Vessel Arrival Priority Determination in VTS Management: A Dynamic Scoring Approach Integrating Expert Knowledge

Abstract

Vessel arrival priority determination is a critical factor affecting port safety and efficiency in maritime traffic management, yet existing approaches relying on First Come, First Served (FCFS) principles or empirical judgment have limitations in systematic decision-making. This study aims to develop a systematic decision-making framework that overcomes these limitations by creating an automated, expert knowledge-based priority determination system for vessel traffic services. A dynamic score-based vessel arrival priority determination model was developed integrating the Delphi technique and Fuzzy Analytic Hierarchy Process (Fuzzy AHP). Basic score evaluation factors were derived through Delphi surveys conducted with 50 field experts, and weights were calculated by differentially applying Fuzzy AHP and conventional AHP according to hierarchical complexity. The proposed model consists of a dynamic scoring system integrating basic scores reflecting vessel characteristics and operational conditions, special situation scores considering emergency situations, and risk scores quantifying safety intervals between vessels. To validate the model performance, simulation-based evaluation with eight scenarios was conducted targeting experienced VTS (Vessel Traffic Services) officers, demonstrating strong agreement with expert judgment across diverse operational conditions. The developed algorithm processes real-time maritime traffic data to dynamically calculate priorities, providing port managers and maritime authorities with an automated decision support tool that enhances VTS management and coastal traffic operations.

1. Introduction

Maritime traffic possesses unique characteristics that distinctly differentiate it from other transportation modes such as road or air traffic. In particular, the increasing size and high autonomy of vessels, combined with factors such as large inertia, diversity in vessel sizes, navigation adjacent to physical boundaries, and the “point of no return” during port entry, create unique operational challenges. These challenges are particularly pronounced in environments with limited maneuvering space, such as ports and straits [1]. Maritime traffic is distinguished from general process control systems in several aspects. First, maritime traffic is geographically widely distributed, and the system constantly changes as traffic participants continuously enter and leave. Second, while vessels approach from different directions, they face the special constraint of maintaining regular intervals and entering in a single-line queue when entering ports. These characteristics suggest that determining vessel entry sequence in port approach areas is one of the core challenges in maritime traffic management.

Maritime traffic density has increased rapidly in recent years, along with a trend toward larger and faster vessels, resulting in significantly elevated navigational risks in congested waterways [2]. This intensified traffic creates more complex maritime scenarios, inevitably accompanied by heightened risks [1,3]. Vessel traffic management in confined waterways such as ports and straits is therefore important from both safety and efficiency perspectives. From the safety perspective, maintaining appropriate temporal and spatial intervals is essential to minimize collision risks between vessels, while from the efficiency perspective, maximizing port facility utilization and minimizing vessel waiting times are important objectives. Achieving these goals requires centralized planning and coordination, which is primarily conducted through VTS systems [4].

However, vessel arrival priority determination in many ports currently relies mainly on First Come, First Served (FCFS) principles or empirical judgment by traffic controllers. This approach has limitations, since it fails to comprehensively consider various vessel characteristics, operational conditions, and special situations. Particularly in large ports with heavy traffic, more systematic priority determination methods are required that consider various factors such as vessel size, cargo type, urgency, and safety requirements. The need for priority-based systems over simple FCFS approaches has been demonstrated in other critical domains, such as emergency medical services where triage systems effectively prioritize patients based on urgency and severity [5]. Moreover, there are virtually no systematic decision-making frameworks that incorporate the experiential knowledge and practical judgment criteria of field experts such as VTS operators and pilots, who bear direct responsibility for safety and efficiency in vessel arrival processes.

Particularly in narrow fairway entry sections, overtaking between vessels is impossible and maintaining minimum safety intervals is essential, making systematic priority determination in the pre-fairway entry stage even more important.

Against this background, a dynamic score-based vessel arrival priority determination model is proposed in this study, which comprehensively considers physical vessel characteristics, operational situations, special circumstances, and safety requirements. The proposed model is based on evaluation factors and weights derived through the Delphi technique Fuzzy AHP, calculating integrated dynamic scores for each vessel and determining arrival priorities accordingly. The qualitative novelty of combining Delphi–Fuzzy AHP with risk reduction lies in transforming expert judgment into a systematic framework that simultaneously maintains operational expertise while dynamically enhancing maritime safety through objective priority determination, creating a decision support tool that bridges subjective experience with quantitative risk management. In particular, this model has dynamic characteristics that can reflect real-time changes in vessel positions and conditions, supporting more flexible and effective decision-making than existing static priority determination methods.

The Delphi, AHP, and Fuzzy AHP surveys used in this study were administered to a total of 50 participants, comprising 40 VTS operators with more than 5 years of operational experience and 10 pilots from Busan Port, ensuring systematic reflection of the participating experts’ experiential knowledge.

The structure of this paper is as follows. Section 2 comprehensively reviews existing research on decision-making frameworks and methodological approaches in the maritime field, and Section 3 presents the methodological framework of the proposed dynamic score-based arrival priority determination model. Section 4 analyzes the results of weight derivation through the Delphi technique and Fuzzy AHP and model performance evaluation results through eight scenarios, Section 5 conducts comprehensive discussion of the experimental results, and, finally, Section 6 discusses the conclusions of the research and future research directions.

2. Literature Review

A comprehensive literature review was conducted using the Web of Science (WoS) database as of April 2025, to identify relevant studies in vessel arrival priority optimization and VTS decision support systems. Initially, a search for ‘vessel traffic service’ AND ‘priority’ conducted across all years yielded 25 documents, with 8 papers directly relevant to VTS-based priority decision making. This indicated limited research in systematic vessel arrival sequencing within VTS operational frameworks.

To understand recent research trends, the focus was then placed on the past decade (2015–2024), broadening our search to include multi-criteria decision-making approaches in maritime traffic management. The search terms included combinations of ‘vessel arrival priority,’ ‘ship scheduling optimization,’ ‘AHP,’ ‘fuzzy AHP,’ ‘Delphi method,’ and ‘VTS decision support.’ After excluding studies focused solely on berth allocation without priority considerations, container terminal operations, and underwater vessel studies, 13 papers were identified as directly relevant to our research focus on dynamic vessel arrival priority determination. These papers were systematically analyzed across five key dimensions: research focus/topic, methodology, and findings/contributions, and are summarized in

Table 1. Analysis of previous studies on maritime decision-making frameworks: focus, methodology, and key contributions.

