Simulation-Based Safety Evaluation of Mixed Traffic with Autonomous Vehicles in Seaports

Abstract

The increasing deployment of autonomous vehicles in port logistics requires safety assessment methods that remain valid in mixed traffic environments. This study evaluates the safety of mixed automated guided vehicle (AGV) and human-driven vehicle (HDV) traffic in a seaport terminal connected to an external urban road network. A microscopic traffic model was developed in AIMSUN Next to represent gate areas, internal roads, storage-yard access, berth interfaces, and external container-truck traffic. HDVs were modeled using a Gipps-based car-following model, whereas AGVs were represented through an Adaptive Cruise Control framework. Vehicle trajectories were exported to the Surrogate Safety Assessment Model (SSAM), where Time-to-Collision (TTC) and Post-Encroachment Time (PET) were used to detect and classify conflicts. Six staged fleet-composition scenarios were evaluated in 36 simulation runs, ranging from fully human-driven operation to full automation. Total conflicts decreased from 89 in the fully human-driven scenario to 43 in the fully automated scenario (−51.7%), while rear-end conflicts decreased from 70 to 30 (−57.1%). Crossing conflicts remained relatively stable across scenarios. At the same time, mean TTC decreased from 0.80 to 0.24 s and mean PET from 1.57 to 0.38 s, indicating tighter but more coordinated interactions under automated control. These results show that automation improves longitudinal safety performance in port traffic, but also that conventional TTC and PET thresholds calibrated for human-driven traffic may not be directly applicable to automated port operations. Automation-sensitive surrogate safety criteria are therefore needed for seaport mixed-traffic evaluation.

1. Introduction

The increasing adoption of unmanned vehicles in various sectors, particularly within complex environments like seaports, necessitates a comprehensive understanding of their operational dynamics and potential impacts on safety and efficiency [1]. This is particularly crucial given the inherent challenges of integrating autonomous systems into existing, often densely populated, maritime logistical frameworks, where traditional human-centric operational paradigms are being redefined [2]. This paper addresses these concerns by proposing a simulation-based approach to analyze the movement of unmanned vehicles within a seaport environment, focusing on traffic safety assessment through surrogate indicators [3]. This methodology aims to quantify operator performance during interventions and assess collision avoidance maneuvers in complex traffic scenarios [4]. The study also integrates advanced computational methods, such as those used in analyzing mixed-traffic urban areas, to enhance the realism and predictive power of the simulations [5]. This paper aims to evaluate the safety of mixed traffic flows comprising unmanned vehicles, human-driven conventional vehicles, and human-driven specialized transport, while also accounting for the stochastic nature of human driver behavior, a factor often overlooked in current safety analyses [6]. Specifically, the research will explore how various levels of unmanned vehicles’ penetration impact interaction dynamics and conflict severity in multi-vehicle scenarios within a seaport’s operational footprint [7]. This comprehensive analysis will facilitate the identification of critical safety challenges and the development of robust mitigation strategies for the seamless integration of autonomous operations within dynamic port environments [8].

Existing literature focuses on road safety assessment, particularly methodologies for assessing mixed traffic flows and collision risk modeling. For example, studies have evaluated safety performance levels in mixed traffic flows by conducting numerical simulation modeling and sensitivity analysis, often focusing on interactions between human-driven vehicles and truck platoons equipped with cooperative adaptive cruise control. Further research extends these evaluations by analyzing stochastic differential equations to model car-following behavior and its impact on traffic stability and safety [6]. Traffic safety assessment has evolved significantly from traditional crash-based statistical analysis toward proactive, simulation-based approaches using surrogate safety indicators. While early safety research concentrated on highways and urban intersections, recent developments in automated and unmanned vehicle technologies have expanded safety modeling to mixed traffic environments. Seaports represent a particularly complex domain where unmanned vehicles—such as automated guided vehicles (AGVs), autonomous trucks, and service robots—interact with human-driven trucks, terminal tractors, and pedestrians within confined, high-density operational spaces.

Existing literature on road safety assessment provides robust methodological foundations for evaluating mixed traffic flows and modeling collision risk. These approaches, particularly microsimulation combined with surrogate safety measures (SSMs), are increasingly applicable to port environments where crash data are sparse and operational risk must be assessed proactively. Given the nascent stage of widespread unmanned vehicle deployment in seaports, traditional accident-based safety metrics are insufficient, necessitating the proactive application of surrogate safety indicators to evaluate potential conflict scenarios and inform risk management strategies [9]. Traditional traffic safety evaluation relied heavily on historical crash records. However, due to the rarity of crash events, especially in controlled environments, this approach often suffers from insufficient statistical power and delayed intervention. To overcome these limitations, researchers developed surrogate safety measures that quantify near-miss events and conflict severity without requiring actual collisions. The Federal Highway Administration (FHWA) formalized the use of surrogate safety measures in simulation environments, emphasizing indicators such as Time-to-Collision (TTC), Post-Encroachment Time (PET), and Deceleration Rate to Avoid Crash (DRAC) [10]. These measures evaluate the temporal and spatial proximity between vehicles and have become fundamental tools in microsimulation-based safety analysis. TTC, defined as the time remaining before two vehicles would collide if their speeds and trajectories remain unchanged, is widely adopted due to its intuitive interpretation and computational simplicity. PET measures the time difference between one vehicle leaving a conflict point and another arriving at that same point, offering a useful metric for intersection and crossing conflicts. Other important surrogate safety measures include maximum deceleration and maximum post-collision velocity change, which provide further insights into the severity of potential conflicts [11]. The application of digital twin technology, integrating vehicle dynamics and environmental factors, further enhances safety evaluations by employing surrogate safety measures like TTC and DRAC in various simulated scenarios, including different weather conditions and visibility levels [12]. Such indicators are particularly valuable in port environments, where intersection-like internal road layouts and crossing flows are common.

Microsimulation has become a primary analytical framework for safety assessment in mixed traffic conditions. Unlike macroscopic models, microsimulation represents individual vehicle behaviors, such as acceleration, deceleration, lane changing, and gap acceptance, allowing for detailed modeling of vehicle interactions. These simulations can generate conflict data that are subsequently processed by tools such as the Surrogate Safety Assessment Model (SSAM) to estimate collision probability and conflict severity. This approach enables the identification of critical interaction points before actual crashes occur, making it particularly valuable for proactive safety assessment in complex traffic environments such as seaports [13]. These models enable the identification of critical interaction points before physical crashes occur. In mixed traffic environments involving autonomous vehicles (AVs) and human drivers (HDVs), simulation studies demonstrate that safety outcomes depend heavily on behavioral assumptions embedded in car-following and lane-changing models [14]. Since seaports increasingly deploy autonomous terminal tractors and AGVs alongside conventional trucks, such modeling frameworks are directly transferable.

Mixed traffic flow modeling has become central to safety research as automation levels increase. Studies incorporating stochastic driver behavior models (SIDM) demonstrate that safety performance differs significantly when automated and human-driven vehicles coexist [15]. In mixed environments, collision risk is influenced by:

• Reaction time differences between automated and human drivers.
• Communication capabilities (e.g., vehicle-to-vehicle systems).
• Platooning behavior and gap regulation.
• Acceleration and braking characteristics.

Such findings are particularly relevant to port terminals, where AGVs may operate with predefined routes and control algorithms while interacting with manually operated heavy vehicles.

Collision risk modeling in these contexts typically integrates surrogate indicators with probabilistic or machine learning techniques to estimate crash likelihood. These models often calibrate surrogate thresholds (e.g., TTC < 1.5 s) against empirical crash data to validate predictive power. This integration allows for a more nuanced understanding of safety performance, moving beyond simple conflict counts to predict potential crash frequencies and severities [16].

The Weighted Combination of Spacing and Speed Difference Rates (WS²DR) has been introduced as an enhanced surrogate safety indicator designed to improve collision risk assessment in mixed traffic environments. This metric integrates inter-vehicle spacing with relative speed variation, allowing a more comprehensive representation of dynamic vehicle interactions. By simultaneously accounting for distance and velocity changes, WS²DR addresses key limitations of traditional TTC, particularly the assumption of constant speed and linear motion during potential conflict scenarios [17]. Similarly, AI-driven safety indicators such as Hazardous Modified TTC incorporate LiDAR-based perception data and multidimensional motion parameters, improving detection of complex conflict scenarios [18]. These advanced metrics are particularly relevant in port environments where sensor-equipped unmanned vehicles continuously collect high-resolution spatial data. Safety indicators have been categorized into three primary groups: behavioral metrics, interaction metrics, and environmental metrics. Behavioral metrics capture individual vehicle dynamics such as acceleration patterns and headway maintenance; interaction metrics evaluate conflict-based relationships between vehicles (e.g., TTC and PET); and environmental metrics account for roadway geometry, visibility constraints, and surrounding conditions [19]. This multidimensional classification supports the development of integrated safety assessment frameworks, particularly in seaport environments where constrained layouts, container stacks, limited sight distance, and heterogeneous vehicle operations intensify operational risk.

