Composite Spatiotemporal Traffic Instability Metric for Early Congestion Detection in Underground Expressways

Abstract

Traffic flow in long underground expressways is expected to exhibit amplified spatiotemporal variability due to confined geometry, longitudinal gradients, limited recovery space, and heterogeneous vehicle interactions. As these facilities remain at the planning stage, empirical field data are unavailable, necessitating simulation-based methodological development. Conventional performance indicators (average speed) primarily reflect macroscopic deterioration after congestion has materialized and are therefore insufficient for capturing early variability transitions. This study proposes a composite Spatiotemporal Variability Metric (STVM) designed to quantify instability-related variability dynamics and enable early congestion detection in confined expressway environments. The metric structure was established through the synthesis of prior traffic flow instability research and systematic evaluation of 72 predesigned microscopic simulation scenarios representing diverse geometric and operational conditions. STVM integrates six mechanism-informed components: short-term speed and density fluctuations, heavy-vehicle proportion, sectional saturation level, ramp interference intensity, and exit discharge efficiency. Comparative analyses against average speed demonstrated that variability escalation measured by STVM consistently precedes observable speed degradation by 5–20 min. Internal contribution analyses using correlation, regression, and random forest modeling further confirmed the dominant structural roles of fluctuation- and saturation-related components in governing variability escalation. These findings confirm the usefulness of the STVM in analyzing transition dynamics and supporting real-time ITS-based monitoring in confined expressway systems.

1. Introduction

Underground expressways differ fundamentally from surface highways due to enclosed cross-sections, long uninterrupted segments, longitudinal gradients, lane restrictions, and mixed traffic composition. These structural characteristics are expected to amplify spatiotemporal variability in traffic flow by limiting recovery space and increasing driver sensitivity to disturbances. Prior research has shown that traffic behavior in tunnels and underground corridors deviates from that on surface expressways, with geometric constraints and vehicle heterogeneity significantly affecting traffic stability [1,2,3]. Classical tunnel flow studies and instability theory further indicate that minor perturbations in speed or spacing can propagate and evolve into self-reinforcing oscillations, even in the absence of explicit bottlenecks [4,5,6].

Such propagation-based instability may be more pronounced in long confined corridors where external dissipation mechanisms are limited. However, widely used operational indicators, including average speed, occupancy, and flow, primarily reflect macroscopic deterioration after congestion has formed, making them inadequate for detecting early variability escalation and transition dynamics. Single-variable measures are also sensitive to detector placement and local conditions, limiting their ability to represent corridor-level spatiotemporal variability. Recent studies have emphasized the need for composite approaches that integrate temporal fluctuations and spatial heterogeneity. Nevertheless, existing variability metrics are rarely tailored to the structural and operational characteristics anticipated in long underground expressway systems. Because such facilities remain at the planning stage, empirical validation data are unavailable, necessitating simulation-based methodological development.

To address these limitations, this study proposes a composite Spatiotemporal Variability Metric (STVM) designed to quantify variability amplification and support early congestion detection in confined underground corridors. The metric structure is informed by prior instability theory and systematically refined through 72 predesigned microscopic simulation scenarios. The main contributions of this study are as follows:

• A mechanism-informed composite variability formulation tailored to confined environments;
• A systematic scenario-based construction framework;
• Quantitative evidence that variability escalation precedes observable speed degradation by 5–20 min, demonstrating early detection capability beyond conventional performance indicators.

Beyond methodological development, the proposed metric is designed to be directly compatible with detector-based monitoring environments, enabling practical intelligent transportation system (ITS)-oriented traffic state monitoring in confined expressway systems.

2. Related Work

2.1. Traffic Instability in Confined Roadway Environments

Traffic flow instability has been widely characterized as a nonlinear process in which small perturbations in speed or spacing propagate and evolve into congestion [5]. Spatial variability and stochastic driver behavior play critical roles in instability formation [6]. In confined environments such as tunnels and sag sections, geometric constraints can further amplify disturbance propagation and delay recovery [7]. Recent studies indicate that traffic behavior in underground corridors deviates from that on surface expressways due to enclosed cross-sections and limited dissipation mechanisms [8]. These findings suggest that instability dynamics may be intensified in long underground expressway systems.

