Enhancing Prediction Accuracy of Vessel Arrival Times Using Machine Learning

Abstract

Marine transportation accounts for approximately 90% of the total trade managed in international logistics and plays a vital role in many companies’ supply chains. However, en-route factors like weather conditions or piracy incidents often delay scheduled arrivals at destination ports, leading to downstream inefficiencies. Due to the maritime industry’s digital transformation, smart ports and vessels generate vast amounts of data, creating an opportunity to use the latest technologies, like machine and deep learning (ML/DL), to support terminals in their operations. This study proposes a data-driven solution for accurately predicting vessel arrival times using ML/DL techniques, including Deep Neural Networks, K-Nearest Neighbors, Decision Trees, Random Forest, and Extreme Gradient Boosting. This study collects real-world AIS data in the Eastern Mediterranean Sea from a network of public and private AIS base stations. The most relevant features are selected for training and evaluating the six ML/DL models. A comprehensive comparison is also performed against the estimated arrival time provided by shipping agents, a simple calculation-based approach, and four other ML/DL models proposed recently in the literature. The evaluation has revealed that Random Forest achieves the highest performance with an MAE of 99.9 min, closely followed by XGBoost, having an MAE of 105.0 min.

1. Introduction

Maritime transport accounts for more than 90% of the world’s trade while 74% of all goods imported or exported from Europe are carried by ships [1]. Due to economic efficiency, sea transport is considered the most dominant mode of transportation for international trade [2]. In 2022, container ports handled a total weight of more than 12,027 million metric tonnes around the globe, and it is expected to grow by 2.4% until 2028 [1]. Since containerized volume is increasing every day, the size of container vessels has also increased, which can lead to several seaside problems, i.e., port congestion, long waiting times, and accidents. According to a report presented by the United Nations Conference on Trade and Development (UNCTAD) [1], an increase in the waiting time of container ships at the port was noted following the COVID-19 pandemic, especially for developed countries, as depicted in Figure 1. To address this issue, a logistics plan can be developed to enhance the efficiency of sea transportation. The logistics plan may include berth scheduling, quay crane scheduling, vessel path planning, and accurate prediction of vessel arrival times [3]. However, a significant obstacle lies in the fact that vessels must arrive punctually for this plan to succeed. Unfortunately, only 55–89% of vessels follow their schedules and reach on time at the destination port [4,5].

Even in some cases, timely arrived ships need to wait before mooring due to inefficient berth allocation plans [6]. Uncertainty in vessel arrival times also lowers the schedule’s reliability, causing delays and congestion problems and decreasing productivity levels for inland transport operators. Late arrivals of ships at the port cause high costs of vessel operation and the whole supply chain [7]. For example, when ships arrive late, port management authorities must adjust the entire berth allocation schedule. This can result in delays for other ships as new plans are implemented or routes are rerouted. Additionally, frequent changes to berth plans can significantly decrease the performance of the port terminal, as berth planning is fundamental to its operations [8,9,10]. Given the numerous decisions tied to vessel arrival times, precise prediction of vessel arrivals at the terminal is essential for the optimal functioning of any container terminal.

Estimated time of arrival (ETA) is the time when a vessel is expected to arrive at a particular port terminal [11]. Accurate ETA prediction helps terminal managers and stakeholders make quick and efficient collaborative decisions to enhance the terminal’s performance. A study by Michaelides et al. analyzed the arrival time punctuality of container vessels at the Port of Limassol in Cyprus [12]. The study revealed that 45% of container vessels arrive 30 min late, 13% arrive 2 to 6 h late, and another 13% arrive 1 to 3 days later than their ETA. When there is a significant discrepancy between the ETA and the actual arrival time, shipping companies face hefty penalties, and the entire berth allocation plan needs to be revised [13]. At the Port of Limassol, passenger ships demonstrate high arrival punctuality, with 61% arriving within 30 min of their ETA and an additional 31% arriving within 60 min [12]. This high level of punctuality is expected since passenger ships adhere to very strict schedules. However, for other vessel types, the 30-minute arrival punctuality ranges only between 41% and 49% [12]. Some other studies from existing literature also deal with ETA prediction and punctuality analysis, such as a study presented in [14] that predicts ETA for container ships in short sea shipping while exploiting meteorological and automatic identification system (AIS) data. Another study [15] performs ETA prediction using AIS data and proposes a deep learning-based approach. A neural network-based solution is proposed in [16] for ETA predictions using historical ship position data of two dedicated areas in the Netherlands and Germany.

Most of the recent studies on ETA predictions of vessels use machine learning-based methods trained on historical data related to ships’ paths, positions, and other parameters. Although these approaches yield satisfactory results, they are often inadequate for continuous real-time predictions. Therefore, this study aims to propose an accurate data-driven methodology that can predict ship arrival times in real-time using machine learning. Furthermore, our proposed methodology evaluates and selects the most suitable algorithm to perform ETA based on the current situation and creates the best feature/input combination from the available AIS data. This study develops six models, namely Deep Neural Networks (DNN), K-Nearest Neighbors (KNN), Decision Tree (DT), Random Forest (RF), Extreme Gradient Boosting (XGBoost), and Gaussian Naive Bayes (GNB). This paper makes the following key contributions.

