Level of Service Evaluation Method for Waterway Intersections

Abstract

Waterway intersections pose significant risks for vessel navigation due to the complexities of operational conditions in these areas. The lack of clear collision avoidance rules, combined with ineffective communication, exacerbates these dangers. To address this issue, transportation authorities will typically employ flow organization strategies to optimize operations at these intersections. However, effective methods for traffic management, both before and after implementation, are still lacking. This paper proposes a methodology to determine the level of service (LOS) needed for waterway intersections by using the degree of conflict during vessel navigation as a performance measure, while also considering the unique characteristics of vessel encounters in these areas. The methodology was applied to analyze the Yuxingnao waterway, and the results demonstrate its effectiveness in assessing operational conditions and providing a clear classification of service levels over specific time periods. Consequently, this methodology not only enables transportation authorities to evaluate the effectiveness of traffic management strategies, such as route planning and traffic organization, but also helps predict the impact of potential improvement countermeasures.

1. Introduction

With the ongoing globalization of the economy, the United Nations Conference on Trade and Development has projected that maritime trade will continue to grow at an annual rate of 2.1 percent from 2023 to 2027. This projection suggests an increase in the number of vessels navigating the seas. As the world’s largest maritime trading nation, China plays a significant role in both dry bulk and container trade. Each year, over one million vessels navigate China’s coasts and inland rivers [1]. With the growth of the maritime industry, incidents concerning vessel jams and collisions have become increasingly common. According to incomplete statistics from the European Maritime Bureau, an estimated 3200 vessel collisions, groundings, capsizes, and other accidents occurred each year between 2016 and 2020 [2]. Many accidents can be attributed to human error, while the recent increase in traffic density and the average cruising speed of ships hinder effective collision avoidance decision-making [3]. While ensuring the utilization of marine resources is essential, maintaining the safety and efficiency of navigation has become a critical issue. Statistics on vessel navigation risks indicate that waterway intersections are high-risk areas for collisions. This is primarily because these intersections connect multiple waterways and are characterized by heavy traffic and complex vessel-encounter situations.

One of the fundamental tasks in shipping is to ensure the safe navigation of vessels [4]. The high traffic density, complex vessel encounters, and ambiguity of navigation rules in waterway intersections [5,6] have led marine traffic management authorities to implement strict routing systems and optimize traffic flow in these challenging areas. However, evaluating the effectiveness of these optimizations poses a challenge. Current efforts heavily rely on historical data and lack a systematic method for assessing each waterway as a whole. Therefore, it is crucial to develop methods that align with the unique navigation characteristics of waterway intersections, as this holds significant practical value and application potential.

This paper is organized as follows: Section 2 provides a review of the existing literature and identifies research gaps. Section 3 proposes a methodology to determine the level of service for waterway intersections. Following that, Section 4 presents a concrete example to demonstrate the application of the proposed methodology. Finally, Section 5 concludes the research and outlines potential future directions.

2. Literature Review

Changes in maritime navigation, especially in complex waterways, have brought new challenges to sailors [7]. The level of service (LOS) measure was first proposed in the Highway Capacity Manual (HCM) [8] and has continued to evolve for nearly 60 years [9]. Therefore, the LOS methodology for highways is relatively mature compared with that for waterways. As such, a methodology for the waterway LOS was developed by drawing on successful experiences in the field of highway transportation [10]. In addition, while the determination of the LOS for waterways and ports has been extensively studied, specific methods for evaluating the LOS of waterway intersections have not yet been developed.

Previous research on maritime LOS systems primarily focuses on waterways and ports [9,11], often overlooking the crucial nodes that connect various waterways—namely, waterway intersections [12,13,14,15], in which the service measures differ from those of waterways and ports. LOS concerns the service quality of a transportation facility, such as the freedom to maneuver, comfort, and safety, as perceived by users of the facility. Therefore, service measures are typically selected after considering the research results regarding human factors and, in our case, the perception of sailors [16]. For example, Kadali et al. [17] collected the perceived LOS for pedestrians across various land-use types and integrated this data with factors such as traffic volume, ease of road crossing, and safety to evaluate the mixed traffic service level. Papadimitriou et al. [18] evaluated the level of highway service by collecting data on the drivers’ age, gender, driving experience, familiarity with the road, and vehicle capacity, and concluded that an evaluation method using a single service measure has limitations, due to analyzing perceptual data. Huo et al. [19] evaluated the service level of bus facilities by analyzing factors such as arrival time, waiting time, bus speed, and departure time. Urbanski et al. [20] analyzed the dangerous threats that have emerged at sea in this century, which have a profound impact on the safety and security of maritime navigation. Different transportation facilities may have different service measures. In addition, surveys have found that different participants have different opinions on the service levels of the same transportation facility. Therefore, it is important to find service measures that match the personal experience of users and facilitate the division of service quality into different levels.

