential in real operation.

4 Capacity as a system performance metric

The interpretation of railway capacity as a fixed property of infrastructure is increasingly being replaced by a dynamic, performance-oriented perspective in which the achievable traffic volume emerges from the interaction between operational variability, train dynamics, and control responsiveness. In this system view, capacity cannot be reduced to the inverse of a minimum headway or to a compressed timetable diagram; instead, it represents the maximum sustainable output that can be maintained without triggering unstable delay growth. This distinction becomes particularly evident when theoretical capacity values are compared with realised traffic performance under real operating conditions.

Recent trajectory-based analyses using reconstructed operational data show that the effective occupation of infrastructure differs significantly from planned occupation due to train heterogeneity and stochastic operational variations. In a 2024 microscopic capacity assessment, the dominant factor affecting realised capacity was not infrastructure geometry but the sequencing of trains with different running characteristics, while the impact of day-to-day operational variability remained secondary but non-negligible. This result indicates that capacity losses are primarily generated by dynamic interactions between trains rather than by static block occupation alone (Lordieck et al., 2024).

The gap between theoretical and operational capacity is therefore not simply a matter of safety margins but a manifestation of system dynamics. Compression-based methods implicitly assume that train paths can be arranged in a perfectly periodic structure, yet empirical studies consistently demonstrate that even small perturbations disrupt this periodicity and require recovery time that is not captured by static formulations. In a discrete-event simulation of freight operations under semi-automatic blocking, the realistic capacity of a line was estimated at approximately 69 trains per day when random dispatching delays were included, a value that closely matched observed performance but was significantly lower than deterministic estimates (Shukamanov et al., 2025). The reduction was not caused by longer nominal headways but by the temporal dispersion introduced by stochastic delays, which reduced the number of feasible train paths within the same time window. This confirms that operational capacity is governed by the variability of headway rather than by its minimum value.

The relationship between throughput and stability further illustrates why capacity must be treated as a dynamic system output. Increasing traffic density by reducing headway increases nominal throughput, but beyond a critical utilisation level the system enters a regime in which delays propagate nonlinearly. Data-driven analyses of freight corridors based on Swedish infrastructure reports show that high utilisation does not necessarily correlate with higher delays in a linear manner; instead, the relationship becomes highly sensitive to local conditions, indicating that the system transitions between stable and unstable operating states (Armah, 2025). This finding challenges the traditional assumption that capacity utilisation alone is a sufficient indicator of performance and highlights the importance of stability as a complementary metric.

The mechanism behind this behaviour lies in the propagation of disturbances through interacting train sequences. Algorithmic models of delay evolution on double-track lines demonstrate that once a disruption occurs, its cumulative impact depends on the structure of train interactions, the dispatching policy, and the available recovery margins. Performance indicators such as disruption settling time, number of affected trains, and cumulative delay provide a more realistic measure of system capacity than static headway values because they quantify the system’s ability to absorb perturbations (Ma et al., 2024). From this perspective, capacity is reached not when the infrastructure is fully occupied but when the system loses the ability to dissipate delays within an acceptable time horizon.

This dynamic interpretation is supported by predictive real-time traffic management models. Recent real-time simulation frameworks show that the instantaneous capacity of a railway line varies over time as a function of current traffic conditions and control actions. Instead of a single maximum value, capacity becomes a time-dependent envelope determined by the current state of the system (Tan et al., 2025). This result implies that offline capacity calculations cannot capture the actual performance limits of digitally controlled railways, where speed commands, departure times, and routing decisions are continuously updated.

At the network level, the cascading nature of delays provides further evidence that capacity is a systemic property. Systemic-risk analyses based on interaction networks between trains reveal that a small number of services may have a disproportionately large impact on overall performance due to shared resources and conflict points. By quantifying the “systemic impact” of individual trains, it becomes possible to identify critical elements whose regulation yields a higher increase in effective capacity than infrastructure expansion (Daniotti et al., 2023). This result reinforces the conclusion that capacity is governed by the topology of interactions and by control strategy rather than by physical infrastructure alone.

The growing availability of large-scale operational datasets has enabled the direct measurement of capacity as a function of reliability. For example, an integrated dataset covering the entire Finnish railway network from 2018 to 2024 revealed seasonal delay rates exceeding 25% in winter conditions, demonstrating that environmental variability alone can shift the achievable capacity envelope of a network (Borin et al., 2026). Such findings are incompatible with static capacity indicators and highlight the need for performance metrics that account for time-dependent external influences.

From a formal standpoint, the difference between theoretical and effective capacity can be interpreted through the role of headway variance. In idealised conditions, capacity is proportional to the inverse of the mean headway. In real operation, however, the effective throughput is reduced by the dispersion of headways and by the recovery time required after disturbances. This relationship explains why two lines with identical minimum headway can exhibit substantially different realised capacity and why adaptive control that reduces headway variance may increase throughput without reducing nominal separation.

The persistence of static capacity indicators in the literature reflects a methodological separation between safety verification and performance optimisation. In traditional approaches, safety constraints define the minimum headway, and capacity is calculated within these fixed limits. In dynamically controlled systems, safety and performance are coupled: the achievable capacity depends on the accuracy of state estimation, communication latency, and the predictive horizon of control algorithms. As a result, capacity becomes a controllable performance variable rather than an infrastructure constant.