2.2. Variability-Oriented Traffic Metrics

Conventional operational indicators, including average speed and occupancy, primarily reflect macroscopic performance degradation and are limited in capturing early transition dynamics. Variability-oriented approaches have therefore been explored to represent temporal fluctuations and spatial heterogeneity. Urban mobility can be evaluated using multi-dimensional congestion metrics, highlighting that traffic performance cannot be fully captured under average conditions alone and that variability and reliability play roles in understanding congestion dynamics [9]. Composite indicators derived from floating-car data have further shown that variability metrics can outperform mean-value measures in representing congestion states [10,11]. However, existing approaches generally focus on surface networks and lack mechanism-based components specifically tailored to confined underground corridors.

2.3. Research Gap

Although instability theory and variability metrics have been extensively studied, limited research has addressed composite spatiotemporal variability metrics specifically designed for long underground expressway systems. Furthermore, as these facilities remain in the planning stage, empirical field validation is currently unavailable, necessitating simulation-based methodological development. This gap motivates the development of a mechanism-informed composite metric capable of capturing variability escalation and supporting early congestion detection in confined corridor environments.

As summarized in

Table 1. Conceptual comparison between conventional variability measures and STVM.

Dimension	Conventional Measures	Proposed STVM
Variable structure	Primarily single-variable	Six mechanism-informed components
Temporal sensitivity	Lagging response to congestion	Variability escalation precedes speed degradation by 5–20 min
Spatial representation	Limited corridor-level integration	Explicit inter-segment variability integration
Operational interpretability	Raw statistical outputs	Standardized 50–100 instability score
Domain specificity	Surface road oriented	Tailored to confined underground corridors
Mechanism linkage	Implicit or purely statistical	Explicitly grounded in traffic flow theory

, existing variability indicators typically emphasize isolated temporal dispersion or spatial heterogeneity and generally do not integrate multiple mechanism-related factors relevant to confined underground environments. In addition, many conventional measures provide raw statistical outputs that are difficult to interpret within a structured monitoring context. The proposed STVM addresses these limitations by integrating six operational components, incorporating short-term rate-of-change sensitivity, and transforming standardized variability values into a bounded 50–100 scale to enhance interpretability. Simulation results (Section 4) indicate that variability escalation captured by STVM precedes observable speed degradation by approximately 5–20 min across diverse disturbance scenarios. These findings suggest that the multidimensional structure of STVM enables systematic characterization of transition dynamics in confined expressway systems while providing a structured framework for variability-based monitoring. Unlike conventional variability metrics limited to single-variable statistics, the proposed STVM incorporates a mechanism-informed composite structure to capture multiple instability drivers within confined underground expressways. This design identifies early-stage instability often overlooked by standard performance indicators. By linking traffic flow instability mechanisms with a composite metric, the STVM facilitates early detection specifically within structurally constrained environments. In particular, the STVM bridges the gap between statistical variability and underlying traffic flow instability mechanisms, a feature that fundamentally departs from conventional dispersion-based measures.

3. Methodology

3.1. Conceptual and Mechanism-Oriented Basis of STVM

Traffic instability in long underground expressways is structurally distinct from that on surface highways due to persistent geometric confinement, prolonged exposure to disturbances, limited recovery space, and delayed behavioral adaptation. Unlike surface road congestion, which is often dominated by demand–capacity imbalance, instability in confined underground corridors emerges from the interaction and reinforcement of multiple mechanisms operating simultaneously. From a mechanism-oriented perspective, instability processes in long underground expressways can be classified into four interrelated categories.

First, demand-induced pressure mechanisms represent proximity to critical flow conditions and nonlinear amplification of disturbances under high-density regimes. Capacity theory and design guidelines have consistently emphasized that instability probability increases sharply near critical density levels [12]. Under such conditions, even minor perception or acceleration delays can escalate into corridor-level fluctuations. Second, vehicle heterogeneity–induced disturbance mechanisms arise from speed differentials and acceleration asymmetry associated with heavy-vehicle composition. These effects are amplified in confined environments and along longitudinal gradients, where vehicle class interactions intensify fluctuation sensitivity.