• The study generates and evaluates a comprehensive list of feature combinations based on AIS data that can enhance the prediction accuracy of vessel ETA.
• The study proposes a new methodology of splitting data based on vessel routes to avoid bias and overfitting during the training and testing of machine learning models.
• The study evaluates six machine/deep learning algorithms for predicting vessel ETA and compares them against multiple recently proposed machine/deep learning-based approaches.

The rest of the paper is structured as follows: Section 2 presents the literature review. The methodology employed in this study is outlined in Section 3. Section 4 details the experimental evaluation settings, including results and discussion. Section 5 discusses the benefits of accurate prediction of vessel ETAs along with future work. Finally, Section 6 concludes the study.

2. Literature Review

An accurate prediction of ETA for arriving vessels is crucial for any port, as several decisions are taken based on it. For instance, berthing position, berthing time, number of cranes to unload/load cargo, and other equipment usage are finalized based on accurate ETAs. After an extensive literature review in the area, the most relevant papers were selected for analysis in this research work. These papers address the same problem and share similar motivation and techniques with the current research work, enabling better comparison and addressing possible deficiencies that have not been addressed in previous research work in pursuit of the continuation of the effort of accurately predicting vessel ETA. The work of these papers focuses on a set of commonly used machine learning algorithms, which will also be tested with our data, while further experimenting with some additional ones for result comparison.

Several methodologies are proposed in the current literature to deal with ETA prediction. For instance, a study presented in [4] proposed a method to perform ETA while employing Markov Chains (MC) and Bayesian sampling methods. The proposed method was a data-driven approach exploiting AIS data to first predict the trajectories of vessels using reinforcement learning and data mining. Then, based on predicted trajectories of arriving vessels, speed of ground (SoG) and ETA were predicted using MC and Bayesian sampling approaches. The authors of [17] developed an ETA prediction model for container ships at the Port of Rotterdam, Netherlands. They explored artificial neural networks (ANNs), support vector machines, and multi-linear regression. Based on simulations, the study found that multi-linear regression requires minimal data and training time but struggles with complex functions. ANNs demand the most data and training time but excel at handling complex functions. Support vector machines fall between the two, needing more data and training time than linear regression but less than neural networks. They also demonstrate better capability with complex functions compared to linear regression but inferior performance compared to neural networks.

Another study [18] also developed a method to predict ETA while considering weather conditions. This study calculated the route to the destination and voyage speed using the Dijkstra method. Then, based on voyage speed and distance, ETA was predicted using the Bayesian sampling method, while considering weather conditions. Based on experimental results, the authors of [18] claimed that they have achieved 28% higher accuracy than their counterparts.

The authors of [19] proposed a solution for the well-known berth allocation problem while considering predicted ETA. Using machine learning methods, they first predicted the various vessel trajectories based on historical AIS data. Then, based on trajectories, they predicted the ETA for arriving vessels. Based on the experimental analysis, they demonstrated that the terminal authorities could prepare a more feasible berth plan with the help of accurate ETA prediction.

The authors of [20] proposed a data-driven approach to predict the arrival times of ships in port areas. The authors exploited both historical data by ship reporting systems and live AIS data while proposing a path-finding algorithm. Then, based on the predicted path of arriving vessels, they predicted the arrival times of vessels. Finally, several experiments have been conducted to validate their proposed method using real port data from Trieste Port, Italy. The authors also performed a comparative study to validate the proposed method with existing well-known methods (like the Haversine formula).

Another paper [21] presented an ETA prediction strategy using an artificial neural network (ANN). The study utilized AIS data and historical data of long-range trajectories to predict the trajectory of vessels. Then, based on trajectories, ANN was utilized to predict the arrival times of vessels.

Yoon et al. [22] proposed a historical voyage-based predictive algorithm to estimate the ETA of arriving vessels at Busan New Port, South Korea. The proposed method employed a combination of interpolation, segmentation, and optimal parameter selection approaches for optimal ETA estimation. The developed method divided historical voyage data into representative paths and then applied spline interpolation, which helped the algorithm generate accurate, detailed routes for predictions of ETA. For experimental purposes, real data from the Busan New Port, South Korea, were used for four months (20 September 2022 to 13 January 2023). The results demonstrated the effectiveness of the proposed method in terms of high accuracy in ETA prediction with an average MAE of 3 h and 14 min.

The authors of [23] proposed deep learning-based models to predict ETA for arriving vessels at bulk ports. The authors employed a recurrent neural network (RNN) and a convolutional neural network (CNN) to perform ETA predictions using historical traffic data and AIS data. The study also considered weather data and previous port visit data of vessels to reduce prediction errors. The experimental evaluation revealed that the sequence models outperformed the non-sequence models, and all models reduced prediction accuracy in the case of short distances.