Thus, capacity should be understood as the maximum traffic volume that can be sustained over a sufficiently long operational time horizon, such that delay propagation remains bounded and system performance does not degrade under realistic disturbance conditions. The difference between theoretical and operational capacity arises from headway variability, disturbance propagation, and the stability of train sequences. Throughput and stability form a nonlinear trade-off, and the achievable performance is determined by the system’s dynamic response rather than by static spacing rules. Real-time monitoring, predictive dispatching, and data-driven analysis further demonstrate that capacity is a time-dependent property that emerges from the interaction between infrastructure, rolling stock, environment, and control strategy. This system-level interpretation provides the necessary foundation for integrating dynamic headway control with capacity optimisation in the subsequent sections.

5 Modeling paradigms for headway control and capacity assessment

5.1 Analytical and traffic flow models

Analytical modelling remains the most “compact” way to connect headway regulation to capacity, because it turns the operational problem into explicit constraints and performance relationships that can be inspected, differentiated, and stress-tested. The price of this tractability is that many analytical formulations encode capacity as a consequence of static separation logic (minimum headway or blocking constraints) rather than as an output of a closed-loop controller reacting to disturbances. This methodological choice matters: it often produces capacity conclusions that are internally consistent mathematically, yet optimistic when transferred to real operations where dwell variability, communication delays, and control saturation dominate.

A large share of analytical capacity work is built on the blocking time representation and timetable compression logic (e.g., UIC-style approaches), where capacity is expressed through occupation times and minimum separations (Abril et al., 2008; Landex et al., 2008). A representative recent example is the analytical UIC-406 compression model combined with blocking-time stairways proposed for a Chinese high-speed corridor. Instead of prescribing a fixed headway, the authors derive headway from operational data and embed it in a linear programming compression model; the case study reports that headway values on China HSR are “mainly limited” to about 4.5–5 min under the prevailing control constraints, and crucially shows that replacing fixed, rule-of-thumb separations by data-refined headway estimates yields measurable capacity effects. In their reported scenario, the occupation time computed under train-control-system assumptions was 842.75 min, while the blocking-time/headway-theory approach produced 65.42 min less occupation time for the same service pattern, indicating nontrivial headroom that purely conservative headway rules can hide (Wang et al., 2020). At the same time, it also exposes a limitation: the model’s gain is demonstrated mainly via re-parameterization (better headway estimation) rather than via an explicit control law that guarantees stability under stochastic perturbations. In other words, the analytical layer improves the nominal plan, but it does not yet certify that the plan is dynamically sustainable.

Traffic-flow theory and fundamental-diagram (FD) approaches attempt to lift the analysis from local headway constraints to system-level regimes (free flow, saturation, congestion), which is exactly what a “capacity as performance” framing demands (Zheng et al., 2024). Weik (2022) provides a particularly relevant discussion of when macroscopic FDs can meaningfully describe railway corridors with fixed-blocks and how these diagrams reveal operational phases and risks. The analysis explicitly spans block lengths from 500 m to 3 km, covering classical fixed-block operations and more segmented infrastructures that partially resemble continuous control. The paper contrasts deterministic “peak efficiency” regimes with stochastic settings (variability in arrivals and dwell times) and shows how small irregularities shift the system away from the deterministic envelope, i.e., capacity becomes a distribution of achievable flows rather than a single number (Weik, 2022). This is a key analytical insight for headway control: in a macroscopic regime description, the question is not merely “what is the minimum headway?” but “under what density and variability does the system remain on the stable branch of the FD?” The drawback is that FD models typically treat control only indirectly: they identify regimes and thresholds but rarely specify implementable, constraint-aware controllers that keep the system in the desired regime when disturbances occur. Consequently, FD-based capacity claims can still inherit the classic weakness the reviewer called out (“capacity counted without real-time performance”), unless they are paired with a control-consistent disturbance model.

A particularly important development in analytical modelling is the explicit inclusion of train-passenger interaction into macroscopic railway performance representations. Seo et al. (2023) derive a tractable FD that links train-flow (train/h), train-density (train/km), and passenger-flow, and they do so by starting from microscopic operation principles (boarding and cruising) and aggregating upward. One analytically consequential element is that dwell time becomes headway-dependent: the number of waiting passengers scales with headway, which in turn extends boarding time. In the paper’s formulation, dwell time includes a queuing-based component proportional to passenger demand and headway, plus a buffer term for door operations–embedding a feedback mechanism that can produce amplification (“bunching”) under high demand (Seo et al., 2023). This model class matters for headway control because it formalizes a mechanism by which aggressively tightened headways can backfire when the system is demand-saturated, smaller headways can increase interference and reduce effective speed/flow through passenger-induced dwell extensions, pushing the system toward the congested regime even without external incidents. For capacity assessment, that means any analytical approach that assumes dwell times are exogenous (or bounded by static margins) risks systematically mis-estimating the achievable throughput in peak periods, especially in metro-like contexts where passenger congestion is a first-order driver.

The strongest analytical models are those that

• make the control variable explicit (speed, dwell, dispatch headway),
• provide closed-form sensitivity relations (how capacity changes with block length, dwell variability, braking assumptions), and
• expose regime changes (stability loss, “capacity drop”-like behavior) (Gašparík et al., 2025; Bulková et al., 2022).

Yet the analytical paradigm often fails precisely on the dimensions that matter most for dynamic headway control: closed-loop implementability and robustness. In blocking-time and timetable-compression formulations, disturbances are frequently represented as buffers or conservative margins; the approach can tell us how close the schedule is to a nominal limit, but it struggles to predict how fast the system degrades once variability exceeds the buffer. FD-based approaches improve on that by expressing state-dependent performance, but they still require an operational mapping from real-time measurements (density, headway variance, dwell demand) to admissible control actions (speed commands, holding, skipping, dispatch regulation) (Yousefi et al., 2026). Train-passenger analytical models move further by capturing endogenous dwell growth, but their calibration and network generalization can be challenging, and many results remain line-specific unless validated across different rolling-stock and station designs.