Since the discussion of the LOS and service measures of waterway transportation facilities must inevitably draw upon those of highway facilities, it is necessary to present the main differences in the characteristics of waterway traffic and road traffic (see

Table 1. Main differences in the characteristics of waterway traffic and road traffic.

Items		Road Traffic	Waterway Traffic
Physical Characteristics	1. Length 2. Mass 3. Manipulate	1. About 5 to 10 m 2. About 1 to 10 tons 3. Usually 1 driver	1. About 10 to 400 m 2. About 50 to 500,000 tons 3. Involving several sailors
Environment	Infrastructure	Roadway	Waterway
Traffic flow character	1. Volume 2. Velocity 3. Density 4. Acceleration	1. About 0 to 2500 veh/h 2. About 0 to 200 km/h 3. About 0 to 250 veh/km 4. About 0 to 9 m/s2	1. About 0 to 20 vessel/h 2. About 0 to 20 knots 3. About 0 to 10 vessel/n mile 4. About 0 to 0.9 m/s2
Dynamics of traffic flow	1. Traffic delay 2. Conflict	1. Tens of minutes 2. Collision, diversion, confluence	1. Usually tens of hours 2. Head-on, overtaking, crossing

).

Analyzing these various characteristics can help us identify key indicators for evaluating marine traffic service levels. Since ships are significantly heavier than vehicles and operate in a fluid medium, they primarily avoid conflicts by steering around other waterway users instead of braking and stopping like vehicles on roads. Consequently, collecting and statistically analyzing the data on ship delays presents substantial challenges. Furthermore, measuring ship density has limitations; the measure only indicates the number of vessels in a specific area, neglecting crucial information about individual ship locations and the situations encountered [21]. This complicates the accurate assessment of whether ships are impacted while navigating through intersecting waters. For example, many ships may operate simultaneously in a given area without significant interference when moving in an orderly manner. In such instances, the service level of the waterway would be relatively favorable. However, relying solely on ship density metrics could misleadingly indicate poor service levels, which contradicts the actual situation.

Therefore, guided by the principle of reflecting real navigational experiences similar to those encountered by sailors, this paper considers both operation efficiency and the potential impacts on vessels during navigation. It ultimately designates the degree of interference experienced by ships as the primary evaluation index for assessing service levels in these contexts.

Given the differences in transportation facilities, the level of service (LOS) methodology used for waterways and ports cannot be directly applied to waterway intersections. Similarly, because traffic management rules differ between highway intersections and waterway intersections, the measures used to evaluate highway intersections cannot be directly applied to waterways. Therefore, selecting service measures that align with the regulations governing vessel navigation at waterway intersections is essential for effective research into the level of service in this context.

In summary, while research on waterway intersections has continued, there is still a notable lack of studies focused on evaluating service levels. Most of the existing research in this area primarily addresses aspects of vessel collision avoidance [22,23,24,25] and traffic conflict [26,27,28]. However, this research primarily focuses on analyzing the navigational status between two vessels at a microscopic level without worrying about the broader navigational dynamics of vessels across the entire water area. If a systematic service level evaluation system for waterway intersections could be developed, it would not only connect with the service level evaluations of waterways and ports, completing the overall maritime navigation service level assessment, but would also allow for the analysis of navigation status at a macroscopic level. This would provide valuable guidance for managing maritime traffic [29]. This article also addresses the challenge of evaluating optimization strategies for traffic flow organization.

3. The Methodology

The purpose of this study was to establish a reasonable means to determine LOS for waterway intersections. The Highway Capacity Manual (HCM) defines the level of service of a roadway facility as “a quality measure describing operational conditions within a traffic stream, generally in terms of such service measures as speed and travel time, freedom to maneuver, traffic interruptions, and comfort and convenience”. A quality measure ensures that LOS is expressed categorically as a set of levels, such as A, B, and C. Each level corresponds to a specific range of operational conditions, which is represented by an appropriate variable known as the service measure.

Therefore, the methodology to determine the LOS for waterway intersections has to address the following three questions. First, which service measure should be used to represent the operational conditions of waterway intersections? Second, what levels should be designated for the LOS? Third, how can the LOS be determined, based on the selected service measure?

3.1. Determination of the Service Measure

Given that the choice of service measure significantly impacts the rationality, scientific validity, and accuracy of the final results, the research group sought to identify candidate service measures through a review of similar cases, online research, and consultations with experienced vessel pilots. As a result, a set of candidate service measures was determined. These measures were then screened, based on three key aspects: vessel navigation safety, navigation efficiency, and navigation comfort. Finally, a service measure was selected from the candidates, according to the following criteria:

(1) It should be perceivable. The purpose of the LOS is to provide the means to effectively communicate the operational conditions of a transportation facility to users [30,31]. When the users’ personal experiences align with the determined LOS, it fosters a sense of trust in the system. Taking the freeway as an example, its service levels can be assessed using many candidate service measures, e.g., travel time, speed, flow, and density. Obviously, density provides drivers with a more intuitive understanding of the traffic conditions, and, thus, density is the chosen service measure for freeway LOS [32].