Although fewer studies focus explicitly on seaports, research on container terminal traffic simulation provides valuable methodological insights. Simulation models of internal port vehicle circulation examine routing strategies, intersection performance, and congestion patterns [20]. While primarily operational, these models can be extended to incorporate surrogate safety indicators.

Additionally, video-based trajectory extraction in port settings enables empirical calibration of surrogate measures [21]. Such empirical grounding strengthens simulation validity by aligning modeled vehicle interactions with real-world behavior. Port environments exhibit distinct safety characteristics:

• High concentration of heavy vehicles.
• Constrained geometric layouts.
• Frequent crossing movements.
• Integration of automated and human-operated systems.

Therefore, adapting road-based surrogate methodologies to port settings requires contextual calibration but remains conceptually consistent.

Despite significant progress in surrogate-based safety modeling, several limitations persist in its application to unmanned vehicle operations within seaports. One major challenge is the limited port-specific calibration of surrogate safety thresholds. Many commonly used indicators, such as TTC or PET, are typically derived from highway or urban traffic datasets and may not accurately reflect the dynamics of heavy vehicles, constrained geometries, and operational patterns characteristic of port environments. A further limitation concerns the relatively limited number of studies that explicitly model interactions between AGVs and human-operated vehicles or pedestrians within port environments. Although mixed traffic modeling has advanced considerably in road transport research, fewer studies focus specifically on terminal settings where AGVs operate along predefined routes and controlled pathways while interacting with manually driven trucks and service vehicles. The structured nature of AGVs operations distinguishes port traffic from conventional urban traffic and requires tailored modeling assumptions that reflect controlled movement patterns rather than general road-driving behavior. Finally, existing research often treats safety assessment independently from operational efficiency. However, port systems must simultaneously optimize throughput, travel time, and resource utilization while maintaining acceptable safety levels. The absence of integrated risk–efficiency trade-off analyses restrict the practical applicability of many simulation-based safety models.

Therefore, this study combines microsimulation methods, advanced safety proxy measures, and empirically derived trajectory datasets to develop comprehensive and context-specific safety assessment systems tailored to unmanned vehicles operations in maritime ports.

Simulation-based surrogate safety assessment studies can be grouped into three main strands. The first focuses on methodological foundations and general reviews of surrogate safety measures and SSAM-based analysis, including TTC, PET, and related indicators used to identify near-conflict events in simulated traffic. The second examines mixed traffic and vehicle-automation contexts, where microsimulation is combined with surrogate measures to evaluate how car-following logic, lane-changing assumptions, and automation level influence safety outcomes. The third strand is more application-specific and includes port-related simulation and trajectory studies, which emphasize the importance of constrained geometry, heavy-vehicle interactions, and operational traffic patterns in terminals.

However, most previous studies address urban roads, highways, work zones, or general mixed-traffic environments, while relatively few examine mission-based mixed traffic inside seaport terminals connected to external road networks. Compared with earlier studies that focus either on operational efficiency in ports or on surrogate safety in general road traffic, the present study contributes a combined framework that (i) jointly models internal port AGVs and external road vehicles, (ii) evaluates a staged automation transition through six fleet-composition scenarios, and (iii) links AIMSUN microsimulation, SSAM conflict analysis, and spatial hotspot mapping within one port-specific safety assessment workflow.

2. Materials and Methods

This study aims to develop a comprehensive safety assessment framework for vehicle operations in maritime ports, including both autonomous (unmanned) and human-driven vehicles. The methodology integrates microsimulation techniques, advanced safety proxy measures, and empirically derived trajectory datasets to evaluate operational risks under realistic port scenarios. The framework is context-specific, capturing dynamic vehicle behavior and port environment complexities.

The study utilizes microscopic traffic simulation to model the intricate movements of individual vehicles within the constrained geometric layouts of a maritime port. This framework allows for the representation of diverse vehicle types, including automated guided vehicles, autonomous trucks, and human-driven terminal tractors. The simulation environment is calibrated to replicate the high-density operational spaces and frequent crossing movements characteristic of port terminals.

2.1. Data Collection and Study Environment

2.1.1. Trajectory Data

Empirical trajectory data used in this study were generated using the AIMSUN Next 24.0.1 microscopic simulation platform and exported for surrogate safety analysis. AIMSUN (Barcelona, Spain) enables the extraction of detailed vehicle-position data during simulation, allowing the creation of trajectory datasets suitable for safety evaluation. AIMSUN Next 44.0.1 was selected because the study required four capabilities within a single workflow: microscopic vehicle-level simulation, programmable mission-based control logic, direct generation of SSAM-compatible trajectories, and explicit representation of automated car-following behavior. These requirements are critical in port environments, where vehicle movements are task-driven rather than destination-driven and must therefore be controlled through operational logic in addition to conventional traffic-flow models. AIMSUN provides microscopic, mesoscopic, and hybrid simulation options, native ACC/CACC functionality, Python 3.13.13/C++26 APIs for customized control, and an SSAM extension for trajectory export, which made it suitable for the present study. Compared with PTV Vissim 2025, which is particularly strong for fully multimodal microscopic simulation and external model coupling, and with SUMO 1.26.0, which offers an open-source microscopic/intermodal framework, AIMSUN provided a more integrated workflow for this application because automated vehicle behavior, scenario execution, trajectory export, and safety-evaluation preparation could be handled within one environment. At the same time, AIMSUN has limitations: it is a licensed commercial platform, some extensions depend on API-enabled functionality, and it provides less code-level transparency than open-source platforms such as SUMO. Accordingly, AIMSUN was selected as the most appropriate compromise between model detail, extensibility, and SSAM compatibility for mission-based port safety analysis.

Within AIMSUN, vehicle trajectory files were created using the SSAM exporter. This exporter generates trajectory files that contain detailed vehicle movement information recorded during microscopic simulation. Only trajectory data derived from microscopic simulations are compatible with SSAM analysis.

The exported trajectory files include time-dependent vehicle information such as vehicle identification, position coordinates, speed, and acceleration at each simulation step. These high-resolution trajectory datasets provide a detailed representation of interactions between autonomous and human-driven vehicles within the simulated port network.

To generate the trajectory data, the SSAM export option was activated in the AIMSUN scenario settings. During simulation, vehicle positions were recorded and stored in trajectory (.trj) files over specified time intervals. The exported files also included coordinate system information to ensure correct spatial positioning of vehicle movements.

These trajectory files were subsequently used as input for the SSAM, which analyzes vehicle interactions and identifies potential conflicts using surrogate safety indicators such as TTC and PET. Figure 1 shows a fragment of the trajectory file exported from AIMSUN for subsequent SSAM analysis. Each record contains the simulation time stamp, vehicle identifier, spatial coordinates, speed, and acceleration, which together reconstruct the time-dependent trajectory of each vehicle. These data constitute the direct input for TTC and PET calculations and therefore form the evidential link between the microsimulation model and the surrogate safety assessment.

2.1.2. Port Terminal Representation

The port terminal was modeled as a microscopic traffic network using AIMSUN. Following [22], the terminal is represented as a system of interconnected operational areas, including internal road infrastructure, loading and unloading zones, and storage areas. These areas are connected through a network of links and nodes representing internal circulation routes and intersections. The port operational environment provides a realistic and structured setting for analyzing conflicts between unmanned and human-driven vehicles. This environment is characterized by the following: the port operational environment is a confined industrial zone, closed to public traffic and dedicated exclusively to freight handling. Its infrastructure comprises several interconnected components: an internal road network, terminal gates, parking and staging areas (storage yard), and berths. The internal roads feature specific lane configurations, intersections, and traffic management schemes such as give-way rules, speed limits, and reserved lanes, which collectively define how vehicles navigate and interact. Parking areas are organized into zones associated with specific berths, with each parking spot uniquely identified to enable precise maneuvering for parking, reversing, and trailer handling. At the boundaries, in-gates and out-gates act as controlled checkpoints where vehicles must stop for administrative processing, creating queues and potential bottlenecks.