In practical terms, the analytical and traffic-flow paradigm is best viewed as the front-end of a modelling stack for capacity optimization: it excels at

• rapid screening of design choices (block segmentation ranges, nominal headway targets),
• deriving interpretable levers (which parameter dominates capacity in which regime), and
• providing “sanity bounds” for more complex models.

It is least reliable when used alone to justify real-time capacity gains from tighter headways, because it tends to under-represent the very mechanisms that determine whether a nominal headway can be sustained–communication latency, stochastic dwell growth, controller saturation, and delay propagation. This is precisely why the field is progressively shifting toward hybrid formulations where analytical structure (constraints, regime logic) is retained but embedded into simulation/optimization and then informed by data-driven estimation.

5.2 Simulation and optimization approaches

Simulation-based and optimization-oriented models represent the first modelling paradigm in which headway ceases to be a purely geometric constraint and becomes an explicitly controllable variable. Unlike analytical formulations, which evaluate feasibility under idealised assumptions, microscopic and mesoscopic simulations reconstruct the time-space evolution of train trajectories and therefore capture the dynamic mechanisms that determine whether a nominal headway can actually be sustained. This capability is essential for capacity assessment in high-density traffic, where delay propagation, heterogeneous rolling stock, and stochastic dwell times dominate system behaviour.

Microscopic simulation environments allow infrastructure, signalling logic, rolling-stock performance, and timetable structure to be modelled at high temporal resolution (Zhang, 2025). In practical capacity studies, simulation has been shown to reproduce realised traffic performance with a level of accuracy unattainable by compression-based analytical methods. For example, in a detailed OpenTrack-based evaluation of Czech main-line infrastructure, simulated headway and delay distributions closely matched the infrastructure manager’s operational methodology while simultaneously providing additional performance indicators such as conflict frequency and delay compensation potential, which are not available in static approaches (Tischer et al., 2020). This result is critical from a control perspective: capacity becomes measurable through dynamic indicators (delay growth, recovery time, headway dispersion) rather than through minimum separation alone.

The principal strength of simulation lies in its ability to represent disturbances explicitly. In disruption scenarios for urban rail systems, observed service frequency reductions of 30%–70% on the affected line were reproduced through headway evolution in a simulation framework that incorporated both supply and demand responses (Nash and Huerlimann, 2004). Such magnitudes cannot be inferred from static capacity formulations because they emerge from nonlinear interactions between trains and from control actions taken during the disturbance. Consequently, simulation provides the first modelling layer in which effective capacity, defined as the traffic volume that can be maintained under stochastic perturbations, can be evaluated directly.

However, simulation alone does not guarantee improved operational performance, because it is primarily an evaluation tool rather than a decision-making mechanism. This limitation has led to the integration of optimization and optimal-control formulations into the simulation loop. In model predictive control (MPC)-based railway traffic management, the future evolution of train trajectories is optimized over a receding horizon while enforcing hard safety constraints. A key result demonstrated in real freight-network experiments is that safe and feasible traffic regulation can be achieved with short prediction horizons, which dramatically reduces computational requirements and enables near real-time application (Vujanic and Hill, 2021). This finding directly addresses one of the main criticisms of optimization approaches, their computational complexity, and shows that dynamic headway control can be implemented without solving a full-network optimization problem at every time step.

Simulation-based optimization (SBO) further extends this paradigm by treating the simulation as a “black-box” representation of the railway system and searching for control policies that maximise performance. In a large-scale application to the Hong Kong metro network using AFC and AVL data, simultaneous calibration of passenger path choice and train capacity demonstrated that system performance is highly sensitive to crowding-dependent dwell times, and that response-surface optimization methods consistently outperformed alternative algorithms across multiple demand scenarios (Mo et al., 2020). From a capacity perspective, this is a crucial result: the achievable throughput is not determined by infrastructure alone but by the joint optimisation of train trajectories and passenger flow distribution.

Despite their superior dynamic fidelity, simulation and optimization approaches face a fundamental scalability challenge. High-resolution microscopic models require substantial computational resources, and the evaluation of multiple control strategies for large networks can become intractable in real time. Even when receding-horizon optimization is used, the computational effort grows rapidly with the number of interacting trains and conflict points. This creates a trade-off between model fidelity and real-time applicability: the most accurate models are often too slow for operational control, while simplified models sacrifice dynamic detail.

Another critical limitation concerns model calibration and transferability. Simulation-based capacity estimates depend strongly on input assumptions such as dwell-time distributions, reaction times in signalling systems, and rolling-stock performance. Without continuous data assimilation, these parameters quickly become outdated, leading to a divergence between simulated and actual performance. In this sense, simulation models are highly sensitive to disturbances not only in the operational domain but also in the modelling domain itself.

From a control-capability standpoint, however, simulation-optimization frameworks represent a decisive step beyond analytical methods. They allow headway to be regulated through speed commands, holding strategies, or rescheduling decisions and make it possible to evaluate how these control actions affect stability and throughput simultaneously. This dual evaluation is essential for capacity optimisation, because the optimal operating point is determined not by the minimum feasible headway but by the balance between density and recoverability.

