Simulation Modeling for Ship Traffic Flow in Entrance Channel

The design of coastal entrance channel is a complex challenge, considering the stochastic environment and time-consuming calculation works. Therefore, we implement a process-interaction-based simulation model for ship operation (PI-SMSO) using Java language to help the designers to determine the dimensions of entrance channels. The PI-SMSO component simulates ships in and out through a one- or two-way traffic channel, or a one-way channel with a ship-passing anchorage, and ships discharging/loading at berths. Finally, we apply the PI-SMSO to a Chinese coal-import terminal, to explore its possible bottlenecks by evaluating the performance of entrance channel system, and determine the available improvement strategies according to the simulated port performance. The case study proves that the proposed PI-SMSO effectively simulates the ship traffic flow in entrance channel and provides a decision support for evaluating entrance channel system.


Introduction
A coastal entrance channel linking the berths of a port and the open sea is required to provide safe and convenient navigation for ships calling at ports. Recently, the rapid increase in the number and size of ships leads to further pressures on the entrance channels [1,2]. For example, the Senate Appropriations Committee appropriated $33.5 million to deepen and widen the Houston Ship Channel, which deepened the channel from 12.2 to 13.7 m and widened it from 122 to 162 m [3][4][5]; Guangzhou Port will invest $484 million to expand its 66.6 km entrance channel into two-way traffic for container ships of 100,000 deadweight tons (DWT) [6]. Considering the high costs to expand entrance channels, a tool or model is needed to help the designers to evaluate the capacity of entrance channel and then to determine when to expand the channel and to select the dimensions of the expanded channel. An entrance channel system can only be schematized as a complex system as it integrates with different ship types, the layout of water areas, and berths. In consideration of the stochastic characteristics of a port system, to explore the performance of integrated system, queuing theory is not applicable, and a simulation technique has to be used by simulating ship operations in and out of a port via entrance channels, e.g., a one-or two-way channel, especially a longer one-way channel with passing places [7,8]. To simulate the complex port system, the "process description method" or "object-oriented method" is considered to be appropriate and efficient [4,5,7]. Moreover, other important procedures, such as model verification and validation and simulation replication determination, should be conducted before productive simulation runs are started. It seems obvious that these procedures are impossibly time-consuming and complex for the designers. Therefore, we first developed a process-interaction-based simulation model for ship operation (PI-SMSO), which involves moving in and out of a port through entrance channels and handling cargoes at berths and automatically evaluates the performance of the stochastic port system. Finally, the effectiveness and applicability of the PI-SMSO are supported by a case study conducted at a coal terminal in China.
The remainder of this paper is organized as follows. First, the processes of ship operation in entrance channels are discussed for one-and two-way channels and one-way channels with ship-passing anchorage (SPAC). Next, this study implements a process-interaction-based simulation model for ship operation (PI-SMSO), and it classes for PI-SMSO. Then, the proposed PI-SMSO is applied to a Chinese coal-import terminal and used to evaluate entrance channel system and available improvement strategies. Finally, concluding remarks and future researches are presented.