Third, geometric amplification mechanisms reflect the influence of extended enclosed alignments and longitudinal gradients in intensifying disturbance persistence and delaying recovery. Prolonged exposure to confined geometry may alter driver spacing regulation and adaptation timing, increasing the spatial propagation of localized perturbations. Fourth, operational propagation mechanisms govern the disturbance redistribution across lanes and segments through lane-changing interactions, ramp interference, and discharge inefficiencies. Depending on traffic density and control policies, such interactions may mitigate or accelerate shockwave propagation.

To represent these mechanisms quantitatively, six component indicators were selected: speed fluctuation rate, density fluctuation rate, heavy-vehicle proportion, sectional saturation level, ramp interference ratio, and exit discharge efficiency. Each component corresponds to at least one instability mechanism, collectively covering behavioral fluctuation, demand pressure, geometric amplification, and operational redistribution processes. The component set was designed to ensure structural coverage of dominant instability drivers rather than maximize statistical fit. All component weights were initially set to unity to establish a neutral baseline configuration. Because STVM is validated primarily through controlled microscopic simulation experiments, and empirical operational datasets are not yet available, equal weighting avoids scenario-specific bias and reduces the risk of overfitting. The equal-weight configuration is intentionally adopted to ensure structural interpretability and to avoid scenario-specific bias under simulation-based validation, rather than to optimize statistical fit. The formulation remains extendable to alternative weighting strategies once sufficient field observations become available. This design allows the relative influence of each component to emerge from scenario-dependent behavior rather than being imposed through predefined weighting. The conceptual classification was empirically examined through a preliminary sensitivity analysis using 72 systematically designed microscopic simulation scenarios, in which traffic demand, heavy-vehicle proportion, longitudinal gradient, lane configuration, and lane-changing policies were varied under controlled conditions. Across these scenarios, each component exhibited statistically significant contributions under at least one traffic regime, and no additional candidate variables demonstrated independent explanatory power when the six components were jointly considered [13,14]. These findings support the structural adequacy of the selected component set for representing instability dynamics in long underground expressways. The mathematical formulation and aggregation procedure of STVM are presented in the remainder of this Section 3.2, Section 3.3 and Section 3.4. By design, the STVM focuses on the underlying causal factors of instability, moving beyond the simple statistical descriptions typical of conventional variability metrics.

3.2. Mathematical Formulation of STVM

STVM is defined as a composite spatiotemporal variability metric integrating six standardized component indicators.

$$\mathrm{S}\mathrm{T}\mathrm{V}\mathrm{M}\left(\mathrm{t}\right)={\displaystyle {\sum }_{i=1}^6}{w}_i{C}_i\left(t\right),$$

(1)

where $C_i\left(t\right)$ represents the standardized value of the ith component at time $t$, and $w_i$ denotes the corresponding weight. In this study, all weights were set to unity ($w_i=1$) to establish a neutral baseline configuration. This equal-weight structure avoids scenario-specific bias and enables structural validation of the selected components under controlled simulation conditions. The six components correspond to.

• Speed fluctuation ratio
• Density fluctuation ratio
• Heavy-Vehicle mix ratio
• Sectional saturation ratio
• Ramp interference ratio
• Exit discharge efficiency

Each component captures at least one instability mechanism described in Section 3.1.

3.3. Component Quantification

Each component was computed using detector-level measurements aggregated over fixed temporal intervals (5 min) and predefined spatial segments.

3.3.1. Speed Fluctuation Ratio

$$∆v_{i,i+1}^t={\displaystyle \frac{v_{i+1}\left(t\right)-v_i\left(t\right)}{v_i\left(t\right)}},$$

(2)

Here, $∆v_{i,i+1}^t$ is the speed fluctuation rate between segments $\mathrm{i}$ and i + 1 during a unit time interval (km/h), $v_{i+1}\left(t\right)$ is the speed of segment $\mathrm{i}+1$ during the unit time interval (km/h), and $v_i\left(t\right)$ is the speed of segment $\mathrm{i}$ during the unit time interval (km/h).