In comparative terms, simulation without optimization provides high disturbance sensitivity and accurate performance assessment but limited real-time applicability. Optimization without high-fidelity simulation provides faster solutions but risks violating dynamic feasibility. Integrated simulation-optimization approaches offer the highest control capability and the most realistic capacity evaluation but remain computationally demanding. Their practical implementation therefore depends on reduced-order models, rolling-horizon strategies, and efficient solution reuse mechanisms.

From the perspective of dynamic headway control, the most important contribution of this paradigm is that it transforms capacity from a static infrastructure characteristic into a controllable performance variable. By explicitly modelling the time evolution of train interactions and embedding control decisions in the system dynamics, simulation-optimization frameworks provide the first modelling environment in which capacity gains can be validated under realistic, disturbance-rich conditions. At the same time, their computational requirements and calibration sensitivity explain why they are increasingly combined with data-driven prediction methods, which form the next stage in the evolution of railway traffic modelling.

5.3 AI and data-driven methods

The rapid digitalisation of railway systems has led to the emergence of data-driven modelling as a distinct paradigm for headway control and capacity assessment. Unlike analytical formulations, which rely on simplified physical assumptions, and simulation-optimization frameworks, which explicitly reconstruct system dynamics, artificial-intelligence methods learn the behaviour of the railway system directly from operational data. This shift is particularly significant for capacity analysis, because it allows the modelling of nonlinear interactions, context-dependent disturbances, and time-varying performance limits that are difficult to represent in traditional frameworks.

A major area of application is real-time delay prediction, which provides the predictive horizon required for proactive traffic regulation. Machine-learning models trained on large operational datasets have demonstrated a substantial improvement over historical-average-based approaches. In a real-time prediction study using multiple Amtrak corridors, a multilayer perceptron combined with real-time and historical features achieved the highest performance among tested methods, while the inclusion of exogenous variables such as weather, ridership, and accumulated upstream delay significantly improved predictive accuracy. The results confirmed that delay evolution cannot be explained by timetable parameters alone and must be modelled as a multivariate, time-dependent process (Lapamonpinyo et al., 2022).

More recent research has moved beyond single-train prediction toward network-level modelling using graph neural networks (GNNs), where trains, stations, and track sections are represented as interconnected nodes. This representation is particularly suited to headway-controlled systems because delay propagation is inherently a network interaction problem. In a heterogeneous GNN model for railway delay evolution, prediction accuracy remained stable across multiple forecasting horizons (10–30 min), while the learned interaction structure revealed that the strength of train-to-train coupling increases as headway decreases (Li et al., 2026a). From a control perspective, this is a critical result: it provides quantitative evidence that headway is not merely a local separation constraint but a system-level interaction variable that governs delay amplification.

The scalability of data-driven approaches is demonstrated by their application to very large networks. A railway-centric spatio-temporal graph convolutional network trained on the entire Indian Railways system, covering 4,735 stations across 17 zones, achieved consistent improvements over baseline models in station-level delay prediction, while maintaining computational feasibility for network-wide deployment (Chowdhury et al., 2025). Such results indicate that AI-based methods are currently the only modelling paradigm capable of combining high spatial resolution with system-level coverage, which is essential for capacity assessment in large, heterogeneous networks.

Another important development is the integration of operational and environmental data. A recent nationwide dataset for Finland combining 38.5 million operational observations with synchronised meteorological measurements revealed seasonal delay rates exceeding 25% during winter months, demonstrating that environmental variability alone can shift the achievable capacity envelope of a railway system (Borin et al., 2026). This finding has direct implications for capacity modelling: static infrastructure-based indicators cannot capture such time-dependent performance limits, whereas data-driven models can adapt to changing external conditions in real time.

Despite these advantages, the primary limitation of AI-based approaches lies in the gap between prediction and control. Most existing models provide forecasts of delays or dwell times but do not directly generate control actions. Even when high predictive accuracy is achieved, the resulting capacity gain depends on how this information is integrated into dispatching or speed-control strategies (Hou, 2025). A recent graph-neural-network-based timetable-rescheduling framework addresses this limitation by learning the effects of dispatching actions (retiming, reordering, speed adjustment) from operational data and generating rescheduling solutions that outperform rule-based benchmarks under multiple disturbance scenarios, while remaining computationally efficient for real-time use (Huang et al., 2025; D’Amato et al., 2025). This integration of prediction and decision-making represents a decisive step toward closed-loop headway control.

However, data-driven models also introduce new challenges. Their performance depends strongly on data availability and quality, and their transferability to different infrastructure or signalling systems is not guaranteed. Moreover, purely data-driven models may lack the physical constraints required for safety-critical applications, which limits their direct use in control without hybridisation with physics-based models. Recent research therefore focuses on combining graph-based learning with domain-knowledge constraints to achieve a balance between accuracy and interpretability. In a neural-relational-inference framework for network-wide delay prediction, the model automatically learned train-to-train interaction strengths while preserving a physically meaningful structure, enabling both accurate prediction and explainable decision support (Li et al., 2026b). From a disturbance-sensitivity perspective, AI-based models offer a unique advantage: they do not require an explicit enumeration of disruption scenarios, because they learn the statistical structure of delay propagation directly from data. This makes them particularly effective in complex, high-density networks where analytical enumeration of all conflict combinations is infeasible. At the same time, their black-box nature can obscure the causal mechanisms that determine capacity limits, which is why hybrid cyber-physical modelling environments (combining simulation, optimization, and machine learning) are increasingly regarded as the most promising direction for real-time capacity control (Anupriya et al., 2020).