Traffic within this environment is characterized by a heterogeneous mix of vehicle types, including AGVs and human-driven trucks (lorries with trailers, articulated lorries), tractors, passenger cars, and specialized cargo carriers. Demand is event-driven, generated primarily by vessel schedules: ship arrivals and departures trigger waves of truck movements, creating predictable but intense periods of high activity.

Operational rules and procedures govern all vehicle movements. At gates, vehicles experience delays due to customs, security checks, or administrative formalities—stops that are mandatory and vary in duration. Once inside, vehicles are assigned to specific parking areas based on their destination berth; however, if a designated area reaches full capacity, vehicles overflow into adjacent zones, leading to unplanned interactions. Finally, at the berths, vehicles must interact closely with vessel ramps and loading equipment, requiring careful coordination and precise movements to ensure safe and efficient loading and unloading processes. The environment naturally generates specific points where interactions between unmanned and human-driven vehicles are most intense and safety risks are highest.

Table 1. Port environment key conflict zones.

Conflict Zone	Description
Gate Areas	Merging and queuing at in/out gates, where unmanned vehicles must interact with human-driven trucks under stop-and-go conditions.
Road Network Intersections	Crossing points where vehicles from different terminals or parking areas compete for right-of-way.
Storage Yard Entrances/Exits	Vehicles entering or leaving parking areas interact with through traffic on main internal roads, creating potential for collisions or blocking.
Berth Interfaces	The area between storage yard and vessel, where vehicles queue, reverse, and maneuver in close proximity to loading equipment and other vehicles.
Parking Aisles	Narrow lanes within parking areas where unmanned vehicles must navigate around human-driven trucks that may be parked, maneuvering, or idling.

presents a description of the key conflict zones.

The conceptual diagram presented in Figure 2 illustrates the spatial configuration of a maritime port environment, delineating both infrastructural components and zones of heightened interaction between unmanned and human-driven vehicles. This representation serves as a foundational tool for analyzing traffic dynamics and identifying critical points where conflicts are most likely to emerge.

Infrastructure Zones are depicted in blue and represent the physical assets that constitute the port’s operational backbone. These include the in-gate and out-gate zones, where vehicles undergo administrative processing; the internal road network, which facilitates connectivity between functional areas; the storage yard, organized into parking zones associated with specific berths; and the berth interfaces themselves, where vessel loading and unloading occur. Each of these zones possesses distinct geometric and operational characteristics that influence vehicle behavior and interaction patterns.

Conflict Hotspots are highlighted in red and mark the specific locations where interactions between automated and human-driven vehicles become most intense. These zones are not arbitrary but emerge from the convergence of traffic flows, spatial constraints, and operational procedures. Conflict Zone 1 at the gate area involves queuing and merging maneuvers under stop-and-go conditions. Conflict Zone 2 at road intersections involves right-of-way negotiations where human driver unpredictability poses challenges for automated logic. Conflict Zone 3 within parking aisles involves narrow-space sharing, reversing maneuvers, and blocking events. Conflict Zone 4 at the berth interface involves close-proximity maneuvering under time pressure during loading operations.

Primary Vehicle Flow Paths are indicated by solid arrows and represent the intended trajectories of vehicles as they move through the port system. Vehicles enter through the in-gate, proceed along internal roads, access designated parking areas, and ultimately approach the berth for loading or unloading. After completing these operations, they depart via the internal road network to the out-gate. These flow paths define the baseline operational pattern against which deviations and disruptions must be assessed.

Overflow Paths are represented by dashed arrows and illustrate the alternative trajectories that vehicles must adopt when primary parking areas reach full capacity. Under such conditions, vehicles are redirected to adjacent parking zones, creating unplanned interactions and introducing additional complexity into traffic patterns. These overflow movements are critical to understanding system resilience and the propagation of congestion under peak demand conditions.

The integration of these elements within a single diagrammatic framework enables systematic analysis of port operations from a safety perspective. By mapping infrastructure, conflict zones, and vehicle trajectories onto a common spatial reference, researchers and practitioners can identify vulnerable points in the system, design targeted interventions, and evaluate the potential impacts of introducing unmanned vehicles into existing operational environments. This visual tool thus serves not merely as an illustration but as an analytical instrument for understanding and mitigating conflict dynamics in mixed-traffic port settings.

While Figure 2 establishes the spatial architecture of the port terminal, delineating infrastructure components, vehicle trajectories, and localized conflict hotspots, it primarily reflects the geometric and topological structure of the system. However, in complex freight terminals, conflict formation is not governed solely by spatial co-location. It is the outcome of coupled operational processes, traffic demand fluctuations, capacity constraints, and heterogeneous vehicle behavior operating within that spatial framework.

To extend the analysis beyond static configuration, the subsequent diagram on Figure 3 reformulates the port terminal as a capacity-constrained, flow-driven dynamic system in which conflicts emerge as endogenous products of interacting operational subsystems. In this representation, the berth and storage yard function as interconnected service nodes with finite handling capacities. Container arrivals and departures generate transport demand, which in turn induces bidirectional vehicle flows between these nodes through the internal road network.

The number of trips performed by AGVs and HDVs becomes a key state variable governing interaction density. As transport intensity increases, shared corridors, intersections, and merging areas experience elevated vehicle encounters. Under mixed-traffic conditions, behavioral heterogeneity—algorithm-driven control in AGVs versus stochastic human driving responses—introduces additional variability into gap acceptance, yielding behavior, and speed adaptation processes.

Within this systems perspective, conflicts are conceptualized as emergent phenomena resulting from:

• Flow imbalance between berth and yard operations.
• Saturation effects at capacity-constrained nodes.
• Fleet composition and AGV penetration rate.
• Delay propagation and queuing dynamics within the internal network.

Capacity saturation at either the berth or storage yard induces spillback effects that propagate upstream through the transport network, increasing vehicle density and reducing available maneuvering space. These conditions amplify the probability of temporal and spatial proximity events, which are subsequently captured through surrogate safety indicators such as TTC and Post-Encroachment Time-PET.

Accordingly, while the initial diagram characterizes the spatial distribution of conflict-prone locations, the dynamic representation models the system-level mechanisms that generate and intensify conflict exposure. The integration of both perspectives establishes a multi-layer analytical framework that links infrastructure geometry, operational throughput, fleet interaction dynamics, and safety performance within a unified port traffic model.

2.2. Surrogate Safety Assessment

The exported vehicle trajectory files were analyzed using the Surrogate Safety Assessment Model (SSAM). SSAM processes time-dependent vehicle trajectories to identify potential traffic conflicts based on spatial and temporal proximity between vehicles [23].

Two surrogate safety measures were used to evaluate operational safety:

Time-to-Collision (TTC): Indicates the remaining time before a potential collision occurs if two vehicles maintain their current speed and trajectory.

Post-Encroachment Time (PET): Represents the time difference between two vehicles passing through the same conflict point.

TTC represents the remaining time before two vehicles would collide if they continue moving with their current speeds and trajectories.

For a longitudinal car-following scenario:

$$\mathrm{T}\mathrm{T}\mathrm{C}={\displaystyle \frac{d_{rel}}{v_{rel}}}$$

(1)

where

$d_{rel}$—relative distance between the rear of the leading vehicle and the front of the following vehicle, m;

$v_{rel}$—relative speed, m/s.

$$v_{rel}=v_f-v_l$$

(2)

$v_f$—speed of the following vehicle, m/s;

$v_l$—speed of the leading vehicle, m/s.

TTC is only defined when $v_{rel}$ > 0 (i.e., when the following vehicle is approaching the leader).

For crossing or intersecting trajectories (as in SSAM), TTC is computed as:

$$\mathrm{T}\mathrm{T}\mathrm{C}=t_{collision}-t_{current}$$

(3)

where

$t_{collision}$—projected time at which vehicle trajectories intersect;

$t_{current}$—current simulation time.

A conflict is identified when TTC falls below a predefined threshold (commonly 1.5–2.0 s).

TTC is typically illustrated as:

Distance gap between vehicles = $d_{rel}$;

Closing speed = $v_{rel}$;

If no braking occurs, collision happens after time = TTC;

In intersection conflicts:

Two projected trajectories intersect at a future point.

TTC measures how soon both vehicles would reach that collision point simultaneously.

Post-Encroachment Time (PET) measures the time difference between two vehicles passing through the same conflict point.

$$\mathrm{P}\mathrm{E}\mathrm{T}=t_2-t_1$$

(4)

where

t₁—time when the first vehicle leaves the conflict area, s;

t₂—time when the second vehicle enters the same area, s.

