With the rapid development of the shipping industry, the volume of ship traffic has increased significantly in recent years [
1]. The increasing volume of ship traffic makes marine traffic much busier and more crowded, especially in the waterway off the coast, where ship activity is more frequent. Although the increasing ship traffic volume can contribute to the development of the economy, it will also pose more threats to marine traffic safety. On the one hand, the increasing ship traffic volume will lead to an increase in traffic density in the waterway, making the ship traffic more crowded and thus increasing the possibility of collision accidents. On the other hand, the growth of ship traffic also leads to the complexity of ship traffic. The complex ship traffic will make it more difficult for ships to avoid collision [
2]. It will also make it more difficult for marine surveillance operators to monitor and organize the ship traffic in the waterway. In dealing with the complex traffic situation, marine surveillance operators may face the cognization pressure only by their subjective judgment. The efficiency of marine traffic supervision will be damaged and further affect marine traffic safety. Therefore, how to identify the complexity of marine traffic sufficiently and accurately under the increasingly complex traffic situation is helpful to alleviate the risk of collision between ships and improve the efficiency and effects of marine surveillance operators in monitoring and organizing the ship traffic in the waterway.
The rapid growth of maritime traffic in the past decade has led to an increase in marine traffic complexity, which also facilitates the development of navigational equipment. Automatic Identification System (AIS) is one of the advanced navigational equipment; it is an advanced telecommunication and information system, which can broad-cast the information of a ship to other surrounding ships and shore stations by VHF [
3]. AIS data contains plenty of ship information related to real-time sailing. With the information, a lot of information related to marine traffic situations can be extracted and analyzed. In recent years, in order to study marine traffic safety under the conditions of increasing complexity, scholars in the marine traffic field have proposed a lot of new models or methods with plenty of data. Silveira et al. [
4] utilize AIS data to analyze the marine traffic pattern in a dense water area and determine the collision candidate ships by calculating the future distance between ships so as to evaluate the ship collision risk. Wu et al. [
5] depict the global ship density and traffic density map with a bulk of AIS data in different resolutions, which can represent the marine traffic safety level to some extent. Yu et al. [
6] propose a novel method to identify the near-miss collision risk when multiple ships encounter it. The method is established based on ship motion behavior and can evaluate the multi-ship near-miss collision risk from temporal, spatial, and geographical perspectives. The method can also improve the level of risk assessment by identifying the different levels of near-miss collision risk of different ships and also provide some reference and help to put forward the measures to reduce the risk. Zhang et al. [
7] propose a new method to identify collision risk based on a convolutional neural network. The convolutional neural network can analyze and recognize the image built by AIS data to rapidly identify the collision risk under encounter. Bakdi et al. [
8] propose an adaptive ship domain to identify the collision risk and grounding risk under complex traffic situation. The model can also be used to identify the marine traffic risk considering maneuvering limitations. The method can improve the accuracy of real-time marine traffic risk identification under large-scale monitoring. Wen et al. [
9] propose a marine traffic complexity model according to air traffic control. The model can assess the complexity level in the water area by evaluating the density and the collision risk of ship traffic, respectively. The model is established based on ship relative motion parameters and can assess the overall complexity level of ship traffic by interpolation technique. Rong et al. [
10] conduct spatial correlation analysis of ship clusters based on the characteristics of marine traffic. The authors use AIS data to describe the collision hotspots along the Portuguese coast and analyze the correlation between the collision hotspot and the characteristics of marine traffic. The method can be helpful in improving marine traffic safety and reducing the collision risk in the water area. Zhang et al. [
11] propose a two-stage black spot identification model, which can detect more risk in the water area. The model has a higher detection rate for marine accidents. The authors use the model to depict the black spot in the Jiangsu section of the Yangtze River by historical data. The model is helpful in optimizing the search and rescue resources and improving the safety management level. Liu et al. [
12] propose a novel framework for real-time regional collision risk prediction based on a recurrent neural network approach. After identifying the regional collision risk, the optimized RNN method is used to predict the regional collision risk of a specific water area in a short time. The model is useful for collision risk prediction for the water area under complex traffic situations. Liu et al. [