In comparative terms, AI-based methods provide the highest scalability and the strongest real-time applicability among all modelling paradigms. They are highly sensitive to disturbances because they are trained on disturbed operations rather than on idealised schedules. Their control capability, however, remains indirect unless they are embedded in optimisation or feedback frameworks. Consequently, their main contribution to dynamic headway control is not the direct computation of capacity but the provision of predictive state estimation that enables proactive regulation.

From the standpoint of capacity as a system performance metric, the most important conceptual shift introduced by data-driven modelling is the transformation of capacity from a static upper bound into a time-dependent, observable variable. By continuously estimating delay propagation, interaction strength, and recovery potential, AI-based methods make it possible to evaluate how close the system operates to its dynamic stability limit at any given moment. This capability is essential for real-time traffic management and represents the final step in the evolution from infrastructure-based capacity estimation toward control-oriented capacity optimisation.

The fundamental differences between the reviewed modeling paradigms in terms of control representation, scalability, real-time applicability, and disturbance sensitivity are summarized in Table 1.

TABLE 1. Comparative assessment of modeling paradigms for headway control and capacity evaluation from a system-performance perspective.

The comparison highlights that no single approach simultaneously satisfies all requirements for dynamic headway control and capacity optimization. Instead, the results indicate a clear transition toward hybrid cyber-physical frameworks that combine analytical structure, simulation-based feasibility, and data-driven prediction within a unified control loop.

6 Control architectures for capacity optimization

The transition from capacity estimation to capacity control requires a fundamental shift in the role of traffic-management architectures. In conventional signalling, separation is enforced through predefined safety envelopes, and the traffic-management layer operates primarily as a supervisory system. In dynamically controlled railways, by contrast, the achievable capacity becomes a direct output of the control architecture. The performance of the railway is therefore determined not only by infrastructure and rolling stock but by the structure of the feedback loop that regulates train motion, spacing, and conflict resolution in real time. This transformation is most evident in moving-block systems, adaptive headway control, predictive trajectory optimization, and virtual coupling, which together represent successive stages in the evolution from open-loop scheduling toward closed-loop traffic control.

Moving-block signalling replaces the discretized spatial logic of fixed-blocks with a continuous representation of train position and braking capability. The separation between trains is no longer determined by track segmentation but by the dynamically computed safe braking distance, which depends on speed, adhesion conditions, and train performance. This architecture significantly increases the utilisation of existing infrastructure because it eliminates the unused space inherent in fixed-block systems. At the same time, it introduces a new dependency: system performance becomes tightly coupled to the accuracy and latency of communication and positioning. Analytical and simulation-based studies consistently show that moving-block operation shifts the capacity limit from infrastructure geometry to the control and communication layer (Diaz and Tyler Dick, 2021; Ichikawa and Miyatake, 2019).

In practical implementations, the reduction of headway is constrained not only by braking physics but by the update rate of the control loop and by the integrity of train-to-wayside communication (Wang et al., 2019). This leads to a performance regime in which capacity gains are achieved at the cost of increased sensitivity to communication failures and degraded-mode operation. Consequently, the robustness of the system becomes a dominant design parameter: when communication is lost, the system must revert to a safe fallback mode, in which train separation is governed by conservative, predefined safety margins rather than continuously updated real-time control. This fallback operation does not imply a return to fixed-block infrastructure, but rather an operational regime with fixed-block-equivalent separation constraints. Such a transition leads to a sudden reduction in throughput and highlights the trade-off between safety assurance and capacity performance under degraded communication conditions.

Adaptive headway control extends this concept by explicitly treating spacing as a controllable variable rather than a derived safety margin. In this architecture, speed commands, dwell-time regulation, and dispatching decisions are coordinated to maintain a target headway distribution rather than a single minimum value. The objective is not to minimise separation at all times but to stabilise traffic flow around a performance-optimal operating point. This shift from minimum-headway logic to distribution-based control is crucial for effective capacity optimisation, because it allows the system to absorb disturbances without entering an unstable regime. From a system-performance perspective, the key indicator is no longer the minimum achievable headway but the variance of headway under stochastic operation. Adaptive control reduces this variance and therefore increases the number of trains that can be operated within a given time window, even if the nominal minimum separation remains unchanged.

Predictive control architectures represent the first class of solutions in which headway and capacity are optimised simultaneously under explicit dynamic constraints. In model predictive control (MPC), the future evolution of train trajectories is computed over a finite horizon while enforcing safety constraints and operational limits (Wang et al., 2022). This approach enables the coordinated regulation of multiple trains and allows conflicts to be resolved before they propagate through the network. In distributed MPC implementations for virtually coupled or closely spaced trains, different coordination strategies (cooperative, serial, and decentralized) have been shown to provide different trade-offs between computational complexity and stability guarantees (Liu et al., 2022). The inclusion of heterogeneous train masses and passenger-load variations in the control model significantly improves robustness, because it prevents the controller from relying on nominal performance parameters that are no longer valid during operation (Xun et al., 2022). The main limitation of predictive control lies in its computational burden. The complexity of the optimisation problem grows rapidly with the number of interacting trains and constraints, which restricts real-time applicability in large networks. Practical implementations therefore rely on hierarchical architectures in which a high-level traffic-management layer defines feasible trajectories while local controllers enforce safety and tracking.