No.	Author(s)	Focus/Topic	Methodology	Findings/Contributions
1	Shin et al. [6]	Assessment of VTS Workload	DELPHI-AHP Method	Workload Assessment and Comparison of All VTS Centers in Korea
2	Emovon [7]	Ship system maintenance strategy selection	DELPHI-AHP-TOPSIS hybrid methodology	Hybrid MCDM framework with criteria reduction and reduced computational complexity
3	Shao et al. [8]	Virtual arrival optimization	NSGA-2 (Non-dominated Sorting Genetic Algorithm II) algorithm with comprehensive mathematical model	Dual-objective optimization that significantly reduces waiting time and CO2 emissions compared to FCFS
4	Xue et al. [9]	Maritime safety factor prioritization for autonomous ships	Gray relational analysis (GRA) combined with fuzzy theory	Novel gray-fuzzy hybrid approach for factor prioritization with enhanced sensitivity
5	Ren et al. [10]	Port tugboat scheduling optimization under uncertainty	Multi-objective fuzzy programming with Stackelberg game and Self-Organizing Ant Colony Particle Genetic (SOAPG) algorithm	Game-theoretic framework with superior performance over traditional algorithms
6	Tang et al. [11]	Service priority in berth allocation and crane assignment	Mixed Integer Programming Model solved by Genetic Algorithm with service priority weighting	Service priority system more effective for large vessels with significant delay reduction
7	Wen et al. [12]	Ship scheduling with congestion and environmental considerations	Multi-objective programming model with queuing theory (M/M/1 and M/M/c) solved by Multi-objective Gray Wolf Optimizer (MOGWO) and NSGA-II	MOGWO outperforms NSGA-II, with improved queuing system efficiency
8	Liu et al. [13]	Vessel scheduling with variable speed in one-way channel	Mixed Integer Linear Programming (MILP) model with Minimum Safety Time Interval (MSTI) concept solved by Genetic Algorithm (GA)	Variable speed consideration with MSTI concept showing substantial improvement over priority-based methods
9	Celik and Akyuz [14]	Fuzzy AHP-TOPSIS for maritime equipment selection	Interval Type-2 Fuzzy Sets (IT2FSs) with AHP and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)	IT2FSs integration for enhanced uncertainty handling
10	Georgoulas et al. [15]	AHP-based port selection decision support	AHP integrated with Decision Support System (DSS)	Fast decision-making tool with user-friendly visualization
11	Praetorius and Lützhöft [16]	VTS decision support for dynamic risk management	Ethnographically inspired methods including observations, interviews, and focus groups within Naturalistic Decision Making (NDM) and High Reliability Organization (HRO) frameworks	VTS operator decision-making framework emphasizing expert knowledge and user needs
12	Çağlayan, Ö. and Aymelek [17]	Sustainable ship queuing policy via VTS	Integrated FAHP and PROMETHEE II methodologies with exploratory sequential mixed methods research approach	Eight-criteria hierarchical structure with significant CO2 reduction and complete ship ranking
13	Lee and Kim [18]	Priority index for intelligent vessel traffic monitoring	Density-Based Spatial Clustering of Applications with Noise (DBSCAN) clustering with Fuzzy Inference System (FIS) using CPA and TCPA parameters	Location-based clustering with fuzzy membership functions, improving search time efficiency

.

2.1. Decision-Making Frameworks in the Maritime Field

The most significant development in decision-making frameworks within maritime traffic management has been overcoming the limitations of traditional FCFS approaches. Çağlayan and Aymelek [17] developed a VTS-based decision support model for sustainable ship queuing policy, achieving CO₂ emissions reduction of 32.8% to 45%, compared to existing FCFS policy. Their research established an eight-criteria hierarchical structure with safety (32%), business (29%), efficiency (25%), and environmental (15%) priority weights, replacing the inefficient FCFS system with a complete ship ranking system that supports a Just-In-Time Arrival (JITA) initiative.

In the field of maritime traffic safety risk factor prioritization, Xue et al. [9] developed a comprehensive risk assessment framework for autonomous ships. They prioritized 33 influencing factors within four categories using GRA combined with fuzzy theory, identifying summary force, relative wave direction, and relative wind speed as top factors.

Maritime traffic optimization research has focused on simultaneously considering multiple objectives. Shao et al. [8] concentrated on virtual arrival optimization for traffic organization scenarios, achieving dual objective optimization for carbon reduction and waiting time minimization. Their research realized 31.41% reduction in waiting time versus FCFS, 65.37% improvement versus VALS, and 23.29% minimum CO₂ emission reduction. Wen et al. [12] focused on multi-objective optimization for ship scheduling with port congestion and environmental considerations, presenting the important finding that service unreliability is more sensitive to port congestion than cost and emissions.

In maritime traffic monitoring and priority determination, Lee and Kim [18] concentrated on developing a priority index for intelligent vessel traffic monitoring systems in VTS areas. They used location-based vessel traffic clustering to consider regional navigation characteristics, constructing fuzzy membership functions for 17 clusters reflecting area-specific CPA/TCPA thresholds, and successfully identified all high-risk vessel pairs within operational time constraints.

In VTS operator decision support, Praetorius et al. [16] conducted research focusing on user needs for dynamic risk management. Their ethnographic study revealed that VTS operator decision-making in dynamic, uncertain environments heavily depends on expert knowledge and experience, identifying technical user needs including the right information at the right time, trustworthy AIS data sources, and information consistency between shore and ship systems.

In port operations, various optimization problems have been addressed through decision-making frameworks. Tang et al. [11] focused on the effect of service priority on integrated continuous berth allocation and quay crane assignment problems after port congestion. Their research demonstrated that service priority using squared handling volume (C²) is more effective for large vessels, with large vessel prioritization reducing delay time by 45.24%, compared to unweighted scenarios. Liu et al. [13] concentrated on vessel scheduling optimization based on variable speed in seaports with one-way navigation channels, achieving an average 2–359% improvement over priority-based scheduling methods while ensuring whole voyage safety constraints.

In port tugboat scheduling, Ren et al. [10] focused on port tugboat scheduling optimization under uncertainty. They developed a Stackelberg game-theoretic framework for tugboat operator–port dispatcher interaction, integrating three scheduling principles: shortest distance, first available, and fairness.

In port selection decision-making, Georgoulas et al. [15] concentrated on developing an AHP-enabled port selection multi-source decision support system within the ENIRISST project. Their system combined multiple AHP studies from academic literature with benchmarking capabilities.

Decision-making framework research has also been conducted in the maritime transportation engineering field. Celik et al. [14] focused on decision-making problems for ship loader selection in dry-bulk cargo terminals. They validated the robustness of their proposed approach through sensitivity analysis across 12 cases.

In ship system maintenance, Emovon [7] conducted research focusing on ship system maintenance strategy selection. They achieved criteria reduction from 22 to 12 while reducing computational complexity, and identified OFCBM as the optimal strategy.

The development of decision-making frameworks across the maritime field demonstrates an evolution from simple rule-based approaches to sophisticated systems incorporating multi-criteria evaluation, expert knowledge integration, uncertainty handling, and environmental considerations. These frameworks pursue the common goal of supporting systematic and scientific decision-making while addressing unique challenges within their specific domains.

2.2. Methodological and Algorithmic Approaches

Hybrid methodologies combining the Delphi technique with multi-criteria decision-making approaches provide systematic frameworks for integrating expert knowledge with quantitative analysis in the maritime field. Emovon [7] developed a sequential DELPHI-AHP-TOPSIS integration algorithm structured as a three-stage process: (1) expert consensus derivation through Delphi rounds, (2) weight calculation through AHP pairwise comparison matrices, and (3) final ranking determination through TOPSIS ideal solution proximity algorithms. This hybrid algorithm incorporates criteria dimension reduction functionality while decreasing computational complexity.

Fuzzy theory-based algorithms provide various computational approaches for handling uncertainty and ambiguity in the maritime field. Celik and Akyuz [14] integrated IT2FSs algorithms with AHP and TOPSIS, providing mathematical structures that more effectively handle uncertainty about uncertainty compared to traditional Type-1 fuzzy sets.

Hybrid algorithms combining gray system theory with fuzzy theory provide advanced uncertainty handling techniques in incomplete information environments. Xue et al. [9] developed a novel gray-fuzzy hybrid algorithm combining GRA with fuzzy theory. The core of this algorithm is integrating weighted linguistic terms into the gray relational coefficient calculation process, improving the traditional GRA’s equal-weight approach by producing weighted gray relational coefficients that quantitatively reflect expert knowledge.

Multi-objective evolutionary algorithms offer sophisticated computational techniques for solving complex optimization problems in the maritime field. Shao et al. [8] combined the NSGA-2 algorithm with comprehensive mathematical models. Wen et al. [12] integrated the MOGWO algorithm with queuing theory models (M/M/1 and M/M/c). Comparative analysis showed that MOGWO’s convergence characteristics and diversity maintenance capabilities demonstrated superior performance indicators compared to NSGA-II.