This component measures the relative speed discontinuity between adjacent segments, capturing localized propagation of acceleration–deceleration asymmetry.

3.3.2. Density Fluctuation Ratio

$$∆k_{i,i+1}^t={\displaystyle \frac{k_{i+1}\left(t\right)-k_i\left(t\right)}{k_i\left(t\right)}}$$

(3)

Here, $∆k_{i,i+1}^t$ is the density fluctuation rate between segments $i$ and $i$ + 1 during a unit time interval (vehicles/km), $k_{i+1}\left(t\right)$ is the density of segment $i+1$ during the unit time interval (vehicles/km), and $k_i\left(t\right)$ is the density of segment $i$ during the unit time interval (vehicles/km).

This metric quantifies spatial density imbalance across consecutive segments and reflects localized vehicle accumulation or dispersion patterns.

3.3.3. Heavy-Vehicle Mix Ratio

$$R_i^{hv}\left(\mathrm{t}\right)={\displaystyle \frac{{\sum }_{i=1}^n{hv}_i\left(t\right)}{{\sum }_{i=1}^n{Q}_i\left(t\right)}},$$

(4)

Here, $R_i^{hv}\left(\mathrm{t}\right)$ is the heavy-vehicle mix ratio (%) calculated across all segments of the underground expressway during a unit time interval, ${hv}_i\left(t\right)$ is the heavy-vehicle traffic volume observed in segment $i$ during the unit time interval, and $Q_i\left(t\right)$ is the total traffic volume observed in segment $i$ during the unit time interval. This ratio represents vehicle class heterogeneity and its contribution to interaction asymmetry and disturbance persistence.

3.3.4. Sectional Saturation Ratio

$$S_i^D\left(\mathrm{t}\right)={\displaystyle \frac{q_i\left(t\right)}{C_i}},$$

(5)

Here, $S_i^D\left(\mathrm{t}\right)$ is the sectional saturation at segment i during a unit time interval, $q_i\left(t\right)$ is the observed traffic volume (vehicles/h) at segment $i$ during the unit time interval, and $C_i$ is the operational/target capacity (vehicles/h) of segment i. This indicator quantifies proximity to operational capacity and represents demand-induced instability pressure.

3.3.5. Ramp Interference Ratio

$$I_R^{inflow}\left(\mathrm{t}\right)={\displaystyle \frac{q_R^{inflow}\left(t\right)}{Q_m\left(t\right)}},I_R^{outflow}\left(\mathrm{t}\right)={\displaystyle \frac{q_R^{outflow}\left(t\right)}{Q_m\left(t\right)}},$$

$$Q_m^R\left(\mathrm{t}\right)={\displaystyle \frac{q_{Rb}^m\left(t\right)-q_{Ra}^m\left(t\right)}{2}},$$

(6)

Here, $I_R^{inflow}\left(\mathrm{t}\right)$ is the ramp-merging interference ratio of ramp r during a unit time interval, $I_R^{outflow}\left(\mathrm{t}\right)$ is the ramp-diverging interference ratio of ramp r during a unit time interval, $q_R^{inflow}\left(\mathrm{t}\right)$ is the ramp inflow volume (vehicles/h) of ramp r during a unit time interval, $q_R^{outflow}\left(\mathrm{t}\right)$ is the ramp outflow volume (vehicles/h) of ramp r during a unit time interval, $q_R^{outflow}\left(\mathrm{t}\right)$ is the ramp outflow volume (vehicles/h) of ramp r during a unit time interval, $q_{Rb}^m\left(t\right)$ is the mainline traffic volume (vehicles/h) upstream of the ramp merging or diverging point during a unit time interval, and $q_{Ra}^m\left(t\right)$ is the mainline traffic volume (vehicles/h) downstream of the ramp merging or diverging point during a unit time interval.