Another study [24] performed ETA prediction by proposing a machine learning model in channels and narrow waterways. The study used historical AIS data (2018–2020), performed data preprocessing and feature engineering, and eventually performed arrival times of vessel prediction in channels. A developed model for ETA predictions based on XGBoost disclosed higher performance in all metrics. Further, experiment results demonstrated that the newly developed model can sustain high performance even when using a simplified structure.

In [25], Rahman et al. developed a data-driven method to predict the ETA of arriving vessels at the port of Klang, Malaysia. The study utilized past voyage data and employed an ANN-based approach to perform predictions. Several experiments were conducted on real data collected from real ports. Results showed the proposed method performed well and achieved a MAPE of 36.99%.

Another study [16] developed two ANN-based models to predict the ETA of vessels and utilized historical ship position data. Then, both models were assessed and contrasted with conventional methods for finding average travel times in two locations of Germany and the Netherlands. Simulation results demonstrated that the methods with ANN improved the ETA accuracy by 20.6% for short trips, 4.8% for medium-length trips, and 13.4% for long trips.

3. Methodology

Compared to prior work, this study systematically evaluates and selects a more extensive collection of features from the two position reports (A and B) and the static voyage data of AIS. Our final selection of only AIS-based features makes the training and inference much more efficient, enabling the real-time prediction (and correction) of vessel ETAs. In addition, this study performs a comprehensive comparison of six different machine learning algorithms against six other approaches, namely the estimated time of arrival provided by shipping agents, a simple calculation-based approach, and four other machine/deep learning models proposed recently in the literature.

Figure 2 shows the overall methodology employed by this study for performing vessel arrival times prediction using machine learning models. The process involves collecting AIS data and transforming it (i.e., wrangling) into a format that is readily consumable by the downstream methodology steps (Section 3.1). Next, a long list of features was evaluated and selected for model construction (Section 3.2). To measure the fitness of predictions across multiple models, the popular approach of cross-validation was utilized, while the data were split based on vessel routes to avoid overfitting (Section 3.3). Finally, hyperparameter tuning is performed to identify the best hyperparameters to use for each machine learning model that optimizes its performance (Section 3.4). All steps are further elaborated below.

3.1. Data Collection and Wrangling

This study uses AIS data collected pertaining to the Eastern Mediterranean Sea from 17 AIS base stations operated by the Cyprus Shipping Deputy Ministry, Tototheo Ltd., and Cyprus University of Technology (CUT) between 2020 and 2022 and stored in the CUT-AIS platform [26]. AIS data contain several pieces of information about the vessels moving in the area, such as the position (longitude, latitude), size (length, breadth, draught), type, speed over ground (SoG), course over ground (CoG), rate of turn (RoT), and heading of the vessel as well as the next destination port and ETA provided by the agent [27]. The data related to the destination and actual time of vessel arrivals (ATA) were retrieved from the Port Community System of the Cyprus Ports Authority.

The raw AIS data need to be transformed into a usable format containing only numeric values, which can then be used for training and testing the machine learning models. After decoding the AIS messages, most AIS data values are already in a numerical format (e.g., longitude, latitude, SoG, CoG, etc.) and can be used as is. String values such as the destination and vessel type are converted into numbers using ordinal encoding. In addition, the distance to the destination is computed given the current location and the coordinates of the destination. Finally, the ETA provided by the shipping agent, as well as the ATA, are converted to minutes to the destination by computing the time difference between the time of the AIS message and the ETA and ATA, respectively.

After analyzing the dataset, it is observed that the ETA provided by the shipping agents is often incorrect, with a mean absolute error of 178 min (almost 3 h). Indicatively, the shipping agent, on a specific occurrence, indicated that the ship would arrive in 1745 min (1 day and 5 h) while the ship actually arrived in 2445 min (1 day and 17 h). The worst error observed in our dataset was 4319 min (3 days), showing just how inaccurate the provided ETA can be. Furthermore, it was observed that the shipping agent, in many cases, does not update the ETA as the vessel progresses through the route. In other cases, the ETA indicates that the vessel has arrived while it is actually still on its way to its destination. The reverse is also observed sometimes, where the ETA provided by the shipping agent states that the vessel will arrive much later than the actual arrival time of the vessel. These observations further motivate the need for more accurate predictions of the vessel arrival times.

Finally, errors have been observed in relation to the validity of the vessel location, where some longitude and latitude values are much further away from the vessel route, as depicted by the majority of the position data. This error occurred in about 4.25% of the data and is considered rare. It was also observed that the longitude and latitude are updated every 2–3 s, and wrong values are corrected within 1–2 min. This error can be easily detected while calculating the remaining distance of the vessel route using outlier detection. Hence, data points containing invalid position values are eliminated from the dataset to avoid confusing the model and reducing its performance.