Game theory-based optimization algorithms provide mathematical frameworks for strategic decision-making in multi-agent environments. Ren et al. [10] developed Stackelberg game theory combined with SOAPG hybrid algorithms. In the Stackelberg game structure, port dispatchers play the leader role while tugboat operators play the follower role, sequentially optimizing their respective objective functions. The SOAPG algorithm integrates ant colony optimization’s pheromone update mechanisms, particle swarm optimization’s velocity-position update equations, and genetic algorithm’s selection–crossover–mutation operators in a self-organizing manner.

Integration of mixed integer programming with metaheuristic algorithms provides efficient solutions for large-scale combinatorial optimization problems. Tang et al. [11] developed a methodology for solving mixed integer programming models including service priority weights using genetic algorithms. Liu et al. [13] developed a MILP model introducing the MSTI concept. Their approach includes mathematical transformation techniques that linearize nonlinear safety distance constraints using 0–1 variables and big-M methods.

Integrated algorithms combining clustering with fuzzy inference systems combine spatial pattern recognition with intelligent decision-making. Lee and Kim [18] developed a priority index calculation methodology integrating DBSCAN clustering algorithms with fuzzy inference systems. The DBSCAN algorithm performs density-based clustering using ε-neighborhood and minimum points (MinPts) parameters, identifying 17 regional traffic clusters. For each cluster, they constructed fuzzy inference systems reflecting regional navigation characteristics.

AHP and information system integration methodologies provide systematic approaches for transforming academic decision-making models into practical software tools. Georgoulas et al. [15] developed a decision support system architecture integrating multi-source AHP studies. Their methodology includes meta-AHP algorithms that standardize and integrate pairwise comparison matrices from multiple AHP studies extracted from the literature.

Methodological and algorithmic approaches in the maritime field are evolving into sophisticated computational techniques for hybrid integration, advanced uncertainty handling, multi-objective optimization, and intelligent system implementation. Particularly, the integration of fuzzy theory, game theory, evolutionary algorithms, and machine learning techniques is establishing itself as a systematic computational tool that can effectively solve complex and dynamic decision-making problems in maritime environments.

2.3. Comprehensive Analysis and Research Gaps

Current research primarily focuses on general port optimization rather than vessel arrival priority determination in narrow-channel entries. Çağlayan and Aymelek [17] addressed sustainable ship queuing in wide anchorage areas, while Tang et al. [11] and Liu et al. [13] dealt with berth allocation and intra-port scheduling. However, systematic frameworks considering narrow-channel constraints—overtaking restrictions, safety intervals, and one-way traffic—remain absent.

Expert opinion collection in previous studies targeted general maritime specialists rather than field practitioners. While Praetorius and Lützhöft [16] addressed VTS operator decision-making at a general user requirement level, and Emovon [7] conducted Delphi studies with maintenance experts, no research has systematically incorporated knowledge from VTS operators and pilots who directly manage vessel arrival processes.

Methodologically, existing approaches address static decision-making frameworks. All reviewed studies lack real-time dynamic systems that adjust priorities based on changing vessel positions and traffic conditions. Current studies also focus on single-objective optimization, lacking integrated scoring systems. Çağlayan and Aymelek’s [17] eight-criteria system used static weighted approaches without reflecting temporal changes or dynamic safety risk evaluation based on vessel interactions.

Most studies remain limited to theoretical models with insufficient validation in actual port environments. Research integrating narrow-channel priority determination, field expert knowledge, and real-time dynamic systems represents unexplored areas, supporting this study’s academic contribution and practical value.

3. Methodology

This section presents the analytical methodology for vessel arrival priority determination. Determining vessel priorities in complex maritime traffic environments requires systematic evaluation of various factors. Therefore, the Delphi technique and the AHP are integrated to systematically reflect expert judgment and complex situational factors. The research methodology follows a systematic five-step approach, as illustrated in Figure 1. The process begins with expert knowledge collection through Delphi surveys, followed by weight calculation using Fuzzy AHP methodology. Subsequently, an integrated dynamic score model is developed by combining three core components, which is then implemented and validated through scenario-based testing. To effectively handle uncertainty and ambiguity in the decision-making process, conventional AHP and Fuzzy AHP were applied differentially, based on the hierarchical structure and complexity level of evaluation targets. Fuzzy AHP was specifically applied to basic score evaluation with complex multi-level structures, while conventional AHP was used for components with relatively simple structures such as special situation scores and integrated dynamic score weights. The surveys were administered to 50 participants from Busan Port. Through this methodological approach, an integrated dynamic score system was constructed that dynamically calculates vessel-specific priorities by integrating basic scores, special situation scores, and risk scores, into a single formula. The following subsections explain the integrated framework of the Delphi technique and AHP methodology, then present the specific components of the integrated dynamic score model based on Busan Port’s maritime traffic environment.

3.1. Delphi-AHP Integration Framework

This section first explains the application methods and characteristics of the Delphi technique for expert opinion convergence in Section 3.1.1, followed by detailed coverage of the mathematical models and application processes of AHP and Fuzzy AHP for determining weights of the derived factors in Section 3.1.2.

3.1.1. Delphi Technique

The Delphi technique is a systematized method for reaching a consensus or agreement through iterative and anonymous surveys administered to expert groups in specific fields [19]. This method was applied to derive factors for basic score evaluation in vessel arrival priority determination.

Two rounds of Delphi surveys were conducted for basic score calculation factors. Expert opinions collected through the first survey were analyzed based on response frequency by item, and the second survey questions were constructed focusing on items with the most votes to enhance the level of consensus among experts. This approach enabled systematic derivation of key evaluation factors through expert consensus. Subsequently, the basic evaluation factors derived through the Delphi technique were used to calculate final weights using Fuzzy AHP methodology to effectively reflect uncertainty.

Meanwhile, for special situation score components, since the priority of urgency is already clearly recognized in practice, weights were calculated through conventional AHP surveys only, without separately applying the Delphi technique.

3.1.2. Analytic Hierarchy Process (AHP)

The Analytic Hierarchy Process (AHP) calculates the relative importance of criteria through pairwise comparison [20]. Conventional AHP and Fuzzy AHP were selectively applied, according to evaluation factor characteristics. Basic scores have a three-level hierarchical structure (vessel aspects and operational aspects with sub-factors), requiring Fuzzy AHP to reflect uncertainty in expert judgment. Special situation score components and integrated dynamic score components have single hierarchies, allowing conventional AHP for weight calculation (${\mathsf{\alpha }}_1$, ${\mathsf{\alpha }}_2$, ${\mathsf{\alpha }}_3$).

Fuzzy AHP methodology incorporating fuzzy sets was deemed appropriate to systematically reflect ambiguity in experts’ linguistic judgments [21], effectively managing uncertainty accumulation in multi-level evaluation.

A five-level linguistic scale based on a 9-point Likert scale was designed, adjusted for practical judgment reflecting port operation expert opinions. Linguistic judgments are mapped to triangular fuzzy numbers (e.g., “very important” = (7, 9, 9)), representing minimum, most likely, and maximum values, to express uncertainty ranges. Specific fuzzy scale mapping is presented in

Table 2. Linguistic scales and corresponding triangular fuzzy numbers.

Linguistic Scale	Triangular Fuzzy Number (TFN)	Reciprocal TFN
Absolutely important	(7, 9, 9)	(1/9, 1/9, 1/7)
Very strongly important	(5, 7, 9)	(1/9, 1/7, 1/5)
Strongly important	(3, 5, 7)	(1/7, 1/5, 1/3)
Moderately important	(1, 3, 5)	(1/5, 1/3, 1)
Equally important	(1, 1, 1)	(1, 1, 1)

.

The mapping in Table 2 maintains symmetric structure and mathematical consistency in pairwise comparisons, with fuzzy number ranges expanding as linguistic intensity increases. Fuzzy weights are calculated using triangular fuzzy number arithmetic operations. The addition operation for two triangular fuzzy numbers is defined as

$$\begin{array}{c}{\tilde{m}}_1\oplus {\tilde{m}}_2=(l_1+l_2,m_1+m_2,u_1+u_2)\end{array}$$

(1)

where $l_1$, $l_2$ are the lower bounds, $m_1$, $m_2$ are the modal values, and $u_1$, $u_2$ are the upper bounds of triangular fuzzy numbers ${\tilde{m}}_1$ and ${\tilde{m}}_2$, respectively.