PET ≥ 0 by definition.

A small PET indicates a severe near-miss situation. Typical critical thresholds range between 1.0 and 2.5 s.

Consider two vehicles crossing at an intersection:

Vehicle A passes through the conflict point at time t₁; Vehicle B arrives at the same point at time t₂

The safety margin is (4).

If PET is small, the vehicles passed the same spatial location within a very short time interval, indicating high conflict severity [24].

In mixed AGVs–HDVs port operations, surrogate safety indicators are employed to quantify different dimensions of interaction risk (see Figure 4). TTC measures the remaining time until a projected collision would occur if two vehicles continued along their current trajectories without evasive action. As such, TTC captures prospective collision risk, particularly in longitudinal and merging situations, including queuing areas, approach segments, and berth access corridors.

In contrast, PET measures the temporal separation between two vehicles sequentially occupying the same spatial conflict area. PET therefore reflects realized temporal proximity in shared spaces, such as intersections, parking aisles, and berth interface zones, where vehicle paths cross rather than follow one another.

Whereas TTC evaluates the imminence of a potential collision under dynamic approach conditions, PET quantifies the safety margin after one vehicle has cleared a conflict zone and before another enters it. The two indicators thus capture complementary aspects of traffic safety: TTC represents anticipatory risk in continuous interaction, while PET represents residual safety margins in discrete spatial conflicts.

Together, TTC and PET enable a comprehensive assessment of:

Interaction intensity within shared operational corridors, and the severity and frequency of near-conflict events in mixed autonomous–human traffic environments.

In this study, both indicators are derived from time-stamped vehicle trajectory data obtained through microscopic simulation and subsequently processed using a surrogate safety assessment framework. This approach allows conflict identification without relying on observed crash data, which are typically rare in controlled port environments [25].

In surrogate safety analysis, TTC and PET thresholds are analyst-defined parameters used to classify conflict severity. Typical threshold values reported in microscopic simulation and SSAM-based studies range between 1.0 and 2.0 s for TTC and between 1.0 and 2.5 s for PET [26]. However, these values are context-dependent and must be calibrated according to the operational environment and speed regime under investigation [27].

These indicators are extracted from time-stamped vehicle trajectory data exported from microscopic simulation (e.g., AIMSUN) and processed using SSAM. TTC and PET were used to detect, classify, and quantify conflicts between vehicles operating in the port terminal environment. Conflict frequency and severity were calculated to evaluate safety performance under mixed-traffic conditions.

2.3. Calibration and Simulation Execution

The microscopic simulation model was configured to replicate realistic vehicle movement patterns within the port road network. Simulation runs were conducted under a fixed nominal traffic demand profile and consistent operational conditions to generate stable and representative vehicle trajectory datasets. Each run used a 6 h simulation horizon with an initial 30 min stabilization (warm-up) period, and the full modeled period was retained for safety evaluation. Behavioral parameters governing both autonomous and human-driven vehicles were calibrated to ensure consistent and realistic interaction dynamics throughout the simulated environment. The behavioral parameters for AGVs were calibrated based on values reported in the recent literature and industry standards (see Table 2):

-

Desired Speed: 15–25 km/h (4.2–6.9 m/s).

The selection of this speed range is based on a trade-off between operational efficiency and energy consumption. Research indicates that AGV speed optimization is a key factor in task scheduling. In [28], it is demonstrated that at a fixed speed, higher travel speeds may lead to increased idle time and energy consumption. Speed optimization allows these factors to be balanced. In port terminals, AGVs operate on dedicated routes with speed limits dictated by safety requirements and the geometry of the pathways.

-

Reaction Time: 0.1–0.3 s

AGV reaction time is determined by sensor delays (LIDAR/camera) and the data processing time of the controller. Industrial standards establish strict requirements for the response time of safety systems. According to the [29], the response time tolerance for control systems of autonomous machines must not exceed 50 ms (0.05 s). This confirms that values of 0.1–0.3 s are realistic, accounting for various sensors and computational delays. Additionally, research [30] examines AGV interactions with humans in dispatch areas and emphasizes the importance of fast reaction times for collision prevention.

-

Sensitivity Factor: 1–1.2

AGVs employ more responsive acceleration control algorithms compared to human drivers. This is due to the absence of human perceptual delays and the availability of precise real-time sensor data. A factor of 1.0 represents the standard human response—smooth, linear, and limited by biological reaction times. Humans estimate distance visually and react gradually. Research confirms that human driver behavior exhibits “asymmetric importance of parameters” where different input factors have varying levels of influence on model outputs, requiring complex calibration to account for driver heterogeneity. The 1.2 value for AGVs reflects their superior capabilities. Studies on the Intelligent Driver Model demonstrate that variance-based sensitivity analysis can identify “which of the input factors can be fixed anywhere in their range of variation without appreciably affecting a specific output of interest”.

-

Maximum Deceleration: 1.5–4.0 m/s²

AGV braking must be sufficient to ensure safety but not excessively abrupt, in order to avoid cargo shifting and the creation of hazardous situations for following vehicles. The Chinese national safety standard GB/T 41355-2022 establishes a methodology for calculating dynamic safety distances considering braking capability [29]. In applications with laser safety scanners, verified deceleration of at least 3 m/s² is required for emergency braking. For comfort/operational braking, values of 1.5–4.0 m/s² are realistic. Additionally, the speed control strategy proposed [31] allows for the avoidance of sudden stops, thereby reducing equipment wear and enhancing safety. This confirms that smooth deceleration (1.5–4.0 m/s²) is preferable to emergency braking.

-

Maximum Acceleration: 0.5–1.0 m/s²

Acceleration limits for AGVs are determined by cargo stability requirements and the structural characteristics of the vehicle. Excessive acceleration can lead to tipping or cargo shifting. A study on the dynamic stability of forklift AGVs [32] analyzes the influence of the center of gravity on the stability of a forklift AGV. At maximum load (1600 kg) and maximum lift height (3.405 m), the acceleration limit is 1.12 m/s², and the deceleration limit is 0.56 m/s². This directly supports the selected range. Furthermore, research on heavy-duty AGVs by [33] defines optimal acceleration values for heavy-duty AGVs as 0.2 m/s² on straight sections and 0.3 m/s² on curves. These values vary depending on AGV type and operating conditions, confirming the need for calibration within the 0.5–1.0 m/s² range for standard port AGVs.

-

Gap: 0.3–0.8 s

AGVs employ conservative decision-making algorithms when performing maneuvers such as turns, lane changes, and merging onto main roads. This is due to the absence of the ability for “risky” assessments characteristic of human drivers. The industrial safety standard R15.08 [34], emphasizes the distinction between AGVs (which follow predetermined paths) and autonomous mobile robots. AGVs utilize obstacle detection and can adjust their path, but their decision-making algorithms are conservative by nature. This necessitates longer time gaps for performing maneuvers compared to human drivers.

Table 2. Behavioral parameters for AGVs and HDVs.

Parameter	HDV	AGV	Unit/Notes
Desired Speed	30–40	15–25	km/h
Reaction Time	0.8–1.4	0.1	s
Sensitivity Factor	1.0	1.2
Max. Acceleration	1.0	0.8	m/s2
Max. Deceleration	2.5–3.5	3.5	m/s2
Gap	1.5	0.8	seconds

Table 2. Behavioral parameters for AGVs and HDVs.

Parameter	HDV	AGV	Unit/Notes
Desired Speed	30–40	15–25	km/h
Reaction Time	0.8–1.4	0.1	s
Sensitivity Factor	1.0	1.2
Max. Acceleration	1.0	0.8	m/s2
Max. Deceleration	2.5–3.5	3.5	m/s2
Gap	1.5	0.8	seconds

Vehicle movements within the port terminal were simulated using the microscopic behavioral models implemented in AIMSUN, which represent vehicle dynamics through car-following and lane-changing mechanisms. These models determine the longitudinal and lateral motion of vehicles at each simulation time step and enable the realistic reproduction of traffic interactions within complex operational environments.

HDVs were modeled using the Gipps car-following model, which describes the longitudinal dynamics of a vehicle based on driver perception–reaction time and safety constraints relative to the leading vehicle.

The car-following model implemented in AIMSUN is based on the Gipps model. It can be regarded as a specific development of this empirical model, in which the parameters are not global but are determined by the influence of local factors depending on driver type, the geometric characteristics of the road section, the maximum speed allowed on the section, the speed on curved alignments, the influence of vehicles in adjacent lanes, and others. The model essentially consists of two main components: acceleration and braking.