Entrance channel types
The process of ship operation depends on the types of entrance channels, such as one-or two-way channels, and one-way channels with ship-passing anchorage (SPAC) [2,4,5,9]. As shown in Figure 1, one-way channels only allow vessels to move in the same direction (Figure 1(a)), which is used for low ship traffic or when excavation of larger channel would be very expensive; two-way channels reduce one-way restrictions and allow inbound and outbound ships to pass each other (Figure 1(b)), which is considerable for improving navigation efficiency. However, expanding into a two-way channel costs highly by dredging/excavation especially for the very long channel. In some cases, a compromise is created by constructing SPAC along the longer one-way channel [7]. As illustrated in Figure 1(c), the SPAC divides the channel into two parts (Channel A and B) and provides temporary moorings for lower-time-value ships (outbound ships in Figure 1) waiting until other vessels from opposite directions pass by. In this case, when outbound ships are traveling in Channel B, inbound ships can enter Channel A rather than waiting in the outside anchorage as shown in Figure 1(a). In this way, ships traveling in opposite directions in a one-way channel can pass each other similar to a two-way channel. Figure 2 describes the flow of ship operations in one-and two-way entrance channels, which focuses on the activities conducted in the anchorage area, entrance channel, and at berths. As illustrated in Figure 2(a), ship operation begins with the arrival of an inbound ship. This inbound ship may or may not wait in the anchorage area, depending on the state of weather, berth congestion, and channel navigability. As illustrated in Figure 2(b), on days with good weather, the berth-assigned ship enters entrance channel in the following two cases: (1) for a one-way channel, no outbound ships are in the channel, and both the navigable depth and the distance between fore-and-aft inbound ships (if there are inbound ships in the channel, we call safety distance) satisfy the navigation requirement or (2) for a two-way channel, both the navigable depth and the safety distance satisfy the navigation requirement. Usually, this ship is guided by one or more tugboats to the assigned berth through entrance channel and then starts to unload (load) the cargoes onto (from) the quay after necessary preparation. Finally, once cargo unloading and loading is finished, outbound ship leaves berth, enters channel, and leaves port in the following three cases as illustrated in Figure 2(c) [7,10]: (1) for a one-way channel, no inbound ships are in the channel, and both the navigable depth and safety distance satisfy the safety requirement or (2) for a two-way channel, both the navigable depth and safety distance satisfy the navigation requirement. If a port or entrance channel (or both) is closed due to adverse weather (i.e., strong winds, high waves, or heavy fog), we must know the number of days with adverse weather and how these heavy-weather days are usually distributed in a year. Figure 3(a) shows the overall logic of ship operations in a one-way channel with a SPAC. Setting a SPAC in a one-way channel changes the logic of checking channel availability in Figure 2(a). The detail on changes is discussed in the following:

Ship traffic flow for a one-way traffic channel with a SPAC
(1) Figure 3(b) illustrates the logic flowchart for checking channel availability for an inbound berth-assigned ship (CCA4IS). As shown in Figure 3(b), on days with good weather, the berth-assigned inbound ship enters entrance channel in the   can accommodate these outbound ships, and the last outbound ship in Channel B can reach the SPAC before this ship does.
(2) Figure 3(c) shows the logic of checking the availability of Channel B for an outbound ship at berth after finishing cargo unloading (CCBA4OS). As illustrated in Figure 3(c), the ship deberths and enters entrance channel in the following two cases: (1) if no inbound ships are traveling in Channel A, the navigable depth and safety distance satisfy the safe navigation requirement or (2) if one or more inbound ships are traveling in Channel A, the SPAC has at least one idle mooring Simulation Modelling Practice and Theory 6 position for this outbound ship, and this outbound ship can arrive at the SPAC before the first inbound ship in Channel A.
(3) Figure 3(d) checks the availability of Channel A for an outbound ship from the SPAC (CCAA4OS), and the ship leaves SPAC and enters Channel A in the following two cases: (1) no ships are traveling in Channel A, and no higher-priority ships are waiting in the outside anchorage or (2) if outbound ships are traveling in Channel A, both the navigable depth and the safety distance satisfy the safe navigation requirements.

Simulation modeling of ship operation
To evaluate the performance of the stochastic port system, we implement a process-interaction-based simulation model in Java™ [11], which simulates ship operations in one-or two-way channels, and a longer one-way channel with a SPAC according to the logic flowchart in Section 2.

Process-interaction-based simulation
There are basically three approaches that can be used for discrete event simulation: the event-based, the activity-based, and the process-interaction approach. Process-interaction simulation is a typical discrete event simulation paradigm. Since processes resemble objects in the real world, process-interaction simulation is often easy to understand, which is used in HLA (high-level architecture), DIS (distributed interactive simulation), and other object-oriented distributed simulations [12]. Therefore, we apply the process-interaction approach to the ship operation simulation model in this study.
The process-interaction worldview provides a way to represent a system's behavior from the active entities point of view according to the authors of SIMULA [13]. Thus, a system is modeled as a set of active entities in interaction, and the life cycle of each active entity consists of a sequence of events, activities, and delays. So in the ship operation simulation, a ship is an example of an active entity. Each ship performs the following sequence of activities: arrive at a port area, wait in the anchorage area, transit from anchorage area to berth, get cargo handled, leave the berth and enter the channel, and depart from port. Besides, the model also includes other components providing services for ships, such as anchorage area, entrance channel, and berth.