The ⊕ operator used in Equation (1) denotes fuzzy addition, calculated by adding the minimum, center, and maximum values of each triangular fuzzy number, respectively. This computational approach is based on the extension principle of fuzzy set theory proposed by Zadeh [22], and has the advantage of preserving the uncertainty of fuzzy numbers while yielding mathematically consistent results.

The calculated fuzzy weights are subsequently converted to single scalar values through the defuzzification process, and these values can be interpreted in the same manner as weights derived from traditional AHP. Defuzzification was performed using the Center of Area (COA) method. The COA value for a triangular fuzzy number $\tilde{A}=(l,m,u)$ is calculated as follows:

$$\begin{array}{c}COA(\tilde{A})={\displaystyle \frac{l+m+u}{3}}\end{array}$$

(2)

where $l$, $m$, and $u$ represent the lower bound, modal value, and upper bound, respectively. Pairwise comparison matrices used experts’ 9-point scale evaluations with eigenvector-derived weights normalized to sum to 1. Consistency Ratio (CR) was maintained below 0.1, to ensure judgment consistency. This AHP methodology systematically quantifies expert judgments for port arrival priority determination. The derived evaluation factors and weights form the foundation for the Integrated Dynamic Score model, combining basic scores with special situation scores and risk scores for real-time operational priority determination.

3.2. Busan Port Maritime Traffic Environment

The model is designed around Busan Port’s maritime traffic environment, proposing a vessel priority determination system for this region’s operational zones and traffic flows. Figure 2 illustrates the major traffic zones and model application area.

Three zones are important for model application. The ‘Traffic Safety Designated Area’ (purple lines) is established according to Ministry of Oceans and Fisheries [23] designation, representing high-risk waters due to heavy traffic and frequent passage of large vessels, dangerous cargo carriers, and high-speed passenger ships. This zone requires strict vessel traffic control.

The ‘Inbound Fairway Entry Line’ (blue lines) represents the boundary where vessels officially enter the port approach fairway. This study calculates ‘Remaining ETA to Fairway Entrance’ based on this point, utilized as an evaluation factor in the dynamic scoring system. The ‘Inbound Fairway’ (red lines) represents the official vessel entry route. Vessels must enter only within this fairway area, for port safety management and traffic efficiency.

The ‘Pilot Station’ is located at the fairway beginning, where pilots board to support safe berthing. The integrated dynamic score model is applied in the approach zone between the Traffic Safety Designated Area and fairway entry line (shaded yellow in Figure 2). Vessel priorities are determined by dynamic scores in this section, with rankings fixed after vessels pass the fairway entry line. This operational mechanism optimizes traffic flow while enabling comprehensive priority determination considering various vessel characteristics and operational situations.

3.3. Integrated Dynamic Score Model Configuration

This section presents the configuration and operational mechanism of the Integrated Dynamic Score model for vessel arrival priority determination. This model is based on the Delphi–Fuzzy AHP results derived in Section 3.1, and is designed to reflect the characteristics of Busan Port’s maritime traffic environment analysed in Section 3.2.

The integrated dynamic score model consists of three core elements: Basic Score, reflecting physical vessel characteristics and operational conditions, Special Situation Score, reflecting urgency, and Risk Score, considering safety aspects. This model is designed to adaptively respond to real-time changing maritime traffic environments and has the characteristic of dynamically adjusting priorities according to vessel status changes and surrounding traffic conditions.

The greatest distinguishing feature of this model is that it provides a dynamic decision-making system that can reflect situational factors changing over time in real-time, departing from static priority determination systems. This overcomes the limitations of existing systems that rely on traditional First Come, First Served (FCFS) methods or fixed priority rules, enabling more efficient and safe decision-making in complex port operating environments.

Specifically, the integrated dynamic score model is applied in the section from when vessels pass through the Traffic Safety Designated Area entry line until before passing through the fairway entry line, and vessel priorities are determined based on integrated dynamic scores. After passing through the fairway entry line, priorities are fixed and no longer change, reflecting the maritime traffic safety principle of overtaking restrictions within narrow fairways.

The following subsections provide detailed explanations of the three core components of the integrated dynamic score model—basic score, special situation score, and risk score—and present the mechanism for integrating these to determine final priorities.

3.3.1. Basic Score

The basic score serves as the core foundation of the integrated dynamic score, providing objective evaluation of vessel physical characteristics and operational conditions. This score directly reflects the Delphi–Fuzzy AHP results from Section 3.1. and setting N factors that influence vessel arrival priority, with AHP weight $w_n$ given for each factor $n\in \{\mathrm{1,2},...,N\}$. When the standardized (normalized) score that vessel i has for factor $n$ is denoted as $x_{i,n}(t)$, the basic score element is defined as

$$B{S}_i(t)=\sum _{n=1}^N (w_n\cdot x_{i,n}(t))$$

(3)

where $w_n$ is the fixed weight calculated through the Delphi–Fuzzy AHP process, and $x_{i,n}(t)$ is the factor n score of vessel i at time i, normalized between 0 and 1. The time variable t reflects real-time changes in vessel status and position. Weights are normalized to 1 $\left(\sum _{n=1}^N w_n=1\right)$, ensuring the basic score $B{S}_i(t)$ remains within the 0–1 range for consistent scaling with other components.

Basic score calculation follows a systematic three-step process: (1) raw data collection for each evaluation factor, (2) conversion to standardized scores (0–1) through appropriate normalization functions, and (3) weighted sum calculation using AHP weights. This enables integrated evaluation of factors with different units and scales.

Normalization methods vary by factor characteristics—continuous values use linear or non-linear functions, while categorical data receives assigned scores. This customized approach preserves each factor’s unique characteristics while enabling integrated scoring.

The basic score utilizes weights allocated according to vessel aspects and operational aspects with their hierarchical sub-factors, systematically integrating expert knowledge for objective vessel arrival priority determination.

3.3.2. Special Situation Score

The special situation score reflects vessel urgency and special operational conditions as a component of the integrated dynamic score. It is calculated as a weighted sum, using conventional AHP methodology:

$$N_i=w_1\cdot S_{i,1}+w_2\cdot S_{i,2}+w_3\cdot S_{i,3}+w_4\cdot S_{i,4}$$

(4)

where $w_1,w_2,w_3,w_4$ are normalized weights $(w_1+w_2+w_3+w_4=1)$, and $S_{i,1},S_{i,2},S_{i,3},S_{i,4}$ represent scores for vessel i. All components are constrained to the 0–1 range for consistent scaling. The four factors comprising the special situation score are patient occurrence onboard ($S_{i,1}$), cargo urgency ($S_{i,2}$), berthing schedule ($S_{i,3}$), and POB time ($S_{i,4}$).

Patient occurrence assigns 0 points for no patients, 0.5 for general medical support, and 1.0 for critical life-threatening conditions, reflecting maritime safety priorities. Cargo urgency uses binary classification: 0 for general cargo, and 1.0 for urgent cargo with social impact (medical supplies and hazardous materials). Berthing schedule is calculated based on time relationships:

$$S_{i,3}=max(0,min(1,{\displaystyle \frac{T_{transit}-T_{remain}}{T_{transit}}}))$$

(5)

where $T_{\mathrm{remain}}$ is the remaining time from the current time to the scheduled berthing time (in minutes), and $T_{\mathrm{transit}}$ is the expected time required to reach the berth from the current position (in minutes). The $max()$ and $min()$ functions serve to constrain the calculation results to values between 0 and 1. Detailed calculation examples demonstrating the function of these constraints are provided in

Table 3. Calculation examples for special situation score components.