This metric captures the disturbance intensity induced by merging and diverging flows relative to mainline traffic.

3.3.6. Exit Discharge Efficiency

$$E_{i\to j}(t)={\displaystyle \frac{Q_j\left(t\right)}{Q_i\left(t-\tau \right)}}$$

(7)

Here, $E_{i\to j}\left(t\right)$ is the exit discharge efficiency from entry segment i to exit segment j during a unit time interval, $Q_j\left(t\right)$ is the traffic volume (vehicles/h) at exit segment j in the unit time interval, $Q_i(t-\tau )$ is the traffic volume (vehicles/h) at entry segment i measured at time t, and $\tau$ is the average travel time from entry segment i to exit segment j (i.e., the inverse of the corresponding free-flow speed).

This component evaluates downstream discharge performance and reflects spillback or exit transition instability effects.

3.4. Standardization and Instability Scaling

Because the six STVM components differ in physical interpretation, magnitude, and variability range, direct aggregation would introduce scale dominance and bias. To ensure comparability across heterogeneous indicators, each ratio-based component was standardized using a rolling Z-score normalization.

$$Z_i(t)={\displaystyle \frac{X_i\left(t\right)-{\mu }_i\left(t\right)}{{\sigma }_i\left(t\right)}},$$

(8)

Here, ${\mu }_i\left(t\right)$ and ${\sigma }_i\left(t\right)$ represent the mean and standard deviation computed over a one-hour moving reference window. The rolling-window approach enables adaptive normalization under evolving traffic states while preserving sensitivity to short-term deviations from prevailing operational conditions. The standardized components were aggregated using equal weights to produce a composite variability score.

To enhance the interpretability of operational monitoring, the aggregated standardized score was transformed into a bounded instability index ranging from 50 to 100. The transformation is monotonic with respect to the composite Z-score, thereby preserving relative instability ordering across time and scenarios. The lower bound (50) corresponds to statistically stable flow conditions within the reference window, while higher values indicate progressive amplification of spatiotemporal variability. The bounded scaling concentrates analytical resolution within the transitional regime, where instability escalation is most critical, and prevents extreme deviations from disproportionately dominating the index. Because both normalization and scaling procedures are deterministic, identical input data and aggregation settings yield identical STVM values, ensuring full reproducibility across simulation scenarios. A detailed, step-by-step description of the STVM computation procedure is provided in Appendix A.

4. Simulation Framework and Validation

To evaluate the proposed STVM, traffic simulation was performed using VISSIM, with car-following parameters calibrated against driver behavior data from controlled driving simulator experiments. This approach was adopted to reflect the unique characteristics of underground corridors, where direct field data is not yet available due to the non-operational status of long underground expressways. By comparing surface and underground driving under identical geometric conditions, the driving simulator experiments isolated systematic shifts in behavior most notably a 3–5% reduction in average spacing and altered deceleration sensitivity [15]. These empirical findings were directly translated into the Wiedemann 99 model parameters, including standstill distance and headway time. This calibration ensures that the simulation framework is grounded in experimentally observed psychological constraints rather than relying on default theoretical values [16], proving a realistic approximation of constrained driving environments.

4.1. Dual-Stage Simulation Design

To cover a wide range of operating conditions, 72 development scenarios were systematically constructed using a factor-based experimental design. This design incorporates key variables influencing traffic instability in underground expressways, such as traffic demand level, heavy-vehicle proportion, longitudinal gradient, ramp inflow, and lane management policies. Rather than replicating a specific empirical distribution, the objective was to capture the full spectrum of conditions under which instability may emerge, ensuring the analysis remains within realistic and physically meaningful bounds. To evaluate performance without the risk of circular reasoning, seven separate validation scenarios were selected as representative traffic regimes. This two-stage approach effectively separates structural validation from performance evaluation, providing a robust and interpretable assessment of the STVM across a multidimensional parameter space. First, 72 systematically designed scenarios were used during the development stage of STVM. These scenarios varied traffic demand levels, heavy-vehicle proportions, longitudinal gradients, ramp inflow conditions, and lane management policies. The objective of this stage was to verify the structural adequacy and sensitivity of the six mechanism-informed components under controlled disturbance patterns. Second, seven representative scenario families (

Table 2. Summary of simulation scenarios that reflect traffic patterns observed on surface expressways and expected to occur in underground environments.