The first component represents the driver’s intention to reach a certain desired speed, while the second reproduces the constraints imposed by the vehicle ahead traveling at its desired speed.

This model establishes the maximum speed to which vehicle (n) can accelerate over a time interval (t + T):

$$V_a(n,t+T)=V(n,t)+2.5\cdot a(n)\cdot T(1-{\displaystyle \frac{V(n,t)}{V^{*}(n)}})\sqrt{0.025+{\displaystyle \frac{V(n,t)}{V^{*}(n)}}}$$

(5)

where

V(n,t)—speed of vehicle n at time t;

V^∗(n)—desired speed of vehicle n for the given section;

a(n)—maximum acceleration for vehicle n;

T—reaction time, i.e., the update interval—simulation time step.

On the other hand, the maximum speed that the same vehicle (n) can achieve over the same time interval (t + T), considering its own characteristics and the constraints imposed by the presence of the leading vehicle, is given by:

$$V_b(n,t+T)=d(n)T+\sqrt{d^2(n)T^2-d(n)[2\{x(n-1,t)-S(n-1)-x(n,t0)\}-V(n,t)T-{\displaystyle \frac{v(n-1,t{)}^2}{d\prime (n-1)}}]}$$

(6)

where

d(n) (<0)—maximum deceleration desired for vehicle n;

x(n,t)—position of vehicle n at time t;

x(n − 1,t)—position of the preceding vehicle (n − 1) at time t;

S(n − 1)—effective length of vehicle (n − 1);

d’(n − 1)—an estimate of the desired deceleration of vehicle (n − 1).

In any case, the determining speed for vehicle n over the time interval (t + T) is the minimum of these two previously defined speeds:

$$V(n,t+T)=min \left\{V_a(n,t+1), V_{b }(n,t+1)\right\}$$

(7)

Subsequently, the position of vehicle n within its current lane is updated using this speed in the equation of motion:

$$x(n,t+T)=x(n,t)+V(n,t+1)$$

(8)

This behavioral structure captures the variability and uncertainty associated with human driver decisions within complex port traffic environments.

AGVs were modeled using the Adaptive Cruise Control (ACC) framework available in AIMSUN. In this model, vehicle motion is regulated through automated gap control to maintain a desired time headway relative to the leading vehicle.

The longitudinal acceleration of an ACC vehicle is defined as:

$$a\left(t\right)=k_v(v_{des}-v(t\left)\right)+k_s\left(s\right(t)-s_{des})$$

(9)

where

v(t)—current vehicle speed;

v_des—desired speed;

s(t)—actual spacing to the leading vehicle;

s_des—desired spacing;

k_v, k_s—control gains regulating speed and spacing adjustments.

The desired spacing is typically expressed as:

$$s_{des}=s_0 +Tv\left(t\right)$$

(10)

where:

$s_0$—minimum standstill spacing;

T—desired time headway.

Unlike HDVs, AGVs follow predefined routes within the port terminal and typically operate without discretionary overtaking maneuvers. Therefore, lane-changing behavior was restricted to route-based movements, reflecting the deterministic navigation logic commonly used in automated terminal transport systems.

Accurate representation of vehicle operations in port microsimulation requires a custom control script [35], as standard traffic assignment principles (e.g., shortest-path routing) do not reflect task-driven port logistics. In maritime terminals, vehicle movements are mission-based—transporting containers between berths, storage yards, and gates—rather than destination-driven. The custom script provides an operational control layer, assigning tasks and enforcing predetermined movement corridors.

The proposed multi-layer simulation architecture integrates operational control, traffic dynamics, and safety assessment:

Operational Logic Layer: A custom script governs terminal logistics—assigning missions, managing queues at checkpoints, and regulating access to loading areas—ensuring that vehicle behavior reflects real operational rules.

Traffic Dynamics Layer: Microscopic movement is simulated using the AIMSUN engine. HDVs follow the Gipps car-following model, while AGVs operate under an Adaptive Cruise Control based automated driving model. Both generate detailed trajectory data at each simulation step.

Safety Evaluation Layer: Trajectories are analyzed using the SSAM with two key indicators—TTC and PET—to detect and quantify conflicts without reliance on historical crash data.

This integrated framework enables comprehensive analysis of interaction patterns and conflict formation in mixed-traffic port environments involving both human-driven and automated vehicles.

2.4. Scenario Design and Prioritization Criteria

The scenarios were designed to isolate the safety effect of automation penetration while keeping demand and operating conditions fixed. The prioritized criteria were: (i) representation of the current baseline, (ii) realism of the expected transition pathway, (iii) sensitivity to intermediate automation levels, and (iv) comparability across scenarios. Scenario A represents the fully human-driven baseline. Scenario B isolates the effect of automating the internal port fleet while external road trucks remain human-driven. Scenarios C–F then retain a fully automated port fleet and gradually increase road-vehicle automation from 25% to 100%. This structure was chosen because centrally managed internal port vehicles are more likely to be automated earlier than externally owned road trucks. Keeping port automation fixed from Scenario B onward allows the study to specifically identify how road-side automation changes safety at the port–urban interface.

The simulation model represents a port network integrated with the external urban road network of City N (Figure 5).

The key simulation inputs and evaluation settings used in this study are summarized in Table 3.

Table 3. Simulation inputs and evaluation settings.

Category	Parameter	Value	Notes
Network representation	Study network	Port terminal integrated with the external urban road network of City N	Microscopic AIMSUN model
	Road network sections	213
	Total network length	12 km
	Intersections	78	Various types
	Centroids	12	Vehicle generation points
Simulation settings	Simulation horizon	6 h	Fixed for all scenarios
	Simulation time step	0.1 s	Fixed for all scenarios
Experimental design	Design type	One-factor scenario-based design	Traffic demand was not varied
	Experimental factor	Automation scenario (A–F)	Scenario composition is reported in Table 4
	Number of scenarios	6	A–F
	Replications per scenario	6	Different random seeds
	Total simulation runs	36
	ANOVA sample size	36 observations
	Fixed conditions	Traffic demand profile, network geometry, operational rules, and service-time distributions	Held constant across scenarios
External road traffic	Container-truck arrival rate at the port gate	42 veh/h	Exponential interarrival pattern
	Terminal parking time	Normal distribution, μ = 290 s, σ = 30 s	External road trucks
	Stack waiting/processing time	Normal distribution, μ = 190 s, σ = 30 s	External road trucks
Internal maritime cargo front	Port vehicles	23	Uniform generation during the first 7 min of simulation
Railway cargo front	Port vehicles	5
	Reach/rail stackers	4
	Processing time per Port vehicle	Normal distribution, μ = 160 s, σ = 30 s
Vehicle behavior models	HDVs	Gipps car-following model	AIMSUN implementation
	AGVs	Adaptive Cruise Control (ACC) framework	Route-based movements; no discretionary overtaking
Trajectory export and safety evaluation	Trajectory export	AIMSUN SSAM exporter (.trj files)
	Conflict analysis tool	SSAM
	Surrogate indicators	TTC and PET
	Reported outputs	Total conflicts; crossing, rear-end, and lane-change conflicts; mean and variance of TTC and PET
Statistical analysis	Group comparison	One-way ANOVA with Tukey HSD post hoc tests	Across six scenarios

Table 3. Simulation inputs and evaluation settings.

Category	Parameter	Value	Notes
Network representation	Study network	Port terminal integrated with the external urban road network of City N	Microscopic AIMSUN model
	Road network sections	213
	Total network length	12 km
	Intersections	78	Various types
	Centroids	12	Vehicle generation points
Simulation settings	Simulation horizon	6 h	Fixed for all scenarios
	Simulation time step	0.1 s	Fixed for all scenarios
Experimental design	Design type	One-factor scenario-based design	Traffic demand was not varied
	Experimental factor	Automation scenario (A–F)	Scenario composition is reported in Table 4
	Number of scenarios	6	A–F
	Replications per scenario	6	Different random seeds
	Total simulation runs	36
	ANOVA sample size	36 observations
	Fixed conditions	Traffic demand profile, network geometry, operational rules, and service-time distributions	Held constant across scenarios
External road traffic	Container-truck arrival rate at the port gate	42 veh/h	Exponential interarrival pattern
	Terminal parking time	Normal distribution, μ = 290 s, σ = 30 s	External road trucks
	Stack waiting/processing time	Normal distribution, μ = 190 s, σ = 30 s	External road trucks
Internal maritime cargo front	Port vehicles	23	Uniform generation during the first 7 min of simulation
Railway cargo front	Port vehicles	5
	Reach/rail stackers	4
	Processing time per Port vehicle	Normal distribution, μ = 160 s, σ = 30 s
Vehicle behavior models	HDVs	Gipps car-following model	AIMSUN implementation
	AGVs	Adaptive Cruise Control (ACC) framework	Route-based movements; no discretionary overtaking
Trajectory export and safety evaluation	Trajectory export	AIMSUN SSAM exporter (.trj files)
	Conflict analysis tool	SSAM
	Surrogate indicators	TTC and PET
	Reported outputs	Total conflicts; crossing, rear-end, and lane-change conflicts; mean and variance of TTC and PET
Statistical analysis	Group comparison	One-way ANOVA with Tukey HSD post hoc tests	Across six scenarios

A one-factor scenario-based design was used in this study. The only experimental factor was the automation scenario (A–F), while traffic demand, network geometry, operational rules, and service-time distributions were kept constant across all runs. Each scenario was replicated six times using different random seeds, resulting in 36 simulation runs in total.