(2) It should be measurable. Although LOS is a subjective description of the operational conditions, its designation must be based on objective criteria. When serving such a purpose, a good service measure should be measurable and quantifiable. Candidate criteria related to personal feelings are unsuitable for this purpose, as they are subjective and can vary from person to person.

(3) It should be unambiguous. This means that a specific value of the service measure must correspond to a unique operational condition. For example, a recorded flow of 200 vehicles per hour on a freeway is ambiguous, as it could represent either light traffic conditions with that level of traffic passing through easily or heavy traffic conditions where only that number can pass through.

(4) It should be distinguishable between different levels. To avoid a too-close-to-call situation, the service measure must clearly differentiate various levels of service. For instance, a service measure is deemed unsuitable if a small change can correspond to a wide range of service levels.

The selection of appropriate service measures is crucial for LOS evaluation, and the final choice must consider the perspectives of sailors and pilots. We investigated the concerns of senior pilots from the Ningbo Port Pilot Co., Ltd. (Ningbo, China) regarding ship navigation, focusing on comfort and safety. Through a questionnaire, we found that senior pilots were particularly concerned about the density of ships, the efficiency of vessel navigation, the incidence of conflicts, and the delay times for vessels passing through a region. Notably, they prioritized safety and disturbances due to other ships over the effects of complex natural conditions or delays.

Analyzing the concerns of the pilots revealed that most vessels in waterway intersections typically avoid obstacles by steering around them rather than braking or stopping. This steering behavior complicates the calculation of delay times for such vessels. Furthermore, vessel density alone reflects only the number of vessels in the area, overlooking critical information such as their positions and encounters. As a result, it becomes challenging to assess the impact of waterway traffic on vessels navigating through waterway intersections.

Therefore, drawing from the pilots’ experience and considering the potential influences of other vessels during navigation, the degree of conflict between vessels was ultimately chosen as the final service measure. More specifically, the degree of conflict refers to the average number of head-on, overtaking, and crossing encounters that occur during vessel navigation. In summary, it represents the average level of conflict experienced by vessels while navigating through a waterway intersection.

3.2. Designation of LOS

In highway transportation, the HCM categorizes the service level of a transportation facility into six levels, labeled A to F. However, due to differences in vessel and vehicle sizes, as well as the distinct characteristics of each mode of transportation, the six levels of service defined in the HCM cannot be directly applied to maritime contexts. For example, the braking time for vessels is significantly longer than that for vehicles, and vessels will typically travel at slower speeds. Additionally, traffic control measures differ; vessels navigating waterway intersections do not encounter red lights and are accustomed to using steering to avoid obstacles, whereas road vehicles often rely on braking and stopping when faced with red lights or blockages.

3.3. Development of the LOS Criteria

The discussion above has established the degree of conflict as the service measure for LOS in waterway intersections. What remains is to determine how to quantify the degree of conflict and how to relate the degree of conflict to the LOS.

3.3.1. Quantification of the Service Measure

Waterway intersections are typically busy, making collision avoidance crucial for vessels navigating through these areas. As a result, sailors must remain vigilant at all times and employ effective skills to prevent collisions. To quantify the degree of conflict in waterway intersections, this paper proposes using various encounter scenarios that commonly occur between vessels, combined with sailing time, to measure the level of conflict.

According to the International Regulations for Preventing Collisions at Sea, there are three types of avoidance actions for powered vessels in open waters with good visibility: head-on, overtaking, and crossing maneuvers. First, we identify the range of vessels in urgent situations and categorize encounter scenarios based on vessels within this range. Next, we dynamically adjust the primary vessel’s sailing coordinate system, setting the vessel’s direction of travel as 0°. Finally, we classify the encounter situations as follows (Figure 1):

1. Based on the primary vessel’s heading, a vessel that appears within ±6° directly ahead of it and with an angle difference relative to the heading of the primary ship within the [90°, 270°] range constitutes a head-on situation.

2. Based on the primary vessel’s heading, a vessel that is within a range of 22.5° to the left or right of the stern has an angle difference relative to the heading of the primary vessel within the [0°, 90°] ∪ [270°, 360°] range, while moving at a speed greater than that of the primary vessel constitutes an overtaking situation.

3. Based on the primary vessel’s heading, a vessel that falls within the [6°, 112.5°] range and has an angle difference relative to the heading of the primary vessel within the [180°, 360°] range, or a vessel within the [247.5°, 354°] range, with an angle difference relative to the heading of the primary vessel within the [0°, 180°] range, constitutes a crossing situation.