Scenario	Mainline Inflow (Vehicles/h)	Ramp Inflow (Vehicles/h)	Ramp Outflow Condition	Total Demand (Vehicles/h)	Heavy-vehicle Share (%)	Rationale
Normal Flow
1	2000	1200	Normal	3200	5	Baseline condition
2	5000	1200	Normal	6200	15	Medium-level demand
3	6000	1200	Normal	7200	30	Effect of increased gradient (downhill)
4	4000	2000	Normal	6000	15	Reflecting concentrated ramp demand
Disturbed Flow
5	5000	1200	Ramp outflow restricted	6200	5	Ramp bottleneck condition
6	6000	1200	Downstream congestion	7200	30	Reflecting surface road congestion
7	4000	2000	Normal	6000	15	Upstream bottleneck at mainline entry

) were selected for performance validation. These scenarios reflect operationally interpretable traffic regimes, including normal flow, demand escalation, heavy-vehicle dominance, gradient-induced disturbance, ramp interference, and combined disturbances. Each scenario was simulated using multiple random seeds to ensure robustness. This two-stage design separates metric construction validation (72 scenarios) from operational performance evaluation (7 scenarios), thereby preventing circular validation bias.

4.2. Early-Response Performance Relative to Speed

Early detection capability was evaluated by comparing STVM trajectories with average speed, a conventional macroscopic operational measure. Figure 1 illustrates representative time series patterns under a disturbance scenario. Across all examined sections, STVM consistently exhibited an earlier upward shift than speed, demonstrating its ability to detect early variability prior to observable speed deterioration. The dotted vertical line indicates the STVM inflection point, while the dashed line marks the corresponding speed drop. The repeated leading-response pattern across sections confirms the robustness of STVM as an early warning indicator for emerging congestion.

While average speed exhibits noticeable degradation only after congestion formation, STVM shows progressive escalation during the transition phase. Lead time was defined as the temporal difference between:

• The first sustained STVM instability escalation beyond the statistical baseline, and
• The onset of a speed-based congestion threshold

Across the seven validation scenarios, STVM demonstrated consistent early response behavior, with median lead times ranging from approximately 5–20 min depending on disturbance type.

As summarized in

Table 3. Early response performance of STVM relative to average speed. (Lead time variability across scenarios: CV 0.1~0.2).

Scenario	Flow Regime	Lead Ratio from Cross-Correlation	Lead Ratio of Inflection Points	Median Inflection Point Lead Time
2	Normal	31.4%	50.4%	+5.0
3	Normal	50.0%	41.7%	+5.0
4	Normal	43.9%	31.1%	+5.0
5	Disturbed	36.8%	52.1%	+5.0
6	Disturbed	48.3%	46.9%	+4.0
7	Disturbed	41.2%	38.7%	+5.0

, cross-correlation lead ratios range from 31.4% to 50.0% under normal conditions and from 36.8% to 48.3% under disturbed conditions. Inflection point lead ratios remain substantial across regimes, reaching up to 52.1% in disturbed scenarios. The median inflection point lead time varies between +4.0 and +5.0 min, indicating that STVM systematically precedes speed-based degradation across traffic regimes. These results confirm that the early detection capability of STVM is structurally consistent rather than scenario-specific.

To evaluate variability across scenarios, the coefficient of variation (CV) was examined, with values ranging from approximately 0.08 to 0.22. This range indicates moderate variability while preserving consistent early response patterns across diverse traffic conditions. Furthermore, prior statistical analyses using this simulation dataset confirmed that key traffic variables maintain statistically significant relationships (p < 0.05), supporting the structural validity of the framework. Rather than being driven by random variation, these results demonstrate that the observed early response behavior reflects stable, system-level dynamics inherent in the simulated environment. These results indicate that the early detection behavior of STVM is not scenario-specific but structurally consistent across varying traffic conditions.