Simulation implementation
According to the process-interaction worldview, an active entity requires special mechanisms for interrupting, suspending, and resuming its execution at a later simulated time. Thus, Java programming language is suitable as it offers at least a SIMULA's coroutine-like mechanism. Therefore, we implement a process-interaction-based simulation model for ship operation (PI-SMSO) in Java programming language, and the implemented Java classes consist of foundational class library for process-interaction simulation (PIS library) and business class library for ship operation simulation (SOS library), as shown in Figure 4.
PIS library is a collection of public classes for process-interaction simulation, such as Process, Entity, Queue, and Simulation as shown in Figure 4. The Process class is the base class for a process-interaction simulation which extends java.lang. Thread and provides all of the necessary operations for the simulation system to control the simulation entities within it, and for them to interact with it and each other, such as activate, suspend, reactivate, and terminate a process. The Entity class represents the entities within a simulation which is derived from Process and has an independent thread of control associated with them at creation time, allowing them to convey the notion of activity necessary for participating in the simulation. The Queue class stores the inactive simulation processes within the simulation. The Simulation class derived from Process, which starts and stops a simulation, schedules the simulation processes: remove the process at the head of the queue and reactivate it. In simulation models, Processes are managed by a Simulation scheduler and are placed on a Queue (the event list).
SOS library is a collection of classes specialized for ship operation simulation, which are derived from the PIS library. Based on the components in a ship operation system, SOS library mainly consists of Ship, Port, Terminal, Anchorage, EntranceChannel, ArrivalSimulation, and EntranceChannelSystem classes as shown in Figure 4. The Port, Terminal, Anchorage, and EntranceChannel classes are permanent entity objects to provide services for Ship entities. The ArrivalSimulation class generates Ship entities randomly according to the ship arrival pattern. The EntranceChannelSystem class, a subclass of Simulation, schedules the processes of ship entities in and out of the port, makes a statistics analysis on simulation results, and outputs every ship's waiting time and berth's utilization ratio. The Ship class, a subclass of Entity, represents a ship entity, which is the core component of a process-interaction ship operation simulation model. The primary Java classes of PI-SMSO are illustrated in Figure 4, and it runs a simulation experiment as follows: (1) Class ShipOperationSimulation is the control class of a simulation experiment. It initializes and activates the ship arrival process (Class ArrivalSimulation) and initializes port resources (e.g., Class Port, Berth, Anchorage, and EntranceChannel) and environmental conditions (e.g., Class Current, Wave, and Tide), then starts the simulation experiment. (2) Class ArrivalSimulation generates a series of Ships according to an interarrival time distribution [10,14,15]. For example, negative exponential distributions (NEDs) can be used to describe the arrival process [2], and its density function is f (t) = λ e − t (λ = arrival rate; t = inter-arrival time).
(3) Class Ship performs all activities of a ship as illustrated in Figure 5 and records all necessary times related to performance measures.
Method arrive records the ship's arrival time and initializes its attributes (e.g., ship tonnage, dimensions, and cargo capacity).
Method allocateBerth requests for a berth according to berth allocation policy and queue priority [16], such as first-come-first-serve rule, longest/shortest processing time, and largest/smallest ship size. If a berth is assigned to this ship, the method records the time of berth availability and steps to Method checkECA4IS. Otherwise, this ship enters anchorage and waits (Method waitInAnchorage).
Method checkECA4IS checks weather, water depth, safety distance, and traffic situation for permission to enter channel as illustrated in Figures 2 and 3. In case a problem exists, the ship enters and waits in anchorage (Method waitInAnchorage). Otherwise, it steps to Method enterPort.
Method waitInAnchorage checks the availability of a free berth for no-berthassigned ships (Method allocateBerth) and/or the availability of entrance channel  for berth-assigned ships (Method checkECA4IS). Once all states meet safety requirements, the ship leaves anchorage, records the waiting time caused by berth occupation or channel unavailability, and enters Method enterPort.
Method enterPort transits this ship to the assigned berth via entrance channel and steps to Method handleCargo.
Method handleCargo discharges/loads cargoes from/onto the ship over a random berth service time and steps to Method checkECA4OS. For example, berth service time for each type of ship is fitted to an Erlang-k distribution [2,17], and its probability density function is f (t) = (k ) k t k−1 e −k t / (k − 1) ! (μ = the number of ship services per day, and k = shape parameter).
Method checkECA4OS checks weather, water depth, safety distance, and traffic situation for permission to enter channel and leave the port. For one-and two-way channels without SPAC, if the checkECA4OS is "RURE," the outbound ship leaves the berth, travels through channel, and steps to Method leaveFromPort. For one-way channels with a SPAC, if the Channel B is available, the outbound ship leaves the berth, seizes an anchorage in SPAC, then travels through Channel B, and steps to Method waitInSPAC.
Method waitInSPAC records the time of arrival at SPAC, accommodates outbound ship mooring, and waits until Channel A is accessible. If Chanel A is accessible, the ship leaves the SPAC and enters Channel A and records the time of departure from SPAC, releases the occupied SPAC's anchorage, travels through Channel A, and steps to Method leaveFromPort finally.
Method leaveFromPort makes the ship entity exit the port system and records its departure time.
(4) Class ShipOperationSimulation finally stops the simulation experiment, updates the turnaround time and number of inbound and outbound ships, performs necessary statistical analysis, and outputs the values of port performance indicators.