3.2. Feature Selection

The process of selecting features for training predictive models is of utmost importance [28]. However, there is a scarcity of research that thoroughly analyzes the most suitable AIS input data for accurate predictions. This study has drawn insights from three relevant papers to guide our feature selection process while also considering several additional features extracted from AIS data. The list of all features considered, as well as the ones employed in past papers and this study, are shown in

Table 1. Features identified and employed in past papers and this study.

Feature	Parolas et al. [17]	Flapper et al. [29]	Kolley et al. [19]	This Study
Longitude	✓	✓	✓	✓
Latitude	✓	✓	✓	✓
Speed over ground (SoG)	✓			✓
Course over ground (CoG)				✓
Rate of turn (RoT)				✓
True heading			✓	✓
Vessel type		✓	✓	✓
Vessel length	✓	✓		✓
Vessel breadth	✓	✓		✓
Vessel draught				✓
Destination port				✓
Distance to destination	✓	✓		✓
ETA provided by the agent	✓			✓
Navigation status		✓		✓
Speed change compared to 3 previous hours	✓
Average speed of the last 12 h	✓
AIS time received		✓	✓
IMO number			✓

.

Using numerous features can lead to overfitting, where the model performs well on the training data but poorly on new data. Therefore, this study prioritizes feature combinations that have been identified as most important in past research. When considering new features, this study only includes those deemed highly relevant for predicting ETA. Recursive feature elimination with a cross-validation process was employed for computing the importance score for each feature. Based on our extensive analysis, the following features used in prior research are excluded from this paper: change in speed compared to the last three hours, average speed of the last 12 h, timestamp when the AIS message was received, and the International Maritime Organization (IMO) number that uniquely identifies a vessel. The first two features strongly correlate with the speed over ground, which is a very important feature, and hence do not provide any additional insight to the model [17]. The timestamp of AIS message reception was omitted as an input feature based on the observation that a route can be traversed multiple times without significant variations in duration. Moreover, the feature did not demonstrate significance according to other researchers’ findings [29]. Finally, the IMO was not included in this study as a feature because it is not related to the vessel’s mobility nor to the route the vessel takes. The complete list of selected features along with their computed feature importance is presented in

Table 2. Features importance based on recursive feature elimination with cross-validation.

Feature Name	Importance (%)
Distance to destination	36.96
ETA provided by the agent	15.50
Navigation status	14.49
Longitude	8.13
Speed over ground (SoG)	6.88
Vessel length	3.59
Vessel breadth	3.52
Destination port	2.78
True heading	2.56
Course over ground (CoG)	1.70
Vessel draught	1.47
Latitude	1.33
Vessel type	0.95
Rate of turn (RoT)	0.14

.

Distance to destination along with speed over ground (SoG) are intuitively important features, serving as the primary metrics of estimation for route completion timeline. Nevertheless, the accuracy of the estimation is affected by other factors represented by the other features. Latitude and longitude are defined as separate values in addition to distance to destination since the Coriolis deflection increases with increasing latitude. A vessel traveling the same distance in higher latitude seas will face much harsher conditions than a vessel traveling in lower latitude [30]. Furthermore, by utilizing the longitude and latitude, the route-specific characteristics can be factored in, e.g., a vessel currently traveling from north to south may be on a route that allows faster transition rather than traveling from east to west. The navigation status indicates idle periods during the course of a vessel, extending the ETA. Metrics of the vessel (i.e., length, breadth, draught, and type) indicate the potential behavior of the vessel related to its physical characteristics, e.g., a large vessel may start decelerating several miles before the port to reach a full stop. Course over ground (CoG) indicates the direction where the ship moves, factoring in longer paths vessels must follow to avoid obstacles and hazards or comply with regulations. The true heading indicates where the ship’s bow is pointed and may differ from CoG. Usually, this occurs to counteract strong currents that may cause the vessel to drift sideways. The rate of turn (RoT) is a potential indication of the vessels’ maneuverability. A less maneuverable vessel in need of performing certain maneuvers to reach its destination will have an increased ETA.

3.3. Model Selection and Evaluation

The next important decision after selecting the input features is choosing the most appropriate machine learning algorithm for the ETA prediction model. Three studies were identified during the literature review process that presented good vessel ETA predictions. As previously mentioned, one of the purposes of this work is to test new machine learning algorithms that have not been studied or tested in-depth by other researchers in studies to predict vessel ETAs, along with creating a better feature/input combination. For this purpose, the following six machine/deep learning algorithms were considered:

• Deep Neural Networks (DNN): Computational models inspired by the human brain consist of layers of interconnected nodes (neurons) that learn from data. The input layer has as many nodes as features while the output layer has only one node for generating the predicted value. Each node has its own associated weight and threshold. When the processed data are above that threshold, the node is activated, sending data to the next layer of the network for further processing. The outcome is a prediction factoring in the assigned weights [16].
• K-Nearest Neighbors (KNN): An algorithm that stores all (or a sample of) available data points and classifies new data points based on a similarity measure (e.g., distance functions) and their distance from other data points. The predicted value for the new case is the arithmetic mean of the target values of the K nearest neighbors [19].
• Decision Trees (DT): A tree-like model of decisions and their possible consequences, with linear regressors at the leaves. The algorithm splits the data recursively into child nodes at each branch based on their value, attempting to group similar data until a stop criterion is met (e.g., max tree depth). A prediction for a new data point is made by following the tree downwards to a leaf node starting from the root. Each leaf contains a linear regression model used to compute the final predicted value [31].
• Random Forest (RF): An ensemble method that builds multiple decision trees and merges them to obtain a more accurate and stable prediction. When a test data point arrives, each decision tree generates a prediction, which is averaged to generate the final predicted value [32].
• Extreme Gradient Boosting (XGBoost): An optimized distributed gradient boosting library designed to be highly efficient, flexible, and portable. XGBoost builds a predictive model by combining the predictions of multiple decision trees, similar to Random Forest, and employs regularization techniques to enhance model generalization [32].
• Gaussian Naive Bayes (GNB): A probabilistic classifier based on Bayes’ Theorem, assuming strong (naive) independence between features. Each new data point is assigned to a class by calculating the maximum value of the posterior probability of the class. The mean and variance of features are calculated for each class during training, and these statistics are used to predict the class of new points based on the likelihood and prior probabilities.

A common practice for evaluating machine learning models is to randomly split the data into a training and test dataset (e.g., 80% training data, 20% testing data). However, the performance estimate of the model can vary significantly depending on how the data are split, while a single random split provides only one snapshot of the model’s performance, which might not be reliable. In addition, if the model is fine-tuned based on the performance of the test set, it can lead to overfitting. To mitigate these downsides, 10-fold cross-validation is employed, which involves splitting the data into 10 folds. For each fold, the other nine folds are used as the training set and that fold as a test set. A model is fit on the training set and evaluated on the (unseen) test set. This process repeats 10 times, one for each fold, and the evaluation scores are averaged to produce the final evaluation score. This procedure generally results in a less biased or less optimistic estimate of the model’s performance than the simple train/test split.

In our specific scenario of arrival time predictions, there is an additional important consideration that is not discussed nor addressed in prior work. In particular, the dataset contains multiple training instances originating from multiple vessel routes. Randomly splitting the data, even for cross-validation, means that training instances from the same vessel route will be contained in both the training and testing splits/folds. As a result, the testing data are infected with data that are very similar to the training data, resulting in in-sample testing. Hence, the evaluation will be biased, and overfitting will occur. To avoid this issue, the study employs an out-of-sample testing methodology that randomly splits the vessel routes into different folds, thereby keeping all data from a single route within a single (training or testing) fold.

To evaluate the quality of the model predictions, key statistical measurements are computed in relation to the difference between model predictions and actual vessel arrival values. The following statistics were recorded in relation to errors: Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE). In addition, to record the relevance of the predictions to the actual values, the Coefficient of Determination ($R^2$ score) and the Explained Variance score are also recorded.

3.4. Hyperparameter Tuning

In the context of machine learning, hyperparameters are variables specific to each model that control the learning process itself and can impact the model’s results. Choosing the optimal hyperparameter values is called hyperparameter tuning and is an imperative part of the overall prediction process. Several methods are available for choosing the optimal hyperparameters, and the three most popular ones are Grid Search, Random Search, and Bayesian Optimization. Grid Search will run all possible combinations of the values provided for hyperparameters and choose the combination that produces the best results. The disadvantage of this approach is that it is the most resource-intensive and slow. Random Search will select random combinations for testing optimal hyperparameters and return the combination that provided the best outcome after several iterations. While faster and less resource-intensive than Grid Search, it may not always produce the most optimal set of hyperparameters. Bayesian Optimization addresses the inefficiency of evaluating several unsuitable combinations seen in Grid and Random Search. It considers the previous evaluation results and uses a probability function to select the following hyperparameter combination that will likely generate better results. This approach reduces the number of iterations needed to identify the (near) optimal hyperparameters. Considering the hyperparameter tuning is needed only once, and enough resources were available, the Grid Search was employed to find the optimal combination of hyperparameter values for each model.

For each hyperparameter, the study identified a list of parameter values based on the literature and the specifications manual of each machine-learning model. Next, the Grid Search method generated all possible combinations of the specified hyperparameter values. For each combination in the grid, the model was trained and evaluated through cross-validation using $R^2$ as the evaluation metric. With this process, the combination of hyperparameters is identified that results in the best model performance.

Table 3. Hyperparameter domains and selected optimal values for all tested machine learning models.