4.3. Component Interaction Analysis

To explore interaction patterns among the STVM components, a random forest model was employed as a diagnostic tool rather than for predictive optimization. Random forest was selected for its ability to capture nonlinear relationships and handle correlated variables without the need for rigid parametric assumptions. With an explanatory performance exceeding R² > 0.85, the model demonstrated that the composite STVM score is reliably constructible from its constituent variables. To ensure the robustness of these estimates, the dataset was partitioned into training and validation subsets, with key hyperparameters such as number of trees and maximum depth maintained at standard settings to prevent overfitting. The consistency of variable importance rankings across various scenarios further suggests that the identified relationships represent structurally meaningful dynamics rather than model–specific artifacts.

Although STVM is formulated as a linear weighted aggregation of standardized components, the six input indicators are not mutually independent. Their interactions under varying traffic regimes may exhibit nonlinear patterns arising from behavioral adaptation, vehicle heterogeneity, and geometric amplification effects. To explore these interdependencies, a nonparametric random forest model was employed as a diagnostic instrument. The model was trained to predict the composite STVM score using the six standardized components as inputs. Permutation-based variable importance measures were applied to assess regime-dependent influence patterns. Importantly, this model was not used to construct, recalibrate, or optimize the STVM formulation, but solely to examine interaction structures within the traffic system. Results indicate that component influence is regime-dependent. Under demand-dominated scenarios, sectional saturation and density fluctuation exhibit the highest relative importance. In contrast, under gradient- or heavy-vehicle-dominated scenarios, heavy-vehicle mix ratio and speed fluctuation display increased joint influence. These findings suggest that while STVM maintains a linear aggregation structure for interpretability and implementation simplicity, the underlying traffic mechanisms captured by its components interact nonlinearly.

4.4. Regime-Dependent Component Contribution

Table 4. Regime-dependent contribution of STVM components under different flow conditions.

Component	Regression Coefficient (Normal)	Relative Importance (Normal)	Regression Coefficient (Disturbed)	Relative Importance (Disturbed)
Speed fluctuation	−0.42	31%	−0.38	26%
Density fluctuation	0.35	26%	0.33	21%
Heavy-vehicle mix	0.22	16%	0.24	17%
Sectional saturation	−0.18	13%	−0.28	18%
Ramp interference	0.12	9%	0.18	11%
Exit discharge efficiency	−0.08	5%	−0.11	7%

summarizes the regression-based contribution analysis under different flow conditions. Under normal flow scenarios, speed fluctuation (31%) and density fluctuation (26%) exhibit the highest relative importance, indicating that short-term spatial discontinuities dominate early instability signals. In contrast, under disturbed flow conditions, sectional saturation increases in influence (18%), reflecting amplified demand-pressure effects during escalation phases. Heavy-vehicle proportion and ramp interference also exhibit moderately increased contributions in disturbed regimes, suggesting enhanced interaction sensitivity under heterogeneous traffic compositions. Although STVM maintains a linear aggregation structure, the regime-dependent variation in component importance confirms that traffic system responses are state-dependent. These findings reinforce that STVM captures multiple instability mechanisms whose relative dominance shifts depending on traffic conditions.

4.5. Network-Level Instability Patterns

To examine spatial propagation characteristics, segment-level STVM scores were visualized under representative disturbance scenarios. The results reveal progressive escalation from localized fluctuations to corridor-level instability, consistent with classical propagation-based instability theory. Under disturbed conditions, elevated STVM values initially emerge in segments near geometric or demand perturbations and subsequently propagate upstream and downstream. Compared with average speed, which typically reflects congestion only after substantial degradation of flow conditions, STVM captures transitional amplification patterns across consecutive segments. This spatial continuity of instability signals supports the suitability of STVM for corridor-level monitoring in confined underground environments, where disturbance dissipation may be limited. As shown in Figure 2, instability under normal flow conditions remains localized and transient, whereas disturbed scenarios exhibit progressive spatial amplification across consecutive segments.