The classification of encounter situations is a fundamental and essential step in analyzing the degree of conflict. Since this paper focuses solely on assessing the level of service in a specific region, it counts the total number of encounters involving vessels navigating within that area, including head-on, overtaking, and crossing situations. As such, the degree of conflict is computed with Equation (1):

$$I={\displaystyle \frac{{{\displaystyle \Sigma }}_{i=0}^N\frac{\alpha e_i^o+\beta e_i^h+\gamma e_i^c}{\Delta T}}{N}},$$

(1)

where $N$denotes the total number of vessels sailing in the region during the observation; $∆T$denotes the observation’s duration; $\alpha$denotes the influence factor of overtaking on the degree of conflict; $\beta$ denotes the influence factor of the head-on situation on the degree of conflict; $\gamma$ denotes the influence factor of a crossing situation on the degree of conflict; $e_i^o$ denotes the total number of times that vessel $i$ encounters an overtaking situation; $e_i^h$ denotes the total number of times that vessel $i$ encounters a head-on situation; $e_i^c$ denotes the total number of times that vessel $i$ encounters a crossing situation; $I$denotes the degree of conflict.

Since different encounter situations exert varying levels of interference on the primary vessel, distinct influence factors are assigned to each type of encounter. This is analogous to roadway intersections, where the severity of conflict varies among diverging, merging, and crossing scenarios. Consequently, the influence factors increase in that order.

Considering that the captain of an overtaking vessel has the discretion to decide whether to carry out a maneuver and can thereby manage the associated risk, the influence factor for overtaking encounters is set to 1 (α = 1). Given that the pointed structure of a vessel’s bow reduces the likelihood of a head-on collision when two vessels are approaching each other with a large angle difference in their headings, the influence factor for head-on encounters is set to 2 (β = 2). Crossing encounters represent the most severe conflict; therefore, the influence factor for crossing encounters is set to 3 (γ = 3). Accepting the above influence factors, the degree of conflict is further formulated as in Equation (2):

$$I={\displaystyle \frac{{{\displaystyle \Sigma }}_{i=0}^N\frac{1e_i^o+2e_i^h+3e_i^c}{\Delta T}}{N}}.$$

(2)

3.3.2. Relating the Service Measure to the LOS

The key aspect of establishing the LOS criteria is determining the boundary values of the service measure for each level of service. Given that the LOS designation is categorical and somewhat subjective, using fuzzy clustering to relate the service measure to the LOS is appropriate [33,34,35].

The service level classification method described in this research relies on a large amount of AIS data to analyze the service level of waterway intersections. These data are then clustered and classified using the service measure to achieve the final classification. The analysis utilizes the data libraries of pandas and numpy in Python for screening, while the machine-learning libraries sklearn and skfuzzy are integrated for fuzzy clustering analysis to categorize the service levels.

Using screening and cleaning methods, approximately 100 gigabytes of the original data were initially processed and extracted into a fixed format upon completion. The processed data were used to screen waterway intersections, and all the vessel distribution information on the screened waterway intersections was extracted at time intervals of 30 s. The vessel distribution information at a specific moment is shown in

Table 2. The studied vessel’s details at a certain point in time.

Number	MMSI	Speed (kn)	Heading (°)	Width (m)	Length (m)	GT (ton)	Lon (°)	Lat (°)
1	369296000	14.0	219.0	32.0	217.0	52,780	122.315022 E	29.751270 N
2	228401800	7.6	286.0	61.0	400.0	191,640	122.341750 E	29.742257 N
3	372926000	10.8	206.0	28.0	195.0	42,370	122.326917 E	29.746844 N
4	563065100	10.0	131.0	28.0	195.0	40,000	122.321084 E	29.741067 N
5	341988000	8.6	225.0	28.0	195.0	42,660	122.318333 E	29.748992 N
6	563115100	13.2	192.0	28.0	170.0	21,940	122.318865 E	29.746543 N
7	477222700	8.5	295.0	48.0	366.0	190,000	122.322259 E	29.748495 N
8	636018382	12.4	213.0	27.0	176.0	38,000	122.320262 E	29.746421 N

.

This paper employs the hierarchical cluster method to determine the optimal number of clustering centers. The silhouette coefficient is used to evaluate the clustering results [36]; values closer to 1 indicate a more significant outcome:

$$\mathrm{S}(\mathrm{i})={\displaystyle \frac{\mathrm{b}(\mathrm{i})-\mathrm{a}(\mathrm{i})}{max\{\mathrm{a}(\mathrm{i}),\mathrm{b}(\mathrm{i})\}}}$$

(3)

$$\mathrm{a}(\mathrm{i})={\displaystyle \frac{1}{\mathrm{n}-1}}\sum _{\mathrm{j}\ne \mathrm{i}}^{\mathrm{n}}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}(\mathrm{i},\mathrm{j})$$

(4)

$$\mathrm{b}(\mathrm{i})={\displaystyle \frac{1}{\mathrm{n}-1}}\sum _{\mathrm{j}\ne \mathrm{i}}^{\mathrm{n}}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}(\mathrm{i},\mathrm{j})$$

(5)

where $\mathrm{S}\left(\mathrm{i}\right)$ denotes the silhouette coefficient. $\mathrm{a}\left(\mathrm{i}\right)$ and $\mathrm{b}\left(\mathrm{i}\right)$ represent the average of the distance between the sample point and all other points in the cluster to which it belongs. $\mathrm{i}$ represents the sample point. $\mathrm{j}$ represents the other points. $\mathrm{n}$ represents the number of samples.