Table 4. Experimental scenario parameters for safety analysis.

Scenario ID	Composition Description	Road AGV Rate	Road HDV Rate	Port Composition
A	All Human-Driven	0%	100%	100% HDV
B	Mixed (Port AGV, Road HDV)	0%	100%	100% AGV
C	Mixed (25% Road AGV)	25%	75%	100% AGV
D	Mixed (50% Road AGV)	50%	50%	100% AGV
E	Mixed (75% Road AGV)	75%	25%	100% AGV
F	Fully Automated (Road + Port)	100%	0%	100% AGV

Table 4. Experimental scenario parameters for safety analysis.

Scenario ID	Composition Description	Road AGV Rate	Road HDV Rate	Port Composition
A	All Human-Driven	0%	100%	100% HDV
B	Mixed (Port AGV, Road HDV)	0%	100%	100% AGV
C	Mixed (25% Road AGV)	25%	75%	100% AGV
D	Mixed (50% Road AGV)	50%	50%	100% AGV
E	Mixed (75% Road AGV)	75%	25%	100% AGV
F	Fully Automated (Road + Port)	100%	0%	100% AGV

3. Results

3.1. Experimental Simulation Scenarios Developing

A one-factor experimental design was used to evaluate six automation scenarios under fixed traffic demand and operating conditions. The experimental factor was vehicle automation scenario (A–F), while network geometry, operational rules, demand settings, and simulation horizon were kept constant. Each scenario was replicated six times using different random seeds, resulting in 36 simulation runs in total. For each experiment, vehicle trajectory data generated by the microscopic simulation were processed using surrogate safety indicators, including TTC and PET, to quantify the frequency and severity of traffic conflicts.

The six-scenario design therefore provides comprehensive coverage of the automation transition pathway, enabling rigorous safety assessment through controlled variation in the key factors governing mixed traffic interactions in port environments as shown in Table 4. Scenario A (100% HDV) establishes the baseline safety performance of current conventional port operations.

Scenario B (100% Port AGV, 0% Road AGV) represents a realistic transitional configuration where port operators automate internal fleets while external trucks remain human-driven. This asymmetric setup generates critical interactions at the port–external network interface, particularly at gate areas.

Scenarios C, D, and E (25%, 50%, and 75% Road AGV) enable gradient analysis of how increasing external vehicle automation affects safety outcomes. This incremental approach captures potential non-linear effects where certain penetration thresholds may produce disproportionate safety impacts.

Scenario F (100% AGV) represents the fully automated future state, providing an upper-bound reference for potential safety improvements.

3.2. Safety Conditions Evaluating

Following the experimental design, simulation runs were conducted for each of the six scenarios (A through F) under consistent operational conditions. The resulting vehicle trajectory files were processed using the SSAM to quantify traffic conflicts by type and severity. All reported conflict counts, TTC values, and PET values were computed over the full 6 h simulation period, including the initial 30 min stabilization phase. A comparative summary of conflict frequencies across scenarios is presented in

Table 5. Summary of traffic conflicts by scenario and conflict type.

Scenario ID	Total Conflicts Number	Number of Crossing	Number of Rear End	Number of Lane Change
A	89	12	70	7
B	72	15	55	2
C	76	17	57	2
D	57	10	44	3
E	55	12	36	7
F	43	11	30	2

.

The simulation results reveal a distinct inverse relationship between the penetration rate of automated vehicles and the frequency of traffic conflicts. Total conflicts decrease progressively from 89 in Scenario A (0% automation) to 43 in Scenario F (100% automation), representing a 51.7% reduction in conflict events under fully automated conditions. This monotonic decline suggests that the introduction of automated vehicles contributes positively to traffic safety within confined port environments, likely due to more consistent and predictable vehicle control algorithms.

Across all scenarios, rear-end conflicts consistently represent the dominant conflict type, accounting for between 69.8% (Scenario F) and 78.7% (Scenario A) of total conflicts. This predominance indicates that longitudinal interactions—car-following behavior, speed adjustments, and deceleration events—constitute the primary safety-critical mechanism in port terminal operations. The progressive reduction in rear-end conflicts from 70 in Scenario A to 30 in Scenario F (a 57.1% decrease) suggests that automated vehicle control systems, particularly ACC logic, are effective in maintaining safer following distances and smoother speed regulation compared to human drivers.

Crossing conflicts exhibit relative stability across scenarios, ranging from 10 to 17 events, with no clear trend associated with automation penetration. This stability implies that conflicts at intersections and crossing points are influenced more by infrastructure geometry and right-of-way rules than by vehicle automation characteristics. The persistence of crossing conflicts even under full automation (11 events in Scenario F) suggests that intersection design and traffic control measures remain critical safety considerations regardless of vehicle type.

Lane change conflicts show limited variation, with values between 2 and 7 events across scenarios. The absence of a systematic reduction pattern may indicate that lateral maneuver conflicts are relatively rare in port environments due to restricted lane-changing opportunities and low-speed operating conditions. However, the slight increase observed in Scenario E (7 events) warrants further investigation, as it may reflect transitional interactions between mixed vehicle types at higher automation penetrations.

Statistical analysis revealed a significant main effect of automation penetration on total conflict frequency (one-way ANOVA: F(5,30) = 18.24, p < 0.001, η² = 0.71), with post hoc Tukey HSD tests confirming significant reductions between the fully human-driven scenario (A: 89.2 ± 4.1) and all mixed scenarios (p < 0.01). Rear-end conflicts exhibited the strongest response to automation (F(5,30) = 22.37, p < 0.001, η² = 0.76), while crossing and lane change conflicts remained statistically unchanged across scenarios (p > 0.05). Pairwise comparisons identified a threshold effect, with scenarios exceeding 50% automation (D, E, F) showing no significant differences among themselves but all differing significantly from lower-penetration scenarios. These findings demonstrate that automation benefits are primarily realized through improved longitudinal control, with diminishing returns beyond 50–75% penetration.

The mean TTC values exhibit a clear decreasing trend as the penetration rate of automated vehicles increases (see

Table 6. Summary of TTC and PET by scenario.

Scenario ID	TTC, Sec		PET, Sec
	Mean	Variance	Mean	Variance
A	0.80	0.39	1.56967	1.59282
B	0.50	0.41	0.890274	1.36032
C	0.44	0.39	0.656573	0.942472
D	0.28	0.31	0.424561	0.791897
E	0.33	0.34	0.419993	0.564949
F	0.24	0.26	0.378118	0.59664

). Scenario A (fully human-driven) demonstrates the highest mean TTC of 0.80 s, indicating that human-driven traffic maintains larger temporal safety margins. In contrast, Scenario F (fully automated) shows the lowest mean TTC of 0.24 s, representing a 70% reduction compared to the baseline human-driven scenario.

Scenario B (port AGVs only, road fully human-driven) yields a mean TTC of 0.50 s—a substantial decrease of 37.5% relative to Scenario A. This suggests that the introduction of automated vehicles within the port itself, even without road automation, significantly reduces temporal proximity between vehicles.

Scenario C (25% road AGV penetration) further reduces mean TTC to 0.44 s, continuing the downward trend. The most pronounced reduction occurs in Scenario D (50% road AGV), where mean TTC drops to 0.28 s—a 65% decrease from Scenario A. Interestingly, Scenario E (75% road AGV) shows a slight increase to 0.33 s, which may indicate transitional interaction effects at higher automation levels where mixed traffic dynamics become more complex.

Scenario F achieves the lowest mean TTC at 0.24 s, confirming that full automation enables the closest vehicle proximity while presumably maintaining safety through precise control algorithms.

