1. Introduction

Globalization is leading to a rapid growth in maritime transport, both in size and number of vessels. The world seaborne trade has increased substantially in the past two decades (UNCTAD, 2013). As shown by Ducruet and Notteboom (2012), the total port throughput has exponentially increased during the last 50 years, and it has been more than doubled just in the last 20 years. The increase in throughput is linked to more vessel movements. Since ports are quite inflexible infrastructures and difficult to expand, the situation has led to higher traffic densities and eventual congestions in some areas. Ports accommodate a higher traffic demand without a waterway infrastructure expansion that implies, in many cases, longer waiting times for vessels, which reduces the efficiency of the system. Because of this increasing demand and the limited nautical infrastructure (berths and sailing areas), vessel navigation related processes in the port become decisive for port performance. Existing ports might need be optimized or expanded and new ports have to be planned considering these limitations. In both cases, their safety and capacity, among other factors, should be guaranteed and tools to assess them in different designs are required.

Maritime transportation simulation models have been proven to be useful tools to represent port operations and processes to assess port performance. Several models have been developed during the last decades with many different purposes, such as strait or waterway performance or maritime risk assessment. Regarding traffic simulation in straits, several models represent navigation systems as queueing systems, with first in first out (FIFO) sequences (Golkar et al., 1998, Köse et al., 2003). Waterway traffic representation has been another subject of interest (Almaz and Altiok, 2012, Hasegawa et al., 2001, Xiao et al., 2012, Xiao et al., 2013, Xu et al., 2015). In relation to risk assessment, a risk index-based model for vessels was developed, the safety assessment model for shipping and offshore on the North Sea (SAMSON) model, by Maritime Research Institute Netherlands (MARIN, 2015). Furthermore, a simulation model for vessel traffic based on ship collision probability has been developed (Goerlandt and Kujala, 2011). Moreover, there are models for detailed port representation and performance analysis (Bellsolà Olba et al., 2017, Groenveld, 1983, Scott et al., 2016, Thiers and Gerrit, 1998).

As described in the previous paragraph, there is a wide range of maritime simulation models with different purposes. In this paper, we present a state-of-the-art of port models and we assess their applicability to port risk and capacity assessment, as a base for the future development of a port assessment methodology based on a suitable simulation model. This research includes some models recently reviewed (Bellsolà Olba et al., 2015) and models that have been developed since then. It includes, to the best of our knowledge, all the current non commercial port simulation models, which features are described in detail in scientific publications. The commercial models are excluded because their details and features are not available. In previous work, the most relevant processes involved in port navigation were identified a more comprehensive description is presented in Section 2. Moreover, this paper reviews and assesses the models already developed on these processes in a more detailed level. The calibration of the models is an important step to ensure that they properly simulate real traffic. Hence, all the models have been assessed based on if they have been calibrated or not.

The outline of this paper is as follows. Section 2 describes the nautical processes in a port. Section 3 identifies all the required criteria for port traffic simulation. Section 4 describes the characteristics of the criteria identified. Based on these, the assessment of simulation models will be discussed in two parts, layout and navigational behaviour, in Section 5. This paper concludes with a discussion of the results with an overall model assessment in Section 6, and conclusions and remarks for future model development in Section 7.

2. Port nautical processes

Ports are complex networks, both from an infrastructure and navigation point of view. This section describes the main processes linked to the nautical infrastructure necessary to represent the vessel traffic in a port and its evaluation (Fig. 1).

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Fig. 1. Diagram of port nautical infrastructure and processes.

Traffic processes in a port start when a vessel arrives and requests access. The vessel traffic service (VTS) provides information about the berth availability and other conditions, such as weather or tide. If it is feasible to enter the port, the traffic situation is checked. Vessels with permission from the port authorities can enter the port and sail towards their destination. Otherwise, they wait outside the port in the anchorage until permission is given. Vessels with specific navigation requirements or limitations will need pilot and/or tug assistance.

Once a vessel is allowed to enter the port, it sails to a specific berth through the approach channel or entrance waterway. Until its arrival at the berthing area, each vessel will sail through different parts of the port, such as turning basins, crossings or inner basins. Each of these areas has specific requirements in sailing and manoeuvring, also depending on the vessel characteristics. Vessels can usually sail in any position inside each section of the port, but, to avoid groundings, there are some fixed corridors or paths for vessels with the deepest draughts.

After the vessel has performed all these steps, the berthing process is performed and loading/unloading operations start. These operations aim to control the movement and storage of cargo within the terminal and stacking area, entry/exit gates and rail or road connections. When the loading/unloading operations are completed, vessels are ready to depart; they are required to ask for new permission to leave the port or sail towards another berth. The reverse navigation process occurs when they are allowed to sail towards their exit.

3. Assessment methodology

Port simulation models have specific requirements to likely represent the overall vessel navigational behaviour. Hence, existing port simulation models (non commercial) are compared with respect to their current ability to represent the different traffic demands in a port and its associated processes. Fig. 1 shows the representative port infrastructure parts and the main processes. The basis of comparison within this review is to assess each of the characteristics of port processes and vessel navigation that an ideal model should be able to replicate for capacity and risk analysis of a port. This study compares the capabilities of existing models, developed with different purposes, to provide a realistic representation of vessel traffic in ports. In the following paragraphs a description of the relevance of the attributes introduced in Fig. 1 is presented.