An overview of the LOS classification in the context of waterways indicates that it is common to categorize service levels into four or five levels, often simplifying the classification. Additionally, a cluster analysis of AIS data from multiple waterway intersections, utilizing big data, suggests that five levels may be more suitable for representing vessel navigation conditions, as illustrated in Figure 2. In addition, designating LOS classes as excellent, good, fair, passable, and poor appears to align well with the cultural backgrounds of people around the world:

• Excellent: This level indicates excellent service. The number of vessels traveling through the waterway intersection is low, resulting in minimal conflict among vessels and a high degree of freedom for sailors to steer. Additionally, there is low vessel density in the area, leading to a high level of navigation efficiency with no risk of collisions at waterway intersections.
• Good: This level indicates good service. The number of vessels traveling through the waterway intersection has increased, leading to more conflicts among vessels and a slight reduction in the freedom of navigation for sailors. Although the density of vessels in the area remains low, a small number of vessels may interfere with each other’s movement, resulting in a slight decrease in navigation efficiency.
• Fair: This level indicates fair service. There is a continuous increase in the number of vessels traveling through the waterway intersection and a continuous increase in vessel conflicts. In addition, there is an increase in the density of the area, congestion can be perceived, the freedom of steering movement for sailors is reduced compared to the good LOS class, the efficiency of navigation is reduced, and there is a potential risk of collision.
• Passable: This level indicates passable service. The number of vessels traveling in waterway intersections is high, resulting in noticeable conflicts among vessels. Sailors experience reduced freedom of steering movement and must have excellent skills to navigate safely through the area. Overall, the safety, efficiency, and comfort of navigation are significantly diminished. The navigation conditions for vessels in the region are unstable and may deteriorate further if the balance of the waterway is disturbed.
• Poor: This level indicates poor service. The number of vessels traveling in waterway intersections reaches the area’s capacity, resulting in obvious vessel conflicts. An uneven spatial distribution and poor orderliness contribute to traffic breakdown. Additionally, navigation is inefficient, and even skilled sailors may struggle to maneuver safely, leading to a high risk of vessel collisions.

The data of waterway intersections in the whole watershed can be mined and summarized using the C-means fuzzy clustering algorithm. The data are divided into a training set and a validation set, and the number of clusters c is set to 5, which is the same as the service levels. In addition, the iteration-stopping threshold is set as error = 0.005, and the fuzzy index is set as m = 1.5 (usually taken as 1.5~2.5) [37,38].

Working according to the C-means clustering algorithm, the membership graph of the service measure is obtained, as shown in Figure 3.

According to the membership graph of the optimal clustering results, the service measures exhibit overlapping ranges of membership across different levels. Based on the principle that a higher membership indicates a stronger match with a level, the intersections of the membership curves between neighboring levels are used as boundaries for the fuzzy division of service levels.

As the training data in the clusters are standardized data, the clustered data under each cluster are extracted and standardized for reduction, in order to restore the real service measures. Finally, the LOS criteria of the waterway intersections are established, as shown in

Table 3. LOS criteria for waterway intersections.

LOS	I
Excellent	0–6
Good	6–12
Fair	12–21
Passable	21–33
Poor	>33

.

As shown in Table 3, the LOS is excellent when the degree of conflict is less than 6; the LOS is good when the degree of conflict falls between 6 and 12; the LOS is fair when the degree of conflict is between 12 and 21; the LOS is passable when the degree of conflict ranges between 21 and 33; the LOS is poor when the degree of conflict is greater than 33.

For this paper, we established a methodology for determining the LOS for waterway intersections. A set of criteria was developed to identify and select the appropriate service measures for these intersections. Subsequently, the service levels were determined and designated. Next, we quantified the service level and explored methods to relate the service measures to the LOS. For this research, we employed C-means fuzzy clustering to establish fuzzy boundaries by comprehensively analyzing the degree of orderliness and navigation efficiency, thereby determining the LOS criteria for waterway intersections.

3.4. Prediction of LOS

The above methodology can be used to compute the service measure from historical data to determine the LOS. However, it is not suitable for predicting future conditions. For instance, after implementing traffic flow optimization at a waterway intersection, it is necessary to predict the LOS in advance to assess the effects, rather than waiting until the intersection is open to traffic and determining the LOS afterward.