13] propose an improved danger sector model to identify the collision risk of encountering ships. The model considers the course alteration maneuver by taking ship maneuverability limitation into consideration. The model is helpful for calculating the collision risk between ships in complex traffic situations. Zhen et al. [
14] propose a novel regional collision risk assessment method, which considers aggregation density under multi-ship encounter situations. The model can more intuitively and effectively quantify the temporal and spatial distribution of regional collision risk under complex traffic situations and improve the efficiency of traffic management. Yu et al. [
15] propose an integrated multi-criteria framework for assessing the ship collision risk under different scenarios dynamically. The framework can identify collision parameters and candidates according to ship offices’ experience, which is useful for analyzing the ship traffic under complex situations. Merrick et al. [
16] analyze the traffic density of the proposed ferry service expansion in San Francisco Bay. They establish a simulation model to estimate the number of vessel interactions and the increment caused by expansion plans. Utilizing the model, the geographic profile of vessel interaction frequency is presented. Altan et al. [
17] analyze the marine traffic in the Strait of Istanbul. The ship attributes are tracked by a grid-based analysis method. Through the analysis, they summarize some conclusions about vessel distribution, draught, speed exceed, and the influence on traffic patterns. Ramin et al. [
18] use AIS data to research the complex marine traffic in Port Klang and the Straits of Malacca. The method applied was time-series models and associative models. Utilizing the methods, the density of ships in Port Klang and the Straits of Malacca can be predicted and forecasted. Kang et al. [
19] use AIS data to estimate the ship traffic fundamental diagrams in the Strait of Singapore, which plays a crucial role in international freight transportation. The ship traffic fundamental diagrams investigate the ship traffic’s speed–density relationship and can be used to estimate the theoretical strait capacity. van Westrenen et al. [
20] utilize AIS data to analyze the traffic on the North Sea. The near misses are detected by using ship-state information. Through the research, they conclude that the near misses are not spread evenly over the sea but are concentrated in a number of specific locations. Du et al. [
21] propose a new method to improve near-miss detection by analyzing behavior characteristics during the encounter process in the Northern Baltic Sea. The ship attributes, perceived risk, traffic complexity, and traffic rule are included in evaluating ship behaviors. Moreover, the risk levels of detected near misses are quantified. Endrina et al. [
22] conduct a risk analysis for RoPax vessels in the Strait of Gibraltar. The first two steps of the IMO Formal Safety Assessment are used to present the results with the accidents statistics covering 11 years. In addition, a high-level model risk for collisions was built through an Event Tree, and the individual and social risks were calculated.
It can be found that most of the recent studies on complex marine traffic are based on a large number of ship data. On the one hand, it benefits from the rapid development of computer and information technology, which enables these data to be stored, analyzed, and calculated. On the other hand, it benefits from the availability of a large number of AIS data. The utilization of these large amounts of real AIS data can improve the accuracy of the model, improve the accuracy of the results, and make the results obtained by the model more realistic. The recent studies also make it possible to study complex marine traffic from temporal and spatial perspectives. Previously, we proposed a ship density model based on the radial distribution function [
23]. The model can calculate the ship density and traffic density in the specified water area and can evaluate the complexity of marine traffic to some extent. The model can help marine surveillance better understand marine traffic in complex situations and improve their monitoring efficiency. However, the model only considers the ship positions and the distance between them and can only quantify the complexity of marine traffic from a position perspective, which makes the accuracy of the complexity results limited in some cases. Therefore, in this article, a new marine traffic complexity model is supposed to be proposed in order to evaluate the complexity level of marine traffic in a waterway. This model not only considers the spatial distribution characteristic of ship traffic but also incorporates the ship motion parameters in it, which can identify the complexity level more sufficiently and accurately in a waterway and assist marine surveillance operators to better acknowledge, monitor, and organize the marine traffic under complex situations. The reminders of the article are arranged as follows. In
Section 2, the marine traffic complexity model was established based on the radial distribution function, which considers the complexity of ship motion and ship position, respectively. In
Section 3, the proposed model was validated by some experimental case studies in Bohai Strait waters with simulated data and real AIS data. In
Section 4, the effectiveness of the proposed model was discussed, and the advantage of the proposed model was analyzed compared with the previous model. Moreover, the limitations of the proposed model were presented. In
Section 5, the conclusion was drawn, and some future studies about this model were presented.