Since manoeuvring areas (where vessels make complex turns) or inner basins can become a key element in the performance of a busy port and their analysis should be possible, the inclusion of all nautical infrastructure parts is necessary. They can lead to substantial variations in the sailing process of a vessel and thus imply variations in sailing times. Detailed research in the anchoring process has already been performed and could be implemented to make this process more realistic Huang et al. (2011). At least anchoring should not be considered as a simple queue process, where the influence of anchorage dimensions and vessel distribution does not affect its performance. In the same line, berthing processes are relevant and should be included as an independent parameter, from terminal operations in simulation models that aim to assess the vessel traffic performance. The rest of the terminal operations could be considered together.

The inclusion of tugs and pilots is necessary for any port simulation model. However, the best way to do that is not clear. Including their position at any time could make it more realistic but more time consuming, so it could be implemented with their dwell or idle times. Moreover, the number of tugs and pilots available should not be assumed to be infinite.

Explicit and detailed traffic rules can allow their assessment individually. A control and traffic verification agent has been shown to be relevant and should be considered (Xiao et al., 2013). A detailed implementation of these rules allows a more accurate analysis of the results. It might also help to identify hidden traffic management problems behind simulation results and new traffic management strategies could be implemented.

Vessel arrivals have been extensively discussed in previous research (Fararoui, 1989, Groenveld, 2001, Nicolaou, 1967, Noritake and Kimura, 1983, Pachakis and Kiremidjian, 2003, Thiers and Gerrit, 1998). It can be agreed that the most suitable distributions for new ports are negative exponential distribution (or Poisson and Erlang-1 as discrete distributions), with the desired and expected parameters. For existing ports, and thanks to AIS data availability, historical data analysis shows to be the best option to adjust the most suitable vessel demand. For new port vessel arrival estimation, AIS data from similar ports could be extrapolated to the new scenario, which would make the estimation closer to reality. Specific idiosyncrasies in vessel arrival process for each port should be taken into account, such as seasonality, because they could cause relevant differences in the final performance.

In terms of fleet composition, making clear groupings of vessels can lead to a more precise simulation model. The classification should be accurate and the different groups should be chosen based on their similarities in navigational behaviour. Although vessel speeds do not change instantaneously, the possibility of a model to include free speed choices and changing with time, fits better an accurate representation of vessel navigation in a port. In addition, the influence on vessel navigation of the infrastructure and encounters between vessels should be included. Free course choice and the influence of the infrastructure or other vessels on vessel navigation is really relevant to assess different situations and specific behaviours that might affect the safety of the port. The inclusion of human factors, such as bridge team behaviour, in the sailing path should be considered (Hoogendoorn et al., 2013). Moreover, there is an extensive research on vessel behaviour based on AIS data (Shu et al., 2012, Xiao et al., 2012) that should be used for new model implementation. These features reassemble vessel navigation close to reality and consider all the specificities given certain infrastructure design and fleet compositions.

External conditions should be evaluated in each case, but a port model should have the possibility of including any option inside their structure. Tidal windows have an important effect on port processes and performance as an operational time limitation. Weather conditions, such as wind speed and direction, can also have relevant weight in vessel traffic navigation, depending on the location of the current study (Thiers and Gerrit, 1998). These conditions should be considered as behavioural effects on vessel behaviour and some correlations can be obtained based on AIS data analysis with different weather scenarios. Another important condition that can be crucial for navigation is current.

Based on the different relevant criteria described, the assessment is divided into two parts: the first part considers the nautical infrastructure representation according to which criteria can be modelled and how detailed is each of the processes according to our purposes, plus the assistance and the traffic rules that applied in the navigation; the second part is related to how navigational characteristics are modelled and how close the simulation resembles to reality. All port infrastructure parts, and the corresponding processes, which are summarized in Fig. 1, should be included in a model, which are: 1) nautical infrastructure, 2) anchoring, 3) berthing and 4) terminal (s) operations, 5) pilot/tug assistance and 6) traffic rules. Moreover, the main criteria that affect navigation depending on each type of vessel are: 1) vessel arrival process, 2) fleet composition, 3) influence of infrastructure design or vessel encounter on the navigation, 4) course choice possibility, 5) speed variation, 6) external effects and 7) model calibration. Thus, these criteria are used as a basis for the assessment criteria in the next section, and below are explained.

The information about each of the simulation models used in this review is obtained from the published papers describing them. Since the authors of this paper do not have the models available, we assume that the description of the simulation models presented in the papers agrees with their real implementation.

4. Assessment criteria for port nautical simulation models

A detailed description of all criteria, both related to port infrastructure or navigation, identified in the previous section are presented in this section. Their influence on port nautical infrastructure processes and traffic is described and a rating system is chosen for each element in order to compare the different models.