	Hyperparameter	Domain	Optimal Value
Deep Neural Networks	hidden layer sizes	(50, 50, 50), (50, 100, 50), (100, 1)	(50, 50, 50)
	activation	identity, relu, tanh, logistic	identity
	alpha	0.0001, 0.05	0.0001
	learning rate	constant, invscaling, adaptive	invscaling
	solver	lbfgs, sgd, adam	lbfgs
K-Nearest Neighbors	n neighbors	4, 5, 6	6
	weights	uniform, distance	distance
	algorithm	auto, ball_tree, kd_tree, brute	brute
	leaf size	20, 30, 40	20
	p	1, 2	1
Decision Tree	splitter	best, random	best
	max depth	1, 5, 15, 20, 25	15
	min samples split	10, 50, 100, 136, 150, 200	200
	min samples leaf	100, 1000, 2000, 2221, 3000	100
	min weight fraction leaf	0.0, 0.1, 0.2	0.0
	max features	1, 2, 3, 4	4
	ccp alpha	0.0, 0.1	0.0
Random Forest	trees	60, 80, 100	100
	max features	sqrt, auto	sqrt
	max depth	20, 40, 60	40
	bootstrap	true, false	false
	minimum sample split	2, 5, 10	5
	minimum sample leaf	1, 3, 4	4
XGBoost	n estimators	60, 80, 100	100
	min child weight	1, 2	1
	max depth	3, 5, 6, 10	3
	learning rate	0.001, 0.05, 0.1, 0.15, 0.2	0.2
	colsample bytree	0.5, 0.8	0.5
	subsample	0.5, 0.8	0.5
Gaussian Naive Bayes	variance smoothing	1 $\times {10}^{-11}$, 1 $\times {10}^{-10}$, 1 $\times {10}^{-9}$	1 $\times {10}^{-9}$

lists the hyperparameters, the list of values tested, and the optimal parameter values for each model.

4. Evaluation Results

This study evaluates six machine learning algorithms for vessel ETA prediction, namely Multi-layer Perceptron Deep Neural Networks (DNNs), K-Nearest Neighbors (KNN), Decision Tree (DT), Random Forest (RF), Extreme Gradient Boosting (XGBoost), and Gaussian Naive Bayes (GNB). For comparison purposes, this study implements four model approaches from prior work: ANN by Parolas et al. [17], Gradient Boosting (GBoost) by Flapper et al. [29], DNN by Kolley et al. [19] and KNN by Kolley et al. [19]. For completeness, a comparison is performed against the ETA provided by the shipping agents as well as a simple estimation of the ETA produced using a time calculation based on the current speed and distance remaining to complete the route. All algorithms are implemented in Python 3.6 using the ‘scikit-learn’ library and all tests were run on a server equipped with two Intel Xeon Silver 4214Y CPUs (24 cores @ 2.20 GHz) and 128 GB of RAM.

For the six compared algorithms, this study used the features resulting from our evaluation (recall Section 3.2) and listed in Table 1, as well as the optimal hyperparameter values listed in Table 3. For the four algorithms from prior work, the original features and hyperparameter values are employed as presented in the respective papers. The dataset consists of AIS data collected from the Eastern Mediterranean region covering a period of two months. The data contain 172 unique vessel routes towards ports in Cyprus and originating from Europe, Asia, and the Middle East. By using a consistent dataset across all tests, the study ensures the comparability of our results with the approaches proposed in the previous research works. All tests were run using the cross-validation method where the dataset is split in folds while taking into account the vessel routes, as discussed in Section 3.3.

Table 4. Cross-validation test results for six machine learning algorithms using the features and hyperparameter values identified in this paper.

Evaluation Metric	DNN	KNN	DT	XGBoost	RF	GNB
$R^2$	0.829	0.817	0.719	0.862	0.880	0.859
Explained Variance	0.847	0.829	0.728	0.871	0.890	0.890
MAE	136.339	129.647	147.077	105.036	99.924	383.269
MSE	47,123.605	51,873.630	76,904.310	39,887.408	35,862.213	471,123.601
RMSE	203.052	210.929	252.011	177.324	163.278	646.277
Max Error	1415.880	1567.755	1726.287	1325.695	1287.346	2936.000

shows the cross-validation test results for the six compared machine-learning algorithms. To obtain a holistic view of the results, five statistical evaluation measurements are used, namely Coefficient of Determination ($R^2$), Explained Variance (EV), mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), and maximum error. $R^2$ and EV measure how closely predictions align with actual results, with values closer to one indicating better performance. EV does not account for systematic offsets and can be biased, while $R^2$ remains unbiased by such deficiencies. Hence, a high EV score coupled with a low $R^2$ score may suggest systematic prediction bias. However, both metrics were consistently close across all models, which indicates the absence of systematic bias in our results, largely due to our proposed data-splitting technique. The highest values for both $R^2$ and EV were achieved by the RF algorithm with scores of 0.88 and 0.89, respectively. GNB achieved the same high EV score of 0.89 as RF but had a slightly lower $R^2$ score (0.86). XGBoost had slightly lower EV (0.87) and $R^2$ (0.86) scores than RF and GNB, while DT, as a much simpler algorithm, yielded the lowest performance with 0.72 $R^2$ and 0.73 EV.