Scenario	${\mathit{T}}_{\mathbf{transit}}$	${\mathit{T}}_{\mathbf{remain}}$	Calculation Process	${\mathit{S}}_{\mathit{i},3}$
On schedule	20	20	$max(0,min(1,{\displaystyle \frac{20-20}{20}}))=max(0,min(\mathrm{1,0}))=max(\mathrm{0,0})=0$	0.000
Moderate urgency	20	15	$max(0,min(1,{\displaystyle \frac{20-15}{20}}))=max(0,min(\mathrm{1,0.25}))=max(\mathrm{0,0.25})=0.25$	0.250
High urgency	20	5	$max(0,min(1,{\displaystyle \frac{20-5}{20}}))=max(0,min(\mathrm{1,0.75}))=max(\mathrm{0,0.75})=0.75$	0.750
Critical urgency	20	0	$max(0,min(1,{\displaystyle \frac{20-0}{20}}))=max(0,min(\mathrm{1,1.0}))=max(\mathrm{0,1.0})=1.0$	1.000

.

This scoring method effectively quantifies the urgency of berthing time compliance. The score approaches 1 when vessels lack sufficient time margin for on-time berthing and approaches 0 when there is sufficient margin. Particularly, when $T_{\mathrm{transit}}\ge T_{\mathrm{remain}}$, that is, when the movement time required for berthing is greater than or equal to the remaining scheduled berthing time, the maximum value of 1 is assigned, giving priority to vessels with high possibility of berthing delay.

Finally, the score $S_{i,4}$, related to POB (Pilot On Board) time reflects the importance of complying with pilot boarding schedules. This is calculated by the following formula:

$$S_{i,4}=max(0,min(1,{\displaystyle \frac{T_{POB}-T_{arrival}}{T_{POB}}}))$$

(6)

where $T_{\mathrm{POB}}$ is the remaining time to scheduled pilot boarding and $T_{\mathrm{arrival}}$ is the expected arrival time at Pilot Station. This score prioritizes vessels that minimize pilot waiting time.

3.3.3. Risk Score

The risk score quantifies safety risks based on time intervals between vessels’ scheduled fairway entry-point passage times. It is defined as

$$R{C}_i(t)={\displaystyle \frac{1}{\mathsf{\Delta }{\tau }_{i,min}(t)+{ϵ}_{\tau }}}\cdot {\displaystyle \frac{1}{R{C}_{max}}}$$

(7)

where $R{C}_i(t)$ is the risk score normalized between 0 and 1, $\mathsf{\Delta }{\tau }_{i,min}(t)$ represents the minimum time difference between vessel i and its immediately preceding and following vessels, and ${\epsilon }_{\tau }$ is set to 0.1 min, to prevent zero denominators.

$R{C}_{max}$ is set to 10, determined from the most dangerous situation when two vessels arrive simultaneously, $\mathsf{\Delta }{\tau }_{i,min}(t)=0$, yielding ${\displaystyle \frac{1}{0+0.1}}=10$. This normalization ensures all risk scores remain within the 0–1 range.

This study adopted minimum scheduled arrival time difference over average time difference. The minimum approach directly measures the most critical temporal proximity between vessels, enabling accurate collision risk capture. In maritime safety management, the ‘weakest link’ principle applies—the single highest collision possibility determines overall navigation safety. This is mathematically defined as

$$\mathsf{\Delta }{\tau }_{i,min}(t)=min(|\mathsf{\Delta }{\tau }_{i,prev}(t)|,|\mathsf{\Delta }{\tau }_{i,next}(t)|)$$

(8)

where $\mathsf{\Delta }{\tau }_{i,\mathrm{prev}}(t)$ represents the scheduled fairway entry-point passage time difference between vessel i and its immediately preceding inbound vessel, and $\mathsf{\Delta }{\tau }_{i,\mathrm{next}}(t)$ represents the scheduled fairway entry-point passage time difference between vessel i and its immediately following inbound vessel.

The risk score functions as a deduction factor, serving as a natural dispersion mechanism for securing safety intervals. This reflects maritime traffic management principles and supports the safety principle that reducing speed is safer than increasing speed in dangerous situations, consistent with COLREG regulations [24].

This approach parallels ‘congestion pricing’ principles [25], imposing additional costs on vessels attempting temporally proximate entry to secure minimum safety intervals and improve system efficiency. The reciprocal relationship creates exponential increases as intervals decrease, reflecting that safety importance increases rapidly with proximity.

The system enables dynamic response to real-time traffic changes, automatically recalculating when scheduled entry times change. The method designed for Busan Port has versatility for other ports by adjusting $R{C}_{max}$ values to match respective port characteristics.

3.3.4. Integrated Dynamic Score Model and Priority Determination

The integrated dynamic score model combines the three elements to determine vessel arrival priorities. The integrated dynamic score $I{D}_i(t)$ of vessel i at time t is defined as

$$I{D}_i(t)={\mathsf{\alpha }}_1\cdot B{S}_i(t)+{\mathsf{\alpha }}_2\cdot N_i-{\mathsf{\alpha }}_3\cdot R{C}_i(t)$$

(9)

where ${\mathsf{\alpha }}_1,{\mathsf{\alpha }}_2,{\mathsf{\alpha }}_3$ are AHP-derived weights normalized to 1 $({\mathsf{\alpha }}_1+{\mathsf{\alpha }}_2+{\mathsf{\alpha }}_3=1)$. Only the risk score has a negative sign, implementing a deduction mechanism where higher risk results in lower priorities.

Vessel priorities are determined directly from calculated scores. At time t, all vessels in approach zone $\Omega (t)$ are ranked according to their integrated dynamic scores. The rank of vessel i is

$$\begin{array}{c}Ran{k}_i(t)=1+{\displaystyle \sum _{j\in \Omega (t),j\ne i}} 1(I{D}_j(t)>I{D}_i(t))\end{array}$$

(10)

where $1(\cdot )$ is an indicator function. This ranking method enables clear and objective rank assignment. Priorities are updated in three situations: (1) Regular Updates: scores recalculated at regular intervals $I{D}_j(t)$ for continuous updates, according to vessel movements. (2) New Vessel Entry: when vessel k enters the Traffic Safety Designated Area, all vessel scores are recalculated. (3) Special Situation Occurrence: emergency situations trigger immediate score updates for rapid response. As an important operational principle, when vessel k passes the fairway entry line in Figure 2, it is excluded from $\Omega (t)$ and its ranking is fixed:

$$\begin{array}{c}k\notin \Omega (t)⟹Ran{k}_k(t)\end{array}$$

(11)

This reflects COLREG [24] restrictions on overtaking within narrow fairways. After fairway entry, vessels follow designated sequences without priority re-evaluation.

The model characteristics include the following: (1) Balance Among Elements: combining three independent elements enables objective priority determination across various situations. (2) Spatiotemporal Continuity: continuous score variation enhances operational stability and transparency. (3) Risk-Based Safety Mechanism: risk scores provide natural traffic dispersion effects similar to congestion pricing principles [25]. (4) Safety-First Decision-Making: deduction factors naturally restrict vessel changes in congested situations, reflecting maritime safety principles.

This integrated system provides systematic decision-making while adapting to real-time maritime traffic environments, enabling VTS operators to determine sequences based on objective criteria while responding flexibly to emergency situations.

3.4. Performance Evaluation Metrics

To objectively evaluate the proposed model, three metrics quantify agreement between model-generated vessel priority rankings and expert judgments. Due to ranking prediction characteristics, simple classification accuracy cannot adequately reflect relative relationships among rankings. Therefore, Spearman’s rank correlation coefficient ($\rho$), Kendall’s tau ($\tau$), and normalized discounted cumulative gain (nDCG) were selected to comprehensively evaluate ranking correlation and top-rank prediction performance.