4.6. Limitations

Because long underground expressways remain in the planning stage, empirical field validation is not yet feasible. This study, therefore, relies on calibrated microscopic simulation models reflecting anticipated geometric and operational characteristics. Although simulation-based validation enables controlled disturbance testing, real-world behavioral variability and environmental uncertainties may introduce additional complexity not fully represented in the model. Future validation using operational data will be necessary once such facilities become active. Adaptive weighting strategies and integration with real-time monitoring platforms constitute potential directions for practical implementation refinement. Despite this limitation, the simulation-based framework enables controlled examination of instability mechanism, providing a structurally valid basis for future empirical application once real-world data become available.

5. Conclusions

This study proposed STVM as a composite indicator designed to overcome the limitations of conventional single-variable measures in structurally constrained underground expressway environments. The STVM distinguishes itself from conventional variability measures by combining mechanism-based components and environment-specific parameters into a unified framework capable of early response detection. By integrating six mechanism-informed components—speed fluctuation, density fluctuation, heavy-vehicle composition, sectional saturation, ramp interference, and exit discharge efficiency—STVM provides a unified spatiotemporal representation of traffic flow instability and transition dynamics. Simulation-based validation using a two-stage scenario design confirmed structural validity and operational sensitivity. Across heterogeneous disturbance regimes, STVM consistently exhibited early response behavior relative to average speed, with lead times ranging from approximately 5–20 min. This leading-response characteristic remained reproducible under variations in heavy-vehicle proportion, longitudinal gradient, ramp inflow intensity, and parameter perturbations, indicating robustness across disturbance conditions. Component-level analyses demonstrated that instability initiation is primarily governed by short-term spatial discontinuities and demand-pressure effects, whereas vehicle heterogeneity and density imbalance play stronger roles in sustained instability phases. Although STVM employs a linear aggregation structure for interpretability and implementation simplicity, regime-dependent variation in component influence reflects the nonlinear nature of underlying traffic system interactions [17]. In this context, the proposed framework aligns with the complex systems perspective on transport networks, which emphasizes that macroscopic system stability can be significantly enhanced through the management of local routing and nodal information [18]. By quantifying local instability through STVM, this study provides a practical mechanism to monitor the nonlinear transition dynamics of traffic flow, supporting the premise that addressing localized fluctuations is a prerequisite for preventing global network breakdown in constrained environments.

The early detection capability of STVM arises from its fluctuation-based formulation. Unlike mean speed, which captures accumulated performance degradation, the variability components detect transient behavioral adaptation discrepancies and localized spatial imbalances preceding macroscopic breakdown. In confined underground corridors, where disturbance dissipation is limited, such fluctuations can accumulate and propagate, making early-phase detection particularly critical. Rather than replicating site-specific operational conditions, this study focused on mechanism-level instability characterization under geometrically constrained and heterogeneity-sensitive environments. Given that these structural characteristics are common to long underground and enclosed expressway systems, the proposed framework supports transferable instability monitoring across comparable facilities. Future research should validate STVM using empirical detector-based datasets once long underground expressways become operational and explore integration with predictive and control-oriented traffic management systems. The principal contribution of this study lies in establishing a reproducible, mechanism-informed, and spatiotemporal instability quantification framework tailored to confined roadway environments. From an operational perspective, the proposed STVM relies exclusively on routinely collected traffic variables and deterministic aggregation procedures, making it computationally feasible for near real-time implementation. Because the metric does not require additional sensing infrastructure, it is structurally compatible with existing detector-based monitoring systems [19,20]. Because the proposed metric relies on standard traffic variables, it is directly transferable to real-world monitoring systems without requiring additional data infrastructure. This compatibility enables potential integration into ITS-based corridor management platforms, where instability escalation signals may support early operational awareness and decision support processes in confined underground environments. The integration of instability mechanisms into a composite variability formulation offers a novel framework for early congestion detection, particularly within the unique constrained of confined roadway environments.