Regarding variability, Scenario D exhibits the lowest variance (0.31), suggesting more consistent and predictable vehicle interactions at 50% automation. Scenario B shows the highest variance (0.41), indicating greater heterogeneity in traffic interactions when only port vehicles are automated. Scenarios A, C, and F demonstrate similar variance levels (0.39, 0.39, and 0.26, respectively), with fully automated conditions showing the most consistent TTC distribution.

Overall, the progressive reduction in mean TTC with increasing automation suggests that automated vehicles operate with tighter temporal proximity, reflecting more efficient space utilization and coordinated movement patterns. However, the slight increase in Scenario E warrants further investigation, as it may indicate a critical transition point in mixed traffic dynamics.

Analysis of Time-to-Collision (TTC) across six automation scenarios revealed a statistically significant main effect of automation penetration on temporal safety margins (one-way ANOVA: F(5,30) = 6.92, p < 0.001, η² = 0.54). Mean TTC values decreased progressively from 0.80 s in the fully human-driven scenario (A) to 0.24 s under full automation (F), representing a 70% reduction in temporal proximity. Post hoc Tukey HSD tests confirmed that Scenario A differed significantly from all scenarios with road automation levels of 25% or higher (p < 0.05), while no significant differences were detected among scenarios D, E, and F (p > 0.05). This plateau effect suggests that once a threshold of 50–75% automation is reached, further increases in automation penetration do not substantially alter TTC distributions. The large effect size (η² = 0.54) indicates that automation level explains over half of the variance in TTC, confirming the strong influence of vehicle automation on conflict temporal dynamics in port environments.

The mean PET values demonstrate a consistent and progressive decline as the penetration rate of automated vehicles increases. Scenario A (fully human-driven) exhibits the highest mean PET of 1.57 s, indicating that human-driven traffic maintains larger temporal gaps at conflict points such as intersections and merging areas. Scenario F (fully automated) shows the lowest mean PET of 0.38 s, representing a 75.9% reduction compared to the baseline human-driven scenario.

Scenario B (port AGVs only, road fully human-driven) yields a mean PET of 0.89 s—a substantial decrease of 43.3% relative to Scenario A. This reduction indicates that automating internal port vehicles alone significantly tightens temporal gaps at conflict points, even when external traffic remains human-driven.

Scenario C (25% road AGV penetration) further reduces mean PET to 0.66 s, continuing the downward trend. The most pronounced reduction occurs between Scenarios C and D, where mean PET drops to 0.42 s at 50% road automation—a 73.0% decrease from Scenario A. Notably, Scenarios D (0.42 s), E (0.42 s), and F (0.38 s) exhibit very similar mean PET values, suggesting that beyond 50% automation, further increases in penetration yield diminishing returns.

Regarding variability, PET variance decreases steadily with increasing automation: from 1.59 in Scenario A to 0.60 in Scenario F. This 68.5% reduction in variance indicates that vehicle interactions become increasingly consistent and predictable as automation levels rise. The highest variance in Scenario A reflects the inherent unpredictability of human driver behavior at conflict points, while the low variance in Scenarios E and F demonstrates the uniform behavior of automated vehicles when negotiating intersections and crossing maneuvers.

The progressive reduction in both mean PET and variance suggests that automation significantly improves the consistency and efficiency of vehicle interactions at conflict points. The stabilization of PET values beyond 50% automation indicates that the most substantial safety benefits at intersections and crossing zones are achieved once a critical mass of automated vehicles is present in the traffic stream.

Analysis of Post-Encroachment Time (PET) across six automation scenarios revealed a statistically significant main effect of automation penetration on temporal gaps at conflict points (one-way ANOVA: F(5,30) = 8.47, p < 0.001, η² = 0.59). Mean PET values decreased from 1.57 s in the fully human-driven scenario (A) to 0.38 s under full automation (F), representing a 75.9% reduction. Post hoc Tukey HSD tests confirmed that Scenario A differed significantly from all scenarios involving automated vehicles (p < 0.05), while no significant differences were detected among scenarios B through F (p > 0.05). This threshold effect indicates that the presence of any automated vehicles substantially reduces PET at conflict points, but increasing automation penetration beyond a minimal level does not produce additional statistically significant improvements. The large effect size (η² = 0.59) confirms that automation level explains over half of the variance in PET, demonstrating the strong influence of vehicle automation on crossing conflict dynamics in port environments. Unlike TTC, which showed a gradual dose-dependent response, PET exhibits a more binary sensitivity to automation presence, suggesting that different safety indicators capture distinct aspects of mixed-traffic interactions.

Figure 6 presents the spatial distribution of detected conflict points for each of the six experimental scenarios. These diagrams provide a visual representation of how the introduction and progressive penetration of automated vehicles affects not only the total number of conflicts but also their spatial concentration within the port network. The comparison of these figures enables the identification of persistent conflict hotspots as well as areas where automation contributes to the reduction or redistribution of safety-critical interactions.

Together with the statistical indicators presented above, the spatial analysis offers a more comprehensive understanding of conflict dynamics in mixed-traffic port environments.

4. Discussion

The findings of this study, while demonstrating a clear progressive reduction in total conflicts and rear-end events with increasing automation penetration, raise important questions regarding the applicability of conventional surrogate safety assessment methodologies to mixed traffic environments involving automated vehicles.

The SSAM and its core indicators—TTC and PET—were originally developed and calibrated based on observational studies of human driver behavior. Recent research has shown that evaluating safety using SSAM has several limitations, including the need for rigorous calibration procedures and the frequent failure of simulation models to accurately represent actual driving behavior, subsequently failing to capture the actual mechanisms generating near-misses [36]. Studies comparing simulated conflicts with field-measured conflicts have highlighted the importance of model calibration and identified several inherent limitations of the SSAM approach [10].

These concerns are particularly relevant when assessing automated vehicles. Ref. [37] systematically evaluated eight conventional safety indicators for connected and automated vehicles, including TTC and PET, and found that these measures can yield different safety implications for CAVs due to their small-gap car-following characteristics. Their research demonstrates that ignoring such characteristics may lead to interpreting small-gap car-following situations as simply dangerous traffic interactions for CAVs, when in fact these closer proximities may represent normal, safe operation enabled by automated control systems. The car-following experiments indicated that TTC, PET, and DRAC are insufficient in measuring the safety implications when successive vehicles operate at similar speeds for CAVs.

Our results illustrate this paradox clearly. The monotonic reduction in total conflicts from 89 in Scenario A to 43 in Scenario F, together with the reduction in rear-end conflicts from 70 to 30, indicates that automation primarily improves longitudinal stability in the port traffic system. This interpretation is consistent with previous mixed-traffic studies showing that increasing automation penetration and automated car-following control improve following stability and reduce unsafe longitudinal interactions [6]. However, our findings extend this line of research to a seaport terminal integrated with an external urban road network, where the dominant safety problem is not only traffic flow instability but also low-speed operational interactions at gates, yard accesses, and berth approaches.

By contrast, crossing conflicts remained within a relatively narrow range across scenarios, suggesting that these conflicts are influenced less by vehicle automation itself and more by infrastructure geometry, right-of-way rules, and bottleneck locations. This result is compatible with port traffic simulation studies emphasizing the importance of terminal layout, routing structure, and node capacity for conflict formation [20,21]. In practical terms, this means that automation alone cannot eliminate all conflict hotspots in the port; geometric redesign and intersection control remain necessary.

Most importantly, the simultaneous reduction in conflict counts and in mean TTC and PET values supports recent studies questioning whether conventional surrogate thresholds can be directly transferred to automated traffic [37]. In our simulations, fewer conflicts were detected as automation increased, yet mean TTC fell from 0.80 to 0.24 s and mean PET from 1.57 to 0.38 s. This indicates that lower TTC and PET values in AGV-dominated traffic may reflect tighter but more coordinated control rather than higher crash risk. Therefore, the interpretation of surrogate safety indicators in port automation studies should be based not only on raw threshold exceedance but also on the control logic and interaction type of the vehicles involved. Rear-end conflicts decreased by 57.1% under full automation compared to the fully human-driven scenario, while simultaneously mean TTC values decreased by 70% and mean PET values decreased by 75.9%. If conventional threshold values (typically 1.0–1.5 s for TTC [38]) were applied rigidly, the lower values observed under automated conditions would be classified as more severe conflicts, contradicting the observed reduction in actual conflict events. This discrepancy suggests that lower TTC and PET values in automated traffic may not indicate increased crash risk but rather reflect the closer, yet still safe, following distances and tighter coordination enabled by automated control systems.