The other four statistical measures allow us to obtain further insights into the results and to better compare our top-performing algorithms. In particular, MAE indicates how much off predictions are from the actual values in the dataset. MSE serves a similar purpose with the differentiation that squaring amplifies larger differences; hence, it is useful in scenarios where large errors have a higher impact, but it is harder to interpret. RMSE is easier to interpret and combines the advantage of sensitivity to large errors found in MSE. As seen in Table 4, RF achieves the lowest scores across all evaluation metrics with an MAE of 99.9 min and RMSE of 163.3 min. These results are twice as good as the corresponding results of the ETA provided by the shipping agents (discussed further below), which have an MAE of 178.4 and RMSE of 305.2 min. Despite the strong performance of GNB in $R^2$ and EV, it exhibits the highest maximum error (2936 min) and RMSE (646 min) among all algorithms, which is 2–2.5× higher than the values of the next highest DT. Hence, GNB is able to follow the overall trends of arrival times but makes several large mispredictions. XGBoost, on the other hand, is only slightly worse (<10%) than RF across all metrics. Finally, DNN and KNN achieve similar performance, which is 20–30% worse than RF across all metrics.

Table 5. Cross-validation test results for the ETA provided by the agents, a simple predictor, and four models proposed by other researchers.

Evaluation Metric	Agent ETA	Simple Predictor	ANN by Parolas et al. [17]	GBoost by Flapper et al. [29]	DNN by Kolley et al. [19]	KNN by Kolley et al. [19]
$R^2$	0.655	0.090	0.800	0.827	0.408	0.401
ExplainedVariance	0.656	0.091	0.830	0.837	0.515	0.472
MAE	178.360	175.690	151.309	126.607	261.932	242.204
MSE	93,139.420	3,212,373.610	53,686.013	50,223.234	147,731.612	151,881.195
RMSE	305.180	1792.310	215.853	198.778	353.183	379.071
MaxError	4319.000	306,747.000	1182.795	1213.396	2289.798	2728.885

shows the cross-validation test results for the ETA provided by the agents, a simple predictor, and four models proposed by other researchers. The ETA provided by the agents yields an $R^2$ score of 0.66, 178 min (∼3 h) MAE, and 305 min (∼5 h) RMSE. These values reveal a big problem with ETA predictability that causes various scheduling problems in the destination ports, as discussed in Section 1. Interestingly, these evaluation metrics are all worse compared to the six machine learning models (with the exception of MAE, MSE, and RMSE of GNB), showing that machine learning is a viable alternative. While the MAE achieved by the simple predictor is very close to the agent’s ETA, all other metrics are much worse, with an extremely low $R^2$ score of 0.09. Hence, simple calculations for computing arrival times are unreliable because vessels typically exhibit complex navigational patterns, moving through specific waterways and at variable speeds.

The ANN model proposed by Parolas et al. [17] and the GBoost model proposed by Flapper et al. [29] produced similar results (albeit a bit worse) to the corresponding DNN and XGBoost models. In particular, ANN by Parolas et al. achieved 0.8 $R^2$ and 151 min MAE, while GBoost by Flapper et al. 0.83 $R^2$ and 126 min MAE. On the other hand, the DNN and KNN models by Kolley et al. [19] yielded much lower performance than our models, with $R^2$ scores of 0.41 and 0.40, respectively, that are even lower than the agents’ ETA prediction method. The biggest differentiating factor between these models is the features that are used for training and testing the models. In particular, the models by Parolas et al. and Flapper et al. use seven features (plus a few others) out of the 14 features proposed in this paper. On the other hand, Kolley et al. use only four out of the 14 proposed features, leaving out some of the most important features (according to our feature evaluation), such as distance to destination and navigation status. Overall, the features identified in this study are important for predicting vessel ETA and can be used effectively for developing strong machine learning models.

To further understand the predictive power of each compared approach, Figure 3 shows results comparing the ETA and ATA values. The blue diagonal line represents the ideal prediction and the red markings the predictions made by the various models. Our first observation is that the predictions generated by the algorithms tend to be worse for larger ETA and ATA values, which is expected since it is harder to predict the arrival time when the vessel is far away (e.g., more than 48 h in advance). The individual plots also give us various interesting insights for the different approaches. For instance, KNN (Figure 3b) seems to underpredict the ETA, while GNB (Figure 3f) typically over-predicts the ETA. In the plot of the agent ETA (Figure 3g), it is observed that a vertical line of predictions for zero ETA, which indicates that the ETA has already passed but the vessel, in reality, is still a few hours away from its destination. The simple estimation plot (Figure 3h) has many points spread far away to the right of the blue line, indicating a lot of inaccurate over-predictions. Finally, the RF plot (Figure 3d) visually verifies the strong predictive power of RF shown in Table 4 since most predictions are mostly gathered around the blue line, with only a few outliers further away.