Model verification and validation
This PI-SMSO model is verified and validated to confirm that it is correctly implemented with respect to the process of ship operation; we can use it to evaluate the port performance and then do more analysis. First, the model is developed through sub-models and individually examined by a subject-matter expert. Second, tracing approach comparing the simulation results with manual calculations is used to check the logic implemented in the model throughout the development of simulation model. Finally, we performed several simulation experiments based on real data on hand and compare the simulated values of key performance indicators with the real operational data, to check the accuracy of the model's representation of the real system [14,18]. In this study, the key performance indicators we focus on are average turnaround time, average waiting time, average service time, waitingtime/service-time ratio, and berth utilization ratio; see Section 3.4.
The ATAT is the total time between ship arrival and departure, which portrays the port capability and the ability to provide services with high productivity and performance [5,20]. The AST is the average value of the time between ship berthing and departure. The AWT is the average value of waiting time for the availability of a berth (AWTB) and the entrance channel (AWTC) [4,5,21]. AWT/AST is the ratio of the AWT to the AST, which is widely used as a measure of the service level of a terminal [21]. Berth utilization is the ratio of time the berth is occupied by vessels to the total time (1 year). High berth occupancy is a sign of congestion (>70%) and hence decline of services, while low berth occupancy signifies underutilization of resources (<50%) [22].

Case study
A specialized coal terminal in southern China serves local coal imports mainly from ports of Qingdao and Rizhao. Currently, this terminal has three berths and a one-way entrance channel, and its port throughputs is 16 million tons per year. According to its master planning, the throughputs of coal imports will be expected to increase to 20, 24.5, and 36 million tons per year in sequence as shown in Table 1, considering the rapid development of thermal power generation and steelmaking industries. Thus, as shown in Tables 1 and 2, more ships, even larger ships (e.g., 70,000-and 100,000-DWT bulk carriers), will call at this terminal, which leads to further pressures on the berths and entrance channel. Therefore, we initiate an evaluation of port system for Stages II, III, and IV, including entrance channel (see Table 3) and berths, to evaluate its performance (i.e., AWT/AST, AST, ATAT, AWTC, AWTB, and AWT, and the acceptable AWT/AST is 0.4) and identify the possible bottlenecks and then explore improvement strategies to improve its port performance based on a proactive long-term vision. Table 4 lists the characteristics of environmental conditions including tides, waves, and current. We also collected historical data, such as the intervals between successive inbound ships, berth service times for each design ship, and port performance (ATAT, AWT, and AWT/AST). And we deduce that both intervals between ship arrivals and berth service time follow exponential distribution, and the parameters of each distribution (μ and λ) are listed in Table 5

Verification and validation
We run a series of simulation experiments based on Tables 4 and 5 and compare the simulated results with real data from this coal terminal of Stage I to verify and validate the proposed simulation model.   results from Table 6, we find that all average values of simulation results lie within 7% difference from the actual values, which means the established simulation model built for this terminal is considered to be close to the actual system.