According to the method used for determining the service measure, predicting the service level of waterway intersections requires forecasting information such as sailing time and the number of encounters in the region. To obtain this information, we use the intersection origin–destination (OD) flow with the following calculation method:

• The time frame for LOS analysis is set to 1 h.
• We determine the inflow and outflow of vessels at the intersection of waterway intersections by using vessel start and end point information.
• The average sailing time $\Delta \mathrm{t}$ is calculated from the average sailing speed $v_f$ in the intersection, and the average sailing time is used as the time interval for each service level determination. The above calculation is formulated in Equation (6), where $n$ is the number of vessels and $s$ is the distance of the path through the intersection.

  $$v_f={\displaystyle \frac{\sum _{i=0}^n{v}_i}{n}},\Delta t={\displaystyle \frac{S}{v_f}}$$

  (6)
• The OD flow is used to predict the number of head-on, overtaking, and crossing encounters. Finally, the LOS of the intersection can be reasonably predicted by combining the probability of the same time slice and the probability of encounters. Building on Equation (7), the predicted service measure can be computed as follows:

  $$\mathrm{I}\left(\mathrm{t}\right)={\displaystyle \frac{{\displaystyle \sum }_{i=0}^N\frac{p_{t-1}^o{E}_i^o+2p_{t-1}^h{E}_i^h+3p_{t-1}^c{E}_i^c}{\Delta T}}{\mathrm{N}}}$$

  (7)

  where $p_{t-1}^o$ is the probability of the occurrence of an overtaking situation in the previous period; $p_{t-1}^h$ is the probability of the occurrence of a head-on situation in the previous period; $p_{t-1}^c$ is the probability of the occurrence of a crossing situation in the previous period; $E_i^o$ is the number of times an overtaking situation may occur for vessel $i$; $E_i^h$ is the number of times a head-on situation may occur for vessel $i$; $E_i^c$ is the number of times a crossing situation may occur for vessel $i$. $\mathrm{I}\left(\mathrm{t}\right)$ is the predicted value of the service measure at moment t.

4. Application of This Methodology

To illustrate the application of this methodology, a concrete example is provided below using real data.

The Zhoushan Maritime Bureau adopted a recommended navigation law for vessels operating in Yuxingnao (which means fish-brain) waters at the beginning of June 2023. As a result, an optimized traffic organization program was officially implemented to manage vessel routes through intersections. The authorities aimed to assess the effectiveness of this new traffic-routing system for reducing conflicts among vessels at the Yuxingnao intersection. To achieve this trial, the proposed LOS methodology will be employed to conduct a before-and-after study, comparing the LOS of the intersection prior to and following the implementation of the new routing system. This comparison will allow for conclusions to be drawn regarding the system’s effectiveness.

To serve this purpose, two months of data, totaling 6 gigabytes, were selected from December 2021 (representing the period before the new routing system was applied) and June 2023 (the period after the new routing system was applied) for comparison.

4.1. Data Preprocessing

Waterway intersections typically involve heavy traffic, a variety of vessel types, and complex encounter situations. Therefore, the field data must be mined and screened to identify the relevant information necessary for this analysis.

Since multiple data transmissions may be sent to the same base station simultaneously during AIS data transmission, the receiver may reach its capacity limit, resulting in some missing AIS data. Therefore, it is essential to clean the AIS data before it can be effectively used [39,40]. The data processing procedure is described as follows (Figure 4):

• MMSI, time-consistent data cleaning;
• Remove the data with fewer than 9 MMSI digits;
• For static missing data, such as vessel length and width, we use the mean values of vessel sizes for the corresponding vessel type to fill in the gaps.

To facilitate convenient time-slicing at waterway intersections and provide a comprehensive view of vessel distribution at any given moment, this paper employs the cubic spline interpolation method to estimate the vessel positions and related information. The cubic spline interpolation algorithm offers several advantages, including high flexibility, a strong emphasis on function smoothness, high accuracy in terms of fitting data, and ease of interpretation. This approach enables a more precise and complete estimation of the required AIS data. Additionally, calculating the distances between vessels using latitude and longitude coordinates can be challenging; therefore, the Mercator projection method is utilized to convert these coordinates into Cartesian coordinates.

Since the position information found in AIS data only reflects the location of the AIS antenna, calculating vessel spacing using the Euclidean distance based on this position alone is inadequate. Treating a vessel as a mass point overlooks its shape. Therefore, both the shape and the bow direction of the vessel must be taken into account. The Hausdorff distance addresses this issue by considering the shape of the polygons representing the vessels, as well as their relative orientations, when calculating the minimum distance between them. This approach effectively resolves the challenge of accurately determining the minimum distance between two vessels. The Hausdorff distance is calculated as follows.