5. Discussion

Accurate ETA prediction has several practical applications, such as management decision support where resources such as pilot boats, tug boats, cranes, berths, personnel, etc., can be scheduled ahead of time using data-driven decisions. Such decisions help in optimizing resource utilization, reducing idle times, cutting delays, reducing costs for port users, and increasing profit for port operators. According to Michaelides et al. [12], an average idle time at the Port of Limassol, Cyprus, for bulk carriers and tankers is over 8 and 12 h, respectively, with a significant possibility of reduction when more accurate planning is introduced. The effects of an efficient port stretch far beyond the port itself since ports serve as hubs through which goods are sourced in and out of local markets. Having an efficient data-driven port scheduling process through which resources are optimized means faster delivery times for goods at reduced costs that will benefit the local community being served by the port.

The Maritime industry is a major contributor to greenhouse emissions, which places it under scrutiny [33]. Furthermore, more than 940 million tons of carbon dioxide emissions are estimated to be emitted through maritime transportation. Therefore, understanding ship emissions’ magnitude and spatiotemporal distribution is crucial for developing effective strategies to reduce emissions [34]. The International Maritime Organization commits to reducing at least 50% of greenhouse emissions from the shipping industry by 2025 [35]. Therefore, accurate ETA predictions are crucial for ports worldwide to minimize vessel waiting times and ensure efficient utilization of port resources. Furthermore, precise ETA prediction supports green shipping practices and benefits the environment. Vessels emit significant amounts of greenhouse gases while idling outside ports, waiting for berths and other resources to become available. Proper planning with accurate ETA prediction, as highlighted by Michaelides et al. [12], can significantly reduce vessel idle time, thereby lowering their carbon footprint. Since ports are often located near densely populated areas, improved air quality resulting from reduced emissions can bring substantial health benefits. Additionally, ports and shipping companies that actively implement green policies are more attractive to investors and more likely to attract business, ultimately increasing their profits and overall value.

Despite the strong predictive performance of the proposed methodology, there are also some potential limitations. First, the accuracy of the predictions for vessels traveling in a particular region is likely to be affected if the model was trained with AIS data from a different region. For example, a model trained with data from the Eastern Mediterranean may not be appropriate for making ETA predictions for vessels traveling in the North Sea or narrow waterways due to differences in vessel routes, sea currents, and weather conditions. In addition, to ensure accurate predictions over time, it might be necessary to retrain the model periodically with fresh AIS data to account for changing vessel routes and the presence of newer ships with more advanced navigational technologies. Finally, any ML-based model cannot make accurate predictions when unexpected events occur. For example, when the Suez Canal was blocked for six days because a container ship had run aground, the ETA of vessels crossing the canal increased dramatically. The aforementioned limitations are all strong candidates for deeper investigation in future research.

AIS data often suffer from inaccurate and missing data that can potentially impact any attempt to accurately predict a vessel’s ETA. Prior work has developed a method based on fuzzy matching to automatically clean and correct the manually entered destination field in AIS signals [27]. Others, like Riviero et al. [36], have proposed models to recognize potential anomalies and outlier points in ship routes. Apart from some basic cleaning and extreme outlier detection, this study does not take these issues into account and raw AIS data are used for both training and testing the ML models. The results reveal the ML models are robust and still able to accurately predict ETA despite the potential presence of these issues. Nonetheless, it would be interesting for future work to investigate the impact of AIS data inaccuracies as well as integrate preprocessing techniques to clean, normalize, and remove abnormalities from AIS data into the proposed pipeline.

6. Conclusions

The ETA of vessels plays a vital role in terminal operations, as several operations and decisions at terminals depend on it, including berth allocation, berth scheduling, and quay crane assignment. Therefore, this study deals with enhancing ETA predictions of incoming vessels. For this reason, multiple machine/deep learning models, including Deep Neural Networks, K-Nearest Neighbors, Decision Trees, Random Forest, Extreme Gradient Boosting, and Gaussian Naive Bayes have been developed and trained on real-world data collected from multiple AIS base stations located in Cyprus. The study also proposes a new methodology of splitting data based on vessel routes to avoid bias and overfitting during the training and testing of machine learning models By identifying and employing important features and optimal hyperparameters specific to each algorithm, the study achieves higher performance across all relevant metrics (i.e., $R^2$, Explained Variance, MAE, MSE, RMSE, and Max Error) compared to baseline and other state-of-the-art approaches. Based on the comparative analysis, the study concludes that Random Forest is the best model in predicting ETA (with MAE of 99.92 and RMSE of 163.28), closely followed by XGBoost (with MAE of 105.04 and RMSE of 177.32). In the future, we plan to integrate preprocessing techniques to alleviate any irregularities or errors that are associated with AIS data, as well as implement automated periodic retraining of the model to ensure it can retain accurate ETA predictions over time.