Spearman’s rank correlation coefficient ($\rho$) measures monotonic relationships between rankings [26], taking values between −1 and 1:

$$\rho =1-{\displaystyle \frac{6\sum _{i=1}^m d_i^2}{m(m^2-1)}}$$

(12)

where m is the total number of vessels being evaluated, and $d_i$ is the difference between the model rank and expert rank for vessel i ${(d}_i=R_{model,i}-R_{expert,i})$. $R_{model,i}$ represents the rank predicted by the model for vessel i, and $R_{expert,i}$ represents the rank assigned by experts for vessel i. ρ = 1 indicates perfect positive correlation (complete rank agreement), ρ = −1 indicates perfect negative correlation (completely opposite rankings), and ρ = 0 indicates no correlation. Kendall’s Tau ($\tau$) measures concordance between ranking pairs [27], and is less sensitive to outliers:

$$\tau ={\displaystyle \frac{C-D}{\frac{m(m-1)}{2}}}$$

(13)

where $C$ is concordant pairs, $D$ is discordant pairs, and the denominator represents total possible pairs. Normalized Discounted Cumulative Gain (nDCG) weights top-rank accuracy more heavily [28], which is important for port operations:

$$nDC{G}_k={\displaystyle \frac{DC{G}_k}{IDC{G}_k}}$$

(14)

where $DC{G}_k$ is the Discounted Cumulative Gain for the top k rankings, and $IDC{G}_k$ is the Ideal Discounted Cumulative Gain. $DC{G}_k$ is defined as

$$DC{G}_k=\sum _{i=1}^k {\displaystyle \frac{re{l}_i}{{\mathrm{l}\mathrm{o}\mathrm{g}}_2(i+1)}}$$

(15)

$re{l}_i$ represents relevance scores based on expert rankings, and $IDC{G}_k$ is the ideal order value. These metrics evaluate performance from different aspects: Spearman’s $\rho$ and Kendall’s $\tau$ show overall ranking correlations with different sensitivities, while nDCG emphasizes top-rank prediction accuracy, crucial for actual operations. This multi-dimensional framework enables comprehensive verification of the integrated dynamic score model performance.

4. Experimental Results and Analysis

This section analyzes basic score evaluation-factor derivation results and the Fuzzy AHP hierarchical structure systematizing these factors. These results apply the Delphi technique and Fuzzy AHP methodology from Section 3 to actual port operating environments. AHP analysis for special situation scores and integrated dynamic score components are addressed in Section 4.1.

Applying the Delphi technique systematically derived the key factors influencing vessel arrival priority determination. Expert opinions converged through the process described in Section 3, confirming detailed factors under vessel aspects and operational aspects. Results were hierarchically structured, as shown in Figure 3.

The hierarchical structure divides into two main criteria (Level 1)—ship aspects and operational aspects—for ship arrival priority determination. Ship aspects subdivide into ship type and gross tonnage, while operational aspects subdivide into remaining ETA to fairway entrance and relative berth position distance (Level 2). Each sub-factor is evaluated through detailed classification criteria (Level 3).

Ship type classification used structured Delphi surveys targeting VTS operators. Through three survey rounds on 10 major ship types, they were classified into four groups with established priority systems. The first priority group (container ships, passenger ships, and naval vessels) received highest priority, while tugboats towing barges were classified as fourth priority, considering vessel economic importance, time constraints, safety requirements, and port operational characteristics.

Gross tonnage classification established four categories considering vessel operational characteristics and safety requirements, referencing Shin and Yang [29]. Small vessels (under 100 tons) include coastal vessels, small–medium vessels (100–500 tons) capable of limited offshore navigation, medium vessels (500–3000 tons) with ocean-going capabilities, and large vessels (over 3000 tons) requiring advanced navigation techniques. This classification is more detailed than international standards, to reflect port operation specificity.

Remaining ETA to fairway entrance was categorized in 5 min units based on the past year AIS data analysis. Time required from the Traffic Safety Designated Area passage until fairway entry was measured, establishing five categories from 0–5 min to over 20 min, considering passage time distribution. Cases exceeding 20 min were designated separately for clear delay criteria, reflecting realistic traffic flows.

Relative berth position distance evaluates vessels according to destination berth position relative to port entrance. This study adopted a rank-based evaluation, considering that fixed sections could result in vessel clustering or ambiguous distances. When the total number of inbound vessels is $M$ and vessel destination berth rank is r (innermost = 1, outermost = $M$), the score is

$$\begin{array}{c}{w}_r={\displaystyle \frac{M-r+1}{\sum _{k=1}^M k}}\end{array}$$

(16)

This rank-based approach provides (1) dynamic adaptability when vessel numbers change, (2) tie prevention through unique berth position scores, (3) integrated evaluation with the 0–1 scale, and (4) balanced weighting for factors without sub-categories.

For example, with five vessels ($M=5$), the innermost berth vessel ($r=1$) receives weight 0.333, while the outermost ($r=5$) receives 0.067. This method reduces tie possibilities in final integrated scores, and efficiently manages port traffic flow by prioritizing inner berth vessels, which impact overall port traffic flow more significantly.

This hierarchical structure serves as the foundation for Fuzzy AHP weight derivation analyzed in Section 4.1, securing transparency and consistency in decision-making by systematically organizing vessel arrival priority determination factors.

4.1. Weight Analysis Results of Integrated Dynamic Score Components

This section presents weight analysis results of integrated dynamic score model components derived through the Delphi technique and AHP methodology. These empirical results from actual port operation experts serve as evidence supporting the proposed model’s practicality and validity. Analysis results are examined in three areas: Section 4.1.1 presents weights of three major integrated dynamic score elements, Section 4.1.2 addresses Fuzzy AHP weight analysis of basic score components, and Section 4.1.3 examines AHP weights of special situation score factors.

4.1.1. Analysis of Integrated Dynamic Score Component Weights

The weight analysis results for the three major components of the integrated dynamic score model (basic score, special situation score, and risk score) are shown in

Table 4. Weights of integrated dynamic score components.

Component	Weight	Rank
Basic Score (α1)	0.5482	1
Special Situation Score (α2)	0.1547	3
Risk Score (α3)	0.2971	2

. These weights are important parameters directly applied to the α₁, α₂, α₃ values in the integrated dynamic score formula Equation (9), explained in Section 3.3.4.

Based on AHP analysis, basic score (α₁) has the highest weight, at 0.5482, indicating that physical vessel characteristics and operational conditions are most important factors in arrival priority determination. Risk score (α₃) ranks second, at 0.2971, reflecting maritime traffic safety importance in port operations as a deduction factor quantifying safety risks according to vessel time intervals. Special situation score (α₂) has the lowest weight, at 0.1547, indicating that while special situations have low occurrence frequency, appropriate priority adjustment is necessary when they occur.

These weights determine the relative contributions of basic score, special situation score, and risk score in Equation (9), enabling comprehensive priority evaluation balancing vessel characteristics, urgency, and safety. This composition reflects realistic port operational conditions and expert opinions, providing a decision-making system prioritizing basic vessel characteristics while considering safety aspects and special situations in balance.

4.1.2. Analysis of Basic Score Component Weights

The basic score is a core component of the integrated dynamic score, reflecting physical vessel characteristics and operational conditions. Based on the hierarchical structure derived in Section 4.1, weight analysis of basic score components was performed using Fuzzy AHP methodology, with results shown in

Table 5. Weights of basic score components.