To facilitate analysis, a dynamic coordinate system centered on the primary vessel is established based on its bow direction, as illustrated in Figure 5. This coordinate system adapts to changes in the primary vessel’s bow direction. By integrating the position information of surrounding vessels relative to the primary vessel, we can determine the bearing of any surrounding vessel with respect to the primary vessel using Equation (8).

$$\theta =\arctan ({\displaystyle \frac{{\mathrm{Y}}_i-{\mathrm{Y}}_0}{{\mathrm{X}}_{\mathrm{i}}-{\mathrm{X}}_0}}).$$

(8)

Here, $\theta$is the steering angle; ${\mathrm{X}}_0$is the distance between the primary vessel and a basic point in the direction perpendicular to the channel; ${\mathrm{X}}_{\mathrm{i}}$ is the distance between the target vessel and a basic point in the direction perpendicular to the channel; ${\mathrm{Y}}_0$ is the distance between the primary vessel and the basic point in the direction along the channel; ${\mathrm{Y}}_i$is the distance between the target vessel and the basic point in the direction along the channel.

In contrast, the coordinate system is established, according to the method shown in Figure 6, to screen the surrounding target vessels. The specific calculation of the distance between two vessels is shown in Equations (9)–(12).

The set of coordinates for the primary vessel is $Q=[q_1,q_2,q_3,q_4]$. The set of coordinates for the target vessel is $O=[o_1,o_2,o_3,o_4]$.

$$H(Q,O)=\mathrm{m}\mathrm{a}\mathrm{x}\left(h\right(Q,O),h(O,Q\left)\right)$$

(9)

$$h(Q,O)=\mathrm{m}\mathrm{a}\mathrm{x}(q\in Q)\mathrm{m}\mathrm{i}\mathrm{n}(o\in O)\Vert o-q\Vert$$

(10)

$$h(O,Q)=\mathrm{m}\mathrm{a}\mathrm{x}(o\in O)\mathrm{m}\mathrm{i}\mathrm{n}(q\in Q)\Vert q-o\Vert$$

(11)

$$D=\sqrt{{(X_i-X_0)}^2+{(Y_i-Y_0)}^2}$$

(12)

Here, D is the Euclidean distance; $H(Q,O)$ is the Hausdorff distance between two vessels; $h(Q,O)$ is the minimum value from each point of the set of the primary vessel to each point of the set of the target vessel, which, then, takes the maximum value; $\Vert q-o\Vert$ is the Euclidean distance between the primary vessel and the target vessel.

4.2. Application 1: Effectiveness Assessment

The study site is located at (30.353550° N, 121.773834° E) and is illustrated in Figure 7.

The data were obtained from the NingBo Maritime Safety Administration and were received through s shore-based AIS receiver. Vessel trajectories that were collected in June 2023 are plotted in Figure 8, illustrating that the intersection was quite busy. The red and green distributions on either side of the cordon lines indicate the volume of traffic entering and exiting the intersection, highlighting the complex traffic conditions at the test site.

This experiment compares the service levels in the region in December 2021 (the period before the new routing system was applied) and June 2023 (the period after the new routing system was applied). The vessel routing systems in both periods are illustrated in Figure 9.

The waterway intersections depicted in Figure 9a,b, where numbers 1 to 5 represent the various approaches to the intersection. To evaluate the effectiveness of the routing systems, service levels in the before and after periods were determined based on the methodology, performing the procedure as follows:

• Process the data according to Figure 4.
• Extract the data within the study site and determine the class of encounter situations according to Figure 1.
• Segment the monthly AIS data into weeks, with each week’s data evaluated on an hourly basis.
• Calculate service measure $\mathrm{I}$ (degree of conflict) for each period according to Equation (2).
• Determine the level of service according to Table 3.

The LOS was determined based on a 6-hour time frame, and the statistics were collected for each week and the whole month. The results are shown in

Table 4. Comparison of LOS results in the before and after periods.

Duration	Period	Excellent (%)	Good (%)	Fair (%)	Passable (%)	Poor (%)
1st week	Before	10.0	53.3	30.0	6.7	0
	After	19.6	33.4	32.2	14.8	0
2nd week	Before	3.4	37.9	44.8	13.7	0.2
	After	13.1	53.8	21.5	7.8	3.8
3rd week	Before	17.2	48.4	20.6	7.0	6.8
	After	16.9	34.6	36.9	11.6	0
4th week	Before	20.6	44.8	17.4	17.2	0
	After	24.6	23.2	44.6	7.6	0

.

As shown in the table, the LOS varied over time; however, the overall distribution across the four weeks was generally consistent. There was a significant increase of 23% in the percentage of Excellent LOS ratings, indicating the positive effect of the new routing system. Conversely, a sharp decline of 39.4% in the percentage of Good LOS ratings suggests a negative impact at this level. For the Fair LOS ratings, one week experienced a notable decrease of 23.3%, while the other two weeks showed increases of 16.3% and 27.2%, resulting in an overall net increase of 22.4% at this level. Although there were fluctuations in the remaining two levels, they largely offset each other, leading to a slight overall decrease of about 3%.