Virtual coupling represents the most advanced control architecture currently under development and fundamentally changes the definition of train separation. Instead of maintaining an absolute braking distance to a fixed reference point, the following train maintains a relative braking distance to the leading train and dynamically adapts its motion to the leader’s behaviour. This concept allows trains to operate as a coordinated convoy without physical coupling and has been shown in system-level assessments to reduce headway by more than 40% compared with moving-block operation, leading to substantial capacity gains on bottleneck sections (Zhang, 2025). The performance benefit arises from the fact that braking effort is shared implicitly between trains: the follower can exploit the deceleration of the leader rather than assuming worst-case independent braking. From a control perspective, this requires a high-bandwidth, low-latency train-to-train communication channel and a safety framework capable of guaranteeing collision avoidance under dynamic conditions. Recent decentralized control solutions based on control-barrier functions show that safety constraints can be enforced in real time through a sequence of quadratic optimisation problems without centralised coordination, which significantly improves scalability (Li et al., 2026).

Despite its theoretical advantages, virtual coupling also illustrates the central trade-off between capacity and system complexity. The closer trains operate, the more tightly their dynamics become coupled, and the more sensitive the system becomes to delays in communication, model uncertainty, and actuator saturation. A failure in the communication link or an unexpected braking behaviour of one train immediately affects the entire convoy. As a result, safety certification becomes significantly more challenging than in moving-block systems, because the protection logic must account for cooperative behaviour and relative motion rather than independent braking envelopes. Comprehensive reviews of virtual-coupling research identify reliable communication, integrated traffic-management architectures, and cyber-security as the main barriers to deployment (Felez and Vaquero-Serrano, 2023). From a system-performance perspective, the progression from moving-block to virtual coupling can be interpreted as a shift from infrastructure-limited capacity to control-limited capacity. In fixed-block systems, the bottleneck is spatial segmentation; in moving-block systems, it is braking physics and communication latency; in virtual coupling, it becomes the robustness of cooperative control. Each stage increases the achievable throughput but simultaneously increases the dimensionality of the control problem. This explains why the practical implementation of advanced control architectures often proceeds in hybrid form, combining predictive trajectory optimisation with conventional signalling fallback modes.

Another critical aspect concerns the safety-capacity trade-off. Any reduction in headway reduces the time available for fault detection and recovery. Therefore, capacity gains can only be realised if the control architecture provides faster and more reliable state estimation than traditional systems. In moving-block and virtual-coupling environments, the integrity of position information and the determinism of communication delays directly determine the safe separation. This transforms communication infrastructure into a safety-critical component and requires redundancy and formal verification, which increase system cost and complexity (Geleta et al., 2026).

The evolution of railway control architectures can be interpreted as a transition from infrastructure-constrained capacity to control-limited system performance. Each stage increases the achievable throughput while simultaneously introducing higher communication dependency, computational complexity, and robustness challenges. This system-level relationship between control paradigm, effective capacity, and implementation constraints is illustrated in Figure 2.

The transition from fixed-block to virtual-coupling operation is accompanied by a shift from infrastructure-limited to control-limited capacity. While advanced architectures enable higher throughput through dynamic headway regulation and cooperative train control, they also introduce increased communication dependency, computational requirements, and robustness challenges. The figure highlights the growing role of feedback-based optimisation in determining effective railway capacity.

In summary, control architectures for capacity optimisation redefine the railway as a cyber-physical system in which throughput is governed by feedback dynamics rather than by static spacing rules. Moving-block signalling increases utilisation by eliminating spatial discretisation but introduces communication-dependent performance limits. Adaptive headway control improves stability by regulating spacing distribution rather than minimum separation. Predictive control enables coordinated conflict resolution but is constrained by computational scalability. Virtual coupling offers the highest theoretical capacity gain but shifts the bottleneck to cooperative control robustness and safety certification. The central challenge is therefore not the physical feasibility of reduced headways but the design of control architectures that can maintain safe and stable operation under real-time disturbances while remaining implementable at network scale.

7 Research gaps and future intelligent control

The transition from static capacity estimation to dynamically controlled railway operation has exposed a fundamental limitation of the current research landscape: the absence of a unified framework that integrates traffic dynamics, real-time control, and system-level performance evaluation. Despite substantial progress in moving-block signalling, predictive traffic management, and cooperative train operation, these developments remain largely isolated within their respective methodological domains. Analytical capacity models still operate under steady-state assumptions, optimisation-based traffic management focuses on conflict resolution without explicit stability boundaries, and data-driven approaches provide accurate prediction but are rarely embedded into safety-critical feedback loops. As a result, railway capacity continues to be evaluated as an offline planning metric rather than as a continuously regulated system variable.

As illustrated in Figure 2, the evolution of railway control architectures leads to an operational regime in which capacity is no longer constrained by infrastructure geometry but by the performance of real-time control and communication. This fragmentation becomes particularly evident at the network scale. Most dynamic-control studies are limited to corridors or single lines, whereas real railway systems are characterised by strong spatial and temporal interdependencies between line sections, junctions, and terminal areas. Empirical analyses of digital signalling deployment show that line-capacity gains are often not translated into network-wide throughput because node operation remains governed by timetable-based logic.

While significant progress has been made in the development of real-time control models, including model predictive control (MPC) and distributed MPC frameworks for headway regulation, their large-scale application remains limited. Most existing implementations are focused on corridor-level or small-network scenarios, and their deployment in complex railway systems is constrained by computational complexity, communication requirements, and integration with existing signalling architectures. As a result, the key challenge is not the absence of real-time control models, but the development of scalable and robust frameworks capable of representing network-wide interactions under real-time constraints.