A fundamental challenge in interpreting the safety implications of mixed-traffic operations lies in the absence of established threshold values specifically calibrated for interactions involving automated vehicles. Research on safety testing and evaluation methods for autonomous vehicles has proposed using fuzzy clustering of natural driving indicator data to determine appropriate threshold ranges for different vehicle types [39]. This approach recognizes that threshold values employed in the past may not be directly transferable to contexts involving automated vehicles.

Recent work examining severity dimensions of traffic conflicts for different simulated mixed fleets involving connected and autonomous vehicles has demonstrated that severity thresholds vary significantly by vehicle automation level [40]. For human-driven vehicles, TTC values below 1.5 s are typically classified as high-severity conflicts. However, for higher levels of vehicle automation, the threshold for high-severity conflicts shifts downward—to below 1.0 s for intermediate automation levels and below 0.75 s for more advanced automated systems. This variation in threshold values across automation levels confirms that applying uniform conflict severity criteria to mixed traffic environments will produce misleading safety assessments.

The question of what constitutes a “safe” or “unsafe” TTC value for an automated vehicle following another automated vehicle, or for an automated vehicle following a human-driven truck, remains insufficiently addressed in the literature. A comprehensive review of surrogate safety indicators has highlighted the need for further research on threshold selection and validation across different traffic contexts [41]. This calibration problem is compounded by the heterogeneity of mixed traffic. In our experimental scenarios, the composition of vehicle types varied systematically, yet the same threshold values would need to be applied uniformly across all interaction types to enable consistent comparison. Such uniform application, however, may obscure important differences in the underlying safety mechanisms.

The port environment adds additional layers of complexity to safety assessment. Unlike conventional road networks, port terminals are characterized by low-speed operations, high vehicle density, mission-based task allocation, and infrastructure designed for freight handling rather than general traffic flow. Research examining mixed traffic flows involving truck platoons on port freeways has demonstrated that the safety levels of mixed traffic flow are influenced by multiple factors including penetration rates, platoon lengths, and headway configurations [6]. The stochastic behavior of human drivers in car-following situations interacts with automated vehicle control algorithms in ways that are specific to the operational context.

Furthermore, the behavioral parameters governing vehicle motion differ substantially between port operations and general traffic. The AGVs in our simulation were calibrated with reaction times of 0.1–0.3 s, maximum acceleration of 0.5–1.0 m/s², and conservative gap acceptance thresholds. These parameters reflect port-specific operational requirements—cargo stability, energy efficiency, and safety margins—rather than general driving behavior. Safety assessment frameworks developed for urban or highway traffic cannot simply be transplanted into this context without recalibration.

The observed patterns in our results suggest that different safety indicators capture distinct aspects of mixed-traffic interactions and respond differently to increasing automation penetration. TTC exhibited a gradual, dose-dependent response to automation level, with significant reductions accumulating progressively as automation increased. PET, in contrast, showed a threshold effect: the introduction of any automated vehicles significantly reduced PET values, but further increases in automation produced no additional statistically significant changes. This divergence implies that a single safety indicator applied with fixed thresholds cannot fully capture the multidimensional nature of safety in mixed-traffic environments. Recent reviews of traffic conflict analysis have emphasized the need for multi-indicator approaches [41].

An adapted methodology for automated vehicle safety assessment would need to address several key requirements. First, indicator-specific thresholds must be calibrated for different vehicle type combinations—automated–automated, automated–human, and human–human interactions may each require distinct threshold values reflecting their underlying control characteristics. Research on fuzzy clustering of natural driving data offers promising approaches for deriving these context-specific thresholds [3]. Second, multiple complementary indicators should be employed to capture different conflict mechanisms: TTC for longitudinal interactions, PET for crossing conflicts, and potentially additional measures such as DRAC or other extended indicators. Studies have shown that PET and other indicators like PICUD can yield different safety implications for CAVs, and ignoring small-gap following characteristics may lead to misinterpretation of traffic interactions.

The findings of this study have practical implications for how safety should be assessed in ports transitioning toward automation. If conventional SSAM thresholds are applied without adaptation, there is a risk of misinterpreting the safety effects of automation—either overestimating risk by classifying close-but-safe automated operations as conflicts, or underestimating risk by failing to capture automation-specific failure modes. The documented limitations of SSAM, including its tendency to overestimate occurrences and underestimate severity of certain conflict types, further reinforce the need for caution when applying this methodology to mixed-traffic environments.

Port operators and safety analysts should therefore exercise caution when applying standard surrogate safety tools to mixed-traffic environments, and should consider developing context-specific threshold values through empirical observation or validated simulation studies calibrated to local conditions. The importance of rigorous calibration procedures cannot be overstated, as research has demonstrated that calibration positively impacts the estimate of safety performance measures obtained through simulation processes.

The quantitative results of this study are configuration-specific and should not be transferred directly to all port terminals [42]. Absolute conflict counts, the spatial location of hotspots, and the balance between rear-end and crossing conflicts depend on terminal geometry, gate-control logic, berth–yard distances, parking layout, demand profile, and local operational rules. Nevertheless, the qualitative mechanisms identified here are likely to be transferable to ports with similar characteristics: low-speed internal circulation, mission-based routing, mixed AGV–HDV traffic, and bottlenecks at gates and intersections. In this sense, the study supports analytical generalization of the mechanisms, but not direct numerical generalization of the reported conflict frequencies.

Compared with previous studies that mainly examine either operational efficiency of automated port equipment or safety of mixed traffic in urban roads and port freeways, the present study addresses a different problem: safety evaluation of mission-based mixed traffic inside a seaport terminal integrated with an external road network. The originality of this study lies in four aspects. First, it jointly represents internal port AGVs and external road vehicles within one microscopic model. Second, it evaluates a staged transition pathway from fully human-driven traffic to full automation through six fleet-composition scenarios. Third, it combines AIMSUN-based microsimulation, SSAM conflict analysis, and spatial hotspot mapping within one framework. Fourth, it demonstrates that conventional TTC and PET thresholds may produce contradictory interpretations when applied to automated port traffic. These features distinguish the study from previous work and show that safety assessment methods developed for urban or freeway traffic cannot be directly transferred to seaport automation without contextual adaptation.

5. Conclusions

This study investigated the safety implications of introducing autonomous vehicles into mixed traffic operations within a port environment using microscopic simulation and surrogate safety analysis. A scenario-based experimental design was implemented to evaluate six automation scenarios ranging from fully human-driven traffic to fully automated operations. A limitation of the present study is that traffic demand was kept constant across all scenarios; therefore, the sensitivity of surrogate safety outcomes to traffic-volume fluctuations was not evaluated and should be addressed in future work. Vehicle trajectory data were analyzed using the surrogate safety indicators TTC and PET.

The results demonstrate a clear reduction in overall conflict frequency as the penetration rate of automated vehicles increases. In particular, rear-end conflicts—representing the dominant conflict type in port operations—decreased substantially under higher automation levels, indicating that automated longitudinal control systems contribute to more stable and predictable vehicle interactions. At the same time, crossing and lane-change conflicts showed relatively limited sensitivity to automation penetration, suggesting that infrastructure layout and operational rules remain critical determinants of safety at intersections and maneuvering zones.

However, the analysis also revealed an important methodological limitation. Although the number of conflicts decreased with increasing automation, both TTC and PET values also declined, indicating closer temporal proximity between vehicles. Under conventional surrogate safety interpretation frameworks, such reductions would typically be associated with increased collision risk. This apparent contradiction suggests that traditional conflict severity thresholds—originally calibrated for human driving behavior—may not be directly applicable to automated or mixed traffic environments.

These findings highlight the need for recalibrating surrogate safety indicators and their threshold values when evaluating automated vehicle operations. Future safety assessment frameworks should account for the specific behavioral characteristics of automated vehicles, including shorter reaction times, more consistent control strategies, and tighter yet stable vehicle spacing. Developing automation-sensitive safety metrics will therefore be essential for accurately evaluating the safety performance of emerging automated transport systems in complex operational environments such as maritime ports.

Overall, the results confirm that vehicle automation has the potential to significantly improve operational safety in port traffic systems, while simultaneously emphasizing the importance of adapting existing safety evaluation methodologies to reflect the changing dynamics of automated mobility. The reported conflict counts should therefore be interpreted as case-specific to the modeled terminal, whereas the identified mechanisms of automation-related longitudinal stabilization and threshold reinterpretation are expected to be relevant to comparable mixed-traffic port environments.