In summary, the statistics present a mixed message: while there were negative impacts on the Good LOS ratings, the overall effect appeared positive, due to improvements in the Excellent and Fair LOS ratings. It would be worthwhile to further investigate the factors contributing to the redistribution of ratings across the three levels. Additionally, the LOS ratings for Passable and Poor remained relatively stable, with only a slight decrease. This suggests that the routing systems may not have adequately addressed challenging operational conditions.

4.3. Application 2: LOS Prediction

The application described above evaluated the LOS using historical data after certain events had occurred. However, there is often a need to predict the LOS before such events actually take place. For instance, the shipping authorities may be interested in understanding the potential impact of further improvements to the routing system beyond the recently adopted changes.

The data collected in June 2023 were used for the prediction study, with the waterway intersections depicted in Figure 9b, where numbers 1 to 5 represent the various approaches to the intersection. By extracting origin and destination information from the AIS data for these vessels, an origin–destination (OD) table was estimated for the time period under analysis. The results are presented in

Table 5. OD flow estimation result.

	Origin	App. 1	App. 2	App. 3	App. 4	App. 5	Production
Destination
App. 1		0	122	100	119	93	434
App. 2		150	0	146	162	85	543
App. 3		70	105	0	70	47	292
App. 4		94	156	94	0	83	427
App. 5		107	94	56	84	0	341
Attraction		421	477	396	435	308	2037

.

The probability of each encounter situation and the total number of possible occurrences were calculated based on the LOS methodology. Following the method outlined in Section 3.4, the probabilities of encounter situations for ships during this period are determined using $p_{t-1}^o=0.1382$, $p_{t-1}^h=0.0112$, and $p_{t-1}^c=0.1798$. Consequently, the prediction results are as follows.

As shown in

Table 6. Prediction results for the level of service.

	24 h	48 h	72 h	96 h	120 h
I (actual)	10.81	10.85	10.39	10.67	9.51
LOS	Good	Good	Good	Good	Good
I (predicted)	6.24	9.32	5.42	7.85	9.00
LOS	Good	Good	Excellent	Good	Good

, some deviation exists between the predicted values and the actual values in this LOS methodology. This discrepancy may be attributed to uncertainty factors in vessel navigation at waterway intersections, such as a vessel’s sailing trajectory not aligning with the predicted path. Despite these differences, the predictions based on multiple data sets demonstrated high accuracy. Thus far, the LOS methodology has successfully transitioned from historical assessments to predictive assessments, establishing a comprehensive LOS system that holds significant reference value for shipping authorities.

5. Conclusions

LOS is a crucial factor for evaluating the traffic performance of waterway intersections. While LOS methodologies have previously been established for highways and extensively researched for waterways and ports, none can be directly applied to waterway intersections, due to differences in transportation facilities. Based on an analysis of vessel navigation data, this paper demonstrates that the complexity of vessel navigation in waterway intersections is greater than that in ports and waterways. Consequently, the methodology incorporates the common features of vessel navigation in these intersections—specifically, complex encounter situations—as the basis for determining the appropriate service measure for waterway intersections and furthering their LOS. For the first time, a method tailored for waterway intersections has been proposed, comprehensively considering both safety and efficiency.

To demonstrate the applications of the proposed methodology, a before-and-after study was conducted to evaluate the effectiveness of the traffic organization optimization system implemented by the Zhoushan Maritime Bureau in Yuxingnao waters in June 2023. The study collected a total of 6 gigabytes of data over one month before and after the implementation of the new routing system. Based on these data, the LOS was assessed within a 6-hour time frame, and statistics on LOS ratings were gathered on a weekly basis. The results indicated that the proposed methodology effectively utilizes the degree of conflict to characterize traffic operational conditions, translating them into the LOS according to the established criteria.

The before-and-after study conveyed a mixed message: some LOS ratings improved, while others deteriorated, and the rest showed little to no change. This suggests that the changes implemented by the authorities may be effective under certain operational conditions, ineffective under others, and indifferent for the remainder. These outcomes provide valuable insights for the authorities, helping them to further refine their traffic organization optimization efforts.

While estimating the LOS is helpful for developing countermeasures to improve traffic operations, predicting the LOS is crucial in situations where understanding the impact of improvement strategies in advance is necessary. This research also presents a predictive application of the methodology. The LOS prediction model utilizes data from the period after application to estimate the origin–destination (OD) table, from which the probabilities of encounter situations for ships during each period are determined. Using these results, LOS predictions are carried out following the proposed method. Although the prediction results exhibit some discrepancies—likely due to uncertainty factors in vessel navigation at waterway intersections, such as a vessel’s sailing trajectory not aligning with the predicted path—predictions based on multiple data sets still demonstrated high accuracy.

However, there are limitations to the method. In assessing the LOS, it was assumed that vessels travel in the same direction and at the same speed within the navigable area, which results in a small deviation between the predicted and actual outcomes. Future research will focus on improving the service level prediction and assessment method to reduce this discrepancy.