Criteria (Level 1)	Weight	Sub-Criteria (Level 2)	Weight	Indicators (Level 3)	Local Weight	Global Weight	Global Rank
Ship Aspects	0.3545	Ship Type	0.5587	Container Ships, Passenger Ships, Naval Vessels	0.4242	0.0840	3
				Bulk Carriers, General Cargo, Reefer, Tanker	0.2993	0.0593	6
				Tug with Barge (Composite Unit)	0.1444	0.0286	10
				Tugboats, Fishing Vessels	0.1322	0.0262	12
		Gross Tonnage	0.4413	Large Vessels (>3000 GT)	0.4457	0.0697	4
				Medium Vessels (500–3000 GT)	0.2683	0.0420	8
				Small–Medium Vessels (100–500 GT)	0.1708	0.0267	11
				Small Vessels (<100 GT)	0.1152	0.0180	13
Operational Aspects	0.6456	Remaining ETA to Fairway Entrance	0.6062	0–5 min	0.3660	0.1433	1
				5–10 min	0.2419	0.0947	2
				10–15 min	0.1706	0.0668	5
				15–20 min	0.1283	0.0502	7
				>20 min	0.0932	0.0365	9
		Relative Berth Position Distance	0.3938	Berth with Rank r (dynamic)	${\displaystyle \frac{M-r+1}{\sum _{k=1}^M k}}$	$0.2542 \times w_r$	-

.

Examining the Fuzzy AHP analysis results, in the upper hierarchy (Level 1) of basic score components, Operational Aspects showed approximately 1.8 times higher importance, with a weight of 0.6456, compared to Ship Aspects (0.3545).

Analyzing the weights of the middle hierarchy (Level 2), within Ship Aspects, Ship Type (0.5587) showed higher importance than Gross Tonnage (0.4413). In Operational Aspects, Remaining ETA to Fairway Entrance (0.6062) was prioritized over Relative Berth Position Distance (0.3938).

From the weight analysis results of the lowest hierarchy (Level 3) indicators, among categorical indicators, vessels within 5 min distance from the fairway entry point showed the highest comprehensive weight (0.1433), followed by vessels at 5–10 min distance (0.0947). In ship type indicators, the group including container ships, passenger ships, and naval vessels showed the highest comprehensive weight, at 0.0840, while in gross tonnage indicators, large vessels over 3000 tons showed the highest weight, at 0.0697.

Relative berth position distance has special characteristics, unlike other indicators. According to the rank-based evaluation method explained in Section 4.1, the comprehensive weight of this indicator was calculated as 0.2542. According to Equation (12), each vessel receives differentiated scores according to destination berth rank (r), and the final score is determined by multiplying this score by the comprehensive weight 0.2542.

This rank-based weight structure is marked as ‘–‘ in Table 4, unlike other categorical indicators, because it is a dynamically calculated value according to rank and cannot be assigned a fixed ranking. AHP analysis results show that within Operational Aspects (0.6456), the weight distribution of Remaining ETA to Fairway Entrance (0.6062) and Relative Berth Position Distance (0.3938) indicates that temporal factors are evaluated as approximately 1.5 times more important than spatial factors. This weight structure suggests that while vessel temporal position is primarily considered, the spatial position of destination berths also exercises considerable influence on arrival priority determination.

For example, assume three vessels A, B, C are simultaneously waiting for entry, all having the same ship type and tonnage with equal remaining time to fairway entry point. If these three vessels’ destination berth ranks are 1 (innermost), 2, and 3 (outermost), respectively, the rank-based scores calculated according to Equation (12) would be 0.5, 0.333, and 0.167, respectively. Multiplying these scores by the global weight 0.2542 results in final scores of 0.127, 0.085, and 0.042, respectively. These differentiated scores provide clear priorities (A > B > C), even when all other conditions are identical, contributing to eliminating decision-making ambiguity and enhancing port traffic flow efficiency.

Thus, rank-based relative berth position evaluation is an approach that can effectively achieve both goals of port traffic flow optimization and clear priority determination, playing an important role in the integrated dynamic score system.

This weight system is directly utilized as weights (w_n) in Equation (3), forming the foundation for basic score calculation within the integrated dynamic score model. By multiplying and summing the global weights presented in Table 4 with scores of each evaluation factor, objective priority determination that comprehensively considers various vessel characteristics and operational situations becomes possible.

4.1.3. Weights of Special Situation Score Components

The special situation score is an important component of the integrated dynamic score, which reflects vessel urgency and special circumstances. Weight analysis for the four factors comprising the special situation score defined in Section 3.3.2 (patient occurrence onboard, cargo urgency, berthing schedule, and POB time) was performed through AHP methodology, with results shown in

Table 6. Weights of special situation score components.

Component	Weight	Rank
Patient Occurrence	0.4326	1
Berthing Schedule	0.2158	2
Cargo Urgency	0.1891	3
POB Time	0.1625	4

.

Examining the AHP analysis results, patient occurrence onboard showed the highest weight, at 0.4326. This is at a level almost similar to the sum of weights of the other three factors, demonstrating that patient occurrence has overwhelming importance, even among special situations.

Berthing schedule was analyzed as the second most important factor, with a weight of 0.2158. This reflects the economic and temporal aspects of vessel operations, representing consideration to minimize port operational disruptions and economic losses that may occur when vessels fail to arrive according to scheduled berthing times.

Cargo urgency appeared as the third most important factor, with a weight of 0.1891. This quantifies the impact that cargo characteristics have on priority determination, showing that for medical supplies or urgent cargo with significant social impact, a certain level of priority is granted, considering socioeconomic impacts from delays.

POB time was analyzed as the fourth most important factor, with a weight of 0.1625. While complying with pilot boarding schedules is important from the perspective of port operational efficiency, it has relatively lower priority compared to other emergency situations.

4.2. Integrated Dynamic Score Model Performance Evaluation

The evaluation scenarios consisted of basic situation (S1), congested situation (S2), general patient occurrence situation (S3-1), emergency patient occurrence situation (S3-2), urgent cargo situation (S4), berthing delay situation (S5), POB delay situation (S6), and risk situation (S7). These scenarios encompassed diverse vessel configurations ranging from four to seven vessels per scenario, with gross tonnages spanning from 80 to 98,000 GT across nine different ship types including container ships, bulk carriers, passenger ships, tankers, general cargo vessels, tug–barge combinations, tugboats, naval vessels, and fishing vessels. Operational parameters included remaining ETA to fairway entrance (4–15 min), minimum arrival intervals between vessels (1–9 min), and relative berth positions (ranks 1–7). Special situation conditions covered medical emergencies (non-critical and critical patients), urgent cargo transport, berthing delays (10 min), and pilot boarding delays (15 min). Complete scenario specifications are provided in Appendix A, to enable replication of the validation methodology, while individual expert ranking responses from all 10 VTS operators are documented in Appendix B, to ensure transparency in the statistical analysis and support future comparative studies.

Model performance was evaluated through Spearman’s rank correlation coefficient (ρ), Kendall’s τ, and normalized discounted cumulative gain (nDCG).

Table 7. Performance evaluation results for each scenario.

Scenario	Spearman’s ρ	Kendall’s τ	nDCG
S1	1.000	1.000	1.000
S2	0.964	0.905	0.999
S3-1	1.000	1.000	1.000
S3-2	1.000	1.000	1.000
S4	0.800	0.667	0.993
S5	0.400	0.333	0.975
S6	0.800	0.667	0.977
S7	0.700	0.600	0.981
Average	0.833	0.771	0.991

shows the performance evaluation results for the eight scenarios.

The performance evaluation results showed that the proposed model demonstrated differentiated performance according to scenario types. In basic situations (S1) and patient occurrence situations (S3-1, S3-2), both Spearman’s ρ and Kendall’s τ achieved 1.000, showing complete agreement with expert judgments.

In congested situations (S2), the model showed high rank correlation with Spearman’s ρ 0.964 and Kendall’s τ 0.905, maintaining excellent performance with nDCG 0.999. In urgent cargo situations (S4) and POB delay situations (S6), identical Spearman’s ρ 0.800 and Kendall’s τ 0.667 were recorded.