Future control frameworks must treat the railway as a distributed cyber-physical system in which infrastructure, rolling stock, communication, and traffic management are co-optimised.

A second important research direction concerns the integration of artificial intelligence into the railway control loop. While earlier studies emphasized the limited role of machine learning in operational control, recent developments demonstrate a growing incorporation of artificial intelligence, particularly reinforcement learning and optimization-based digital frameworks, into real-time railway traffic management. Machine-learning models have shown high accuracy in predicting delays, dwell times, passenger flows, and infrastructure degradation, and recent studies have extended these capabilities to real-time timetable optimization and network-wide rescheduling under dynamic conditions (Eslami et al., 2025; Bafandkar et al., 2025).

Despite these advances, the integration of artificial intelligence into safety-critical closed-loop control remains constrained. The main challenge lies in the incompatibility between data-driven learning and the deterministic safety guarantees required in railway operation. Control architectures rely on formally verified constraints, while many AI models operate as black-box predictors without explicit stability or safety certificates. This creates a structural separation between perception and decision-making layers. A recent comprehensive review confirms that a large proportion of AI applications are still concentrated in monitoring, maintenance, and prediction rather than in certified motion control and traffic regulation (Sarp et al., 2024). Consequently, the key challenge is no longer the absence of artificial intelligence in railway systems, but the development of hybrid control frameworks that combine learning-based adaptability with formally verifiable safety constraints required for real-time railway operation.

Digital-twin technology has rapidly evolved from a conceptual framework to an operational tool already deployed in modern railway systems. A railway digital twin represents a continuously synchronised virtual model of the physical system, integrating real-time data acquisition, predictive simulation, and decision support within a unified operational environment. Recent studies demonstrate that digital twins are actively used for real-time monitoring, predictive maintenance, passenger flow analysis, and disruption management. For example, real-world implementations combining digital twins with deep learning enable high-resolution passenger flow prediction and support operational decision-making under dynamic conditions (Ou et al., 2025). In addition, comprehensive reviews confirm the widespread adoption of digital twin technologies across railway applications, including infrastructure monitoring, operational optimisation, and system-level performance management (Thompson et al., 2025). Despite this maturity, current implementations remain largely focused on monitoring and decision-support functions rather than fully autonomous control. The integration of digital twins into closed-loop traffic control is still limited by challenges related to real-time computational scalability, data synchronisation, and the incorporation of safety-critical control constraints. Consequently, the key challenge lies not in the development of digital twin technology itself, but in its deeper integration into real-time, safety-critical railway control architectures.

Beyond infrastructure management, digital twins are increasingly used for operational decision support. In a real-world case study of an urban rail network, a digital twin combined with deep-learning-based passenger-flow prediction provided high-resolution estimates of disruption propagation and enabled faster traffic-control decisions under non-recurrent conditions (Ou et al., 2025). These results indicate that digital twins can transform capacity into an observable real-time variable, allowing the control system to operate close to the stability boundary instead of relying on conservative offline estimates.

Reinforcement learning represents another key direction for intelligent railway control because it allows control policies to be learned directly from interaction with the system. In contrast to classical optimisation methods that require an explicit model, reinforcement learning can handle nonlinear and stochastic dynamics and can adapt to changing operating conditions. Its potential has already been demonstrated in infrastructure management: the integration of deep reinforcement learning with a railway digital twin reduced maintenance activities by 21% and infrastructure defects by 68% in a 4-year field-data study, while simultaneously improving operational safety (Sresakoolchai and Kaewunruen, 2023). Although this application concerns maintenance rather than traffic control, it clearly illustrates the capability of reinforcement learning to optimise long-term system performance under uncertainty. The extension of such approaches to train regulation and headway control remains an open research challenge.

One of the main barriers to the deployment of reinforcement learning in traffic control is the lack of formal safety guarantees. Current research therefore focuses on learning-based model predictive control and on reinforcement-learning policies operating under safety filters such as control-barrier functions. A recent study on learning-based predictive control for virtually coupled trains demonstrates that adaptive control policies can be trained while maintaining hard safety constraints, indicating that learning-based approaches can be effectively integrated with deterministic protection logic through hybrid control architectures (Vaquero-Serrano et al., 2025). This result suggests that the gap between data-driven learning and safety-critical control can be partially bridged in advanced railway systems.

More broadly, recent surveys on artificial intelligence in safety-critical transportation systems confirm that substantial progress has been made in integrating AI with formally verified control frameworks, particularly through hybrid approaches combining learning-based models with safety filters and control-theoretic guarantees (Perez-Cerrolaza et al., 2024). These developments indicate that the key challenge lies not in the conceptual integration of artificial intelligence into control, but in ensuring robustness, certification, and large-scale deployment in real-world railway environments.

Distributed and multi-agent control represents a well-established research direction in railway traffic management rather than an emerging paradigm. As traffic density increases and train interactions become stronger, centralised traffic-management systems face scalability and robustness limits, which has motivated extensive research into decentralised coordination strategies. Distributed control frameworks allow local decisions to be taken by individual trains or control regions while maintaining global consistency through communication protocols.