Evaluation of current berths and channel system
We evaluate the performances of the berths and entrance channel system for Stages II, III, and IV using the proposed simulation model, provided that the dimensions of entrance channel remain unchanged. Table 7 shows the channel dimensions, the values of port performance indicators for Stages II, III, and IV.  (1) In Stage II, the annual port throughput is expected to hit 20 million tons of coal. If the berths and channel dimensions remain unchanged, the AWT/AST is as high as 1.15 beyond the accepted AWT/AST of 0.4 as shown in Table 7. So the terminal will be running with an extremely low efficiency, which leads to higher vessel wait. Note that 90% of the AWT (17.9 h) is spent waiting for the availability of a berth (AWTB = 16.1 h). Therefore, it seems that more berths should be provided in order to improve port performance.
(2) In Stage III, the expected port throughput is 24.5 million tons of coal; the channel is still a one-way channel, but a new 70,000-DWT berth is built to accommodate deeper-draft bulk carriers. Thus, for serving larger ships, the entrance channel has to be expanded as shown in Table 7: the channel depth being expanded to 17.1 m, channel width being expanded to 180 m, and channel length being expanded to 9810 m. Meanwhile, by building a new berth, the AWT/AST falls to 0.41 from 1.15, the ATAT falls to 28.9 h from 35.4 h, and the AWTB is only 6.0 h with a decrease of 10 h from 16.1 h. Therefore, in Stage III, the terminal with a one-way channel will be operated with an acceptable service level without expanding oneway to two-way channel.
(3) In Stage IV, the expected port throughput is 37 million tons of coal; the channel is still a one-way channel, but a new berth is built to serve the 100,000-DWT bulk carriers. So to serve 100,000-DWT ships, the dimensions of one-way channels are expanded to 17.55 m depth, 224 m width, and 10,200 m length. Meanwhile, the AWT/AST is 0.63, higher than the accepted service level of 0.4. And the ships take 86% of the AWT to wait for the availability of a berth. Therefore, expansion strategies are needed to improve port performance in Stage IV.

Improvement strategies and their performance
According to simulation results and analysis, we propose three types of improvement strategies for Stages II and IV, including setting a ship-passing anchorage (SPAC), expanding into a two-way traffic channel (E2TWC), and building new berths (BNB), and the detailed parameters are given in Table 8.
We run the simulation models to get simulation results for all proposed alternatives and to explore the performance improvements as follows.  As shown in Table 9, for Stage II, when comparing the current AWT/AST of 1.15, the AWT/ASTs for SPAC, E2TWC, and BNB strategies are 0.77, 0.56, and 0.25. Therefore, strategies SPAC, E2TWC, and BNB all improve the service level, and the BNB strategy is the best way. However, according to the required AWT/AST of 0.4, only the BNB strategy by building a new 70,000-DWT berth is practicable in Stage II.
Similarly, we also collect the AWT/ASTs for both SPAC and E2TWC strategies in Stage IV and list them in Table 10. As shown in Table 10, the AWT/ASTs for SPAC and E2TWC strategies are 0.37 and 0.35, so that both SPAC and E2TWC strategies are most effective alternatives in Stage IV from point view of AWT/AST. However, considering the costs of these two strategies, we suggest the strategy SPAC as a practical alternative for Stage IV.
Finally, we list the proposed entrance channel and berths for Stages II, III, and IV in Table 11. Therefore, this application shows that the implemented simulation model is helpful for evaluating the capacity of entrance channel, identifying the bottlenecks in port system, and determining an optimal improvement strategy effectively for improving port performance.