In risk situations (S7), Spearman’s ρ 0.700 and Kendall’s τ 0.600 were achieved, with nDCG 0.981 showing high accuracy in top-rank prediction. In berthing delay situations (S5), Spearman’s ρ 0.400 and Kendall’s τ 0.333 were recorded, reflecting the low overall priority that experts assign to schedule delays. While berthing schedule ranks second among the four special situation factors (0.2158), its actual influence in the integrated score is minimal, due to the low weight of special situations overall (0.1547), resulting in an effective weight of only approximately 0.033. This suggests that VTS operators rarely prioritize vessels simply because they are behind schedule, leading to inconsistent individual judgments when such situations arise. Despite this ranking disagreement, nDCG maintained 0.975, indicating experts still agreed on identifying the highest-priority vessel.

The average performance across all eight scenarios was calculated as Spearman’s ρ 0.833, Kendall’s τ 0.771, and nDCG 0.991. The consistently high nDCG values, above 0.975 across all scenarios, demonstrate that the model reliably identifies top-priority vessels, even in situations where expert judgments vary with regard to secondary considerations such as berthing delays.

5. Discussion

This study’s results demonstrate the effectiveness of integrating expert knowledge into quantitative decision-making frameworks for vessel arrival priority determination. The findings are discussed in relation to the existing literature and model performance characteristics.

5.1. Comparison with Existing Research

The proposed model’s average performance metrics (Spearman’s ρ = 0.833, Kendall’s τ = 0.771, nDCG = 0.991) demonstrate high agreement with expert judgment across diverse scenarios. Unlike Shao et al.’s [8] virtual arrival optimization, which focused solely on waiting time reduction (31.41% improvement), our integrated approach addresses both safety and efficiency through risk-based priority adjustment.

The weight distribution results reveal expert priorities that align with established maritime safety principles. The dominance of operational aspects (64.56%) over vessel characteristics (35.45%) supports Liu et al.’s [13] finding that dynamic operational factors outweigh static vessel properties in scheduling optimization. However, our risk score weight (29.71%) being twice that of special situations (15.47%) contrasts with Tang et al.’s [11] emphasis on service priority for large vessels, suggesting that Korean VTS operators prioritize safety intervals over vessel-specific preferences.

The perfect performance in patient emergency scenarios (ρ = 1.000) validates the hierarchical priority system where human-life safety overrides operational efficiency, consistent with international maritime safety regulations. This finding supports Praetorius and Lützhöft’s [16] observation that VTS operators rely heavily on safety-first decision-making principles. The proposed framework also has broader implications for emerging maritime operational concepts. The dynamic scoring approach supports Just-In-Time Arrival (JITA) implementation by providing objective criteria for vessel sequencing, which consider both operational efficiency and safety requirements.

Unlike traditional FCFS systems that may conflict with JITA optimization, our model’s integration of berthing schedules and temporal factors enables more sophisticated coordination between vessel arrivals and port readiness. Additionally, the systematic priority determination framework becomes increasingly valuable as the maritime industry moves toward more autonomous operations, where explicit algorithmic decision-making criteria are essential for safe and efficient port traffic management.

5.2. Model Performance Analysis

The model showed varying performance across different scenario types, with perfect agreement in basic situations (S1) and medical emergencies (S3-1, S3-2), but lower correlation in berthing delay situations (S5: ρ = 0.400). This variation suggests that expert consensus is stronger for safety-critical situations than for operational efficiency decisions, indicating that the model effectively captures the most critical decision patterns while revealing areas where expert judgment varies.

The fuzzy AHP methodology effectively addressed uncertainty in expert linguistic judgments, consistent with Chen et al.’s [30] successful application of fuzzy approaches in maritime risk assessment.

The consistently high nDCG values (>0.975) across all scenarios indicate reliable top-rank prediction performance, which is crucial for practical VTS operations where identifying the highest priority vessel is most important. This performance characteristic distinguishes our approach from existing scheduling algorithms that focus on overall optimization rather than critical priority identification.

5.3. Policy and Managerial Implications

The proposed model presents significant implications for VTS system integration and maritime governance. From a technical integration perspective, the model’s standardized scoring framework can be incorporated into existing VTS platforms as a decision support module, providing operators with objective priority recommendations while maintaining human oversight for final decisions. Since all required input factors are readily available through current VTS sensor networks, AIS data streams, and VHF communications, the system can automatically recalculate vessel priorities at regular intervals (e.g., every 2–5 min) to reflect real-time changes in maritime traffic conditions.

For port authorities, adopting this systematic approach enables more transparent and defensible priority decisions, potentially reducing disputes between shipping companies regarding fairway access sequences. The explicit weight structure (basic scores: 54.82%, risk scores: 29.71%, special situations: 15.47%) provides clear policy guidelines that can be communicated to maritime stakeholders, enhancing operational predictability and planning capabilities. From a regulatory standpoint, maritime authorities may need to establish standardized protocols for dynamic priority determination systems, including certification requirements for automated decision support tools in VTS operations.

The integration of expert-derived weights suggests the need for periodic recalibration based on evolving operational practices and safety standards. Additionally, the model’s emphasis on safety intervals through risk scoring aligns with international maritime safety regulations while providing quantitative justification for traffic separation decisions that may impact vessel scheduling and port efficiency.

6. Conclusions

This study developed an integrated dynamic score-based vessel arrival priority determination model to overcome the limitations of existing First Come, First Served (FCFS) approaches and subjective decision-making in VTS operations. The model systematically integrates expert knowledge through a three-component framework: basic scores (reflecting vessel characteristics and operational conditions), special situation scores (addressing emergency and urgent conditions), and risk scores (quantifying safety intervals between vessels). The methodology combined the Delphi technique for expert consensus with Fuzzy AHP for weight derivation, incorporating practical knowledge from 50 maritime experts, including experienced VTS operators and certified pilots.

The model operates dynamically in the approach zone between the Traffic Safety Designated Area and fairway entrance, where vessel priorities are continuously updated based on real-time conditions. Performance validation through eight operational scenarios with 10 experienced VTS operators demonstrated strong agreement with expert judgment, achieving average correlation coefficients of 0.833 (Spearman’s ρ) and 0.771 (Kendall’s τ), with consistently high top-rank prediction accuracy (nDCG = 0.991).

The key contributions include (1) transformation of implicit VTS decision-making processes into an explicit, quantitative framework; (2) introduction of a rank-based berth position evaluation method that prevents tie occurrences; and (3) development of a risk-based safety mechanism that naturally promotes traffic dispersion through priority adjustments. While validated specifically for Busan Port’s environment, the methodology demonstrates broad applicability, as port VTS environments share common characteristics including berths, narrow waterways, traffic routes, and diverse vessel types requiring similar priority determination considerations.

However, several limitations of the proposed model should be acknowledged. First, validation was conducted exclusively within the Busan VTS operational context using simulated scenarios with a maximum of seven vessels, which may not reflect performance in high-traffic ports where eight or more vessels simultaneously require priority determination. The computational complexity increases quadratically with the number of vessels, due to risk score calculations requiring pairwise comparisons, potentially affecting real-time performance in dense traffic scenarios. Second, the current weight structure (α₁, α₂, α₃) remains static, regardless of environmental conditions, which may be inappropriate during extreme weather events such as typhoons, where safety considerations should override efficiency factors through adjusted risk score weighting. Third, the model’s performance may differ from simulated results, due to real-world data uncertainties including ETA calculation errors, AIS data quality variations, and communication delays between VTS operators and vessels.

While the AHP methodology proved effective, the expert survey process presented practical challenges including coordinating field visits with operational VTS operators and maintaining consistency across multiple survey rounds. To address these methodological limitations and enhance practical applicability, future research directions should address several specific areas: (1) integration of machine learning algorithms to reduce dependency on repeated expert surveys by learning from historical priority decisions, (2) implementation of predictive analytics for traffic congestion forecasting, and (3) exploration of hybrid human–AI decision support systems that combine automated recommendations with expert validation.