A large body of literature has explored multi-agent coordination and cooperative control for railway systems, including applications in traffic regulation, conflict resolution, and energy-efficient operation. Recent studies further formulate real-time railway traffic management as a distributed constraint optimisation problem, demonstrating that decentralised coordination can significantly improve convergence speed and scalability in large networks compared with centralised approaches (D’Amato et al., 2025). This paradigm is particularly relevant for virtual-coupling scenarios, where cooperative motion requires fast local control loops and cannot rely on a single central decision unit. Despite this maturity, challenges remain in large-scale deployment, particularly with respect to communication overhead, coordination stability under highly dynamic conditions, and integration with safety-critical signalling systems. This paradigm is especially relevant for virtual-coupling scenarios, where cooperative motion requires fast local control loops and cannot rely on a single central decision unit.

The convergence of digital twins, reinforcement learning, and distributed control leads to a new operational concept in which capacity is no longer a fixed infrastructure parameter but a dynamic performance envelope continuously shaped by intelligent control. In such a system, real-time state estimation, predictive simulation, and adaptive control operate in a closed loop. The digital twin provides the predictive environment, reinforcement learning supplies adaptive policies, and distributed control ensures scalability and resilience.

However, several challenges must be addressed before this paradigm can be realised in practice. The first concerns computational scalability: real-time optimisation and learning in large networks require hierarchical architectures and model-reduction techniques. The second is communication reliability, as high-bandwidth and low-latency data exchange becomes a safety-critical requirement for cooperative control. The third is certification. Traditional railway safety assessment is based on deterministic and component-oriented logic, whereas intelligent control systems are adaptive, data-driven, and distributed. New validation and verification methodologies are therefore needed for learning-enabled control.

In summary, the main research gap is not the lack of advanced control algorithms but the absence of a unified cyber-physical framework that integrates modelling, prediction, optimisation, and safety assurance. Digital twins will provide the operational platform for real-time decision-making, reinforcement learning will enable adaptive and disturbance-resilient control, and distributed architectures will ensure scalability at network level. The integration of these technologies will transform railway capacity from a static planning metric into a continuously regulated system-performance variable and represents the key direction for future intelligent railway operation.

8 Conclusion

This review has examined railway capacity not as a static infrastructure characteristic but as a dynamic system-performance variable emerging from the interaction between traffic flow, control architectures, and real-time operational conditions. The conducted analysis demonstrates that the traditional separation between capacity assessment, signalling design, and traffic management is no longer consistent with the requirements of high-density and digitally controlled railway systems. Instead, capacity must be interpreted as the outcome of a closed-loop process in which headway regulation, disturbance propagation, and control responsiveness jointly determine the achievable throughput.

The comparative evaluation of modelling paradigms shows that analytical and timetable-based approaches remain limited to steady-state representations and are therefore unable to capture the dynamic stability boundaries that govern real operation. Simulation and optimisation methods provide higher fidelity but are typically applied in an open-loop planning context, while data-driven approaches offer accurate prediction without direct integration into safety-critical control. This fragmentation explains why significant infrastructure and signalling upgrades do not always result in proportional increases in operational capacity at network level. The key limitation is not the physical separation between trains but the absence of a unified framework that links dynamic modelling, real-time control, and system-level performance. The analysis of control architectures reveals a clear evolutionary trajectory. Fixed-block operation is constrained by spatial segmentation, moving-block systems shift the bottleneck to braking physics and communication latency, predictive traffic management introduces computational and data-dependency limits, and virtual coupling transforms capacity into a function of cooperative control robustness. This progression confirms that the future capacity of railway systems will be primarily control-limited rather than infrastructure-limited. As traffic density increases, the achievable throughput becomes increasingly dependent on the speed, reliability, and scalability of the feedback loop that regulates train motion and spacing.

A central finding of this review is that effective capacity is governed by traffic stability rather than by the minimum feasible headway. The regulation of headway variance, the mitigation of disturbance amplification, and the coordination of train trajectories in real time have a greater impact on throughput than the reduction of nominal separation alone. This shifts the focus of capacity optimisation from geometric constraints to dynamic system behaviour and highlights the importance of feedback-based control strategies.

The identified research gaps indicate that the main challenge for future railway operation is the development of unified cyber-physical control frameworks. Such frameworks must integrate real-time state estimation, predictive simulation, and adaptive decision-making while maintaining formally verifiable safety constraints. Digital twins provide the operational environment for continuous performance evaluation and predictive regulation, reinforcement learning enables adaptive control under stochastic conditions, and distributed coordination ensures scalability in large networks. The convergence of these technologies will transform capacity from an offline planning metric into a continuously regulated performance envelope.

From a system-level implementation perspective, this transformation requires new approaches to communication reliability, computational scalability, and system certification. The increasing dependency of capacity on real-time control implies that communication networks become safety-critical components, hierarchical architectures are needed to maintain real-time feasibility, and new validation methodologies must be developed for learning-enabled and cooperative control systems. Against this background, the main contribution of this review is the formulation of a closed-loop conceptual framework in which control architecture, headway dynamics, traffic stability, and effective capacity are treated as interdependent elements of a single system. This perspective provides a unified interpretation of recent developments in railway traffic management and establishes a foundation for the design of future intelligent control strategies.

Taken together, these findings indicate that the transition toward dynamically controlled railway operation represents a paradigm shift from infrastructure-based capacity expansion to performance-based capacity regulation. The ability to operate close to the stability boundary while maintaining safety will define the next-generation of high-capacity railway systems and will require the integration of control theory, artificial intelligence, and cyber-physical system design into a coherent operational framework.

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Footnotes

Edited by: Alireza Talebpour, University of Illinois at Urbana-Champaign, United States

Reviewed by: Shayan Bafandkar, University of Illinois at Urbana-Champaign, United States

Gloria Gori, University of Florence, Italy