Simulation Modelling of Maritime Port Operations: Analysing the Impacts of Disruptions on Ports

Abstract

Ports serve a vital role in global trade as they facilitate the transportation of goods by providing points at which intermodal transportation can occur. Increasing capacity demand at maritime ports coupled with the growing need to increase the efficiency of ports has led ports to increasingly adopt various information technologies and operational technologies (IT/OT) in order to improve port efficiency. These IT/OT assets help automate and efficiently run various operations in the port. Any disruption that compromises the availability of these IT/OT assets (particularly crane assets) has the potential to cause disruption to port activities, causing wide-ranging delays to port operations and potentially also affecting the wider supply chain. In particular, this paper looks to propose and use a port operations simulation model to estimate how the availability of crane infrastructure affects port operations and port efficiency. The paper uses the simulation model to estimate relations between crane asset disruption and port throughput, port service times and port queue lengths. In order to illustrate the use of the simulation model, the paper uses a major EU maritime port-the port of Valencia-as a basis on which analysis is conducted.

Full text

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Simulation Modelling of Maritime Port Operations:
Analysing the Impacts of Disruptions on Ports
Kemedi Moara-Nkwe1, Kimberly Tam1, Rory Hopcraft1, and Kevin Jones1
1Maritime Cyber Threats Research Group, University Of Plymouth
Abstract
Ports serve a vital role in global trade as they facilitate the transportation of goods by providing points at which inter-
modal transportation can occur. Increasing capacity demand at maritime ports coupled with the growing need to increase
the efficiency of ports has led ports to increasingly adopt various information technologies and operational technologies
(IT/OT) in order to improve port efficiency. These IT/OT assets help automate and efficiently run various operations
in the port. Any disruption that compromises the availability of these IT/OT assets (particularly crane assets) has the
potential to cauğse disruption to port activities, causing wide ranging delays to port operations and potentially also
affecting the wider supply chain. In particular, this paper looks to propose and use a port operations simulation model
to estimate how the availability of crane infrastructure affects port operations and port efficiency. The paper uses the
simulation model to estimate relations between crane asset disruption and port throughput, port service times and port
queue lengths. In order to illustrate the use of the simulation model, the paper uses a major EU maritime port - the port
of Valencia - as a basis onto which analysis is conducted.

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I. Introduction
Maritime ports play a very important role in global trade and are vital for components of the global supply chain. They
act as points to facilitate the inter-modal transportation of a wide variety of goods including containerised cargo, bulk
cargo, liquid bulk and even passenger traffic. It is therefore very important for all stakeholders to have a very clear
understanding of how these important elements work and also better our understanding of how they can be made more
resistant to external shocks.
Simulation models have played a major role in the modelling of complex port operations by giving practitioners and
researchers tools they can use to assess the impact disruptions have on port operations [1] [2] [3]. These disruptions could
come about due a wide range of reasons including human error and/or cyber attacks. The work in [1] looks at the problem
of analysing complex port operations using discrete event simulation techniques. The work characterised the key physical
processes that take place in a maritime port and investigated how these changes affect key port performance indicators
such as throughput and average port service times. The goal of the work was to investigate how sensitive these indicators
are to different variables in a port. Another key piece of research work in this area can be seen in [2], here the authors use
simulation modelling to investigate the problem of re-routing of ships in the event that a port, or a sub-set of ports, where
to become unavailable to service any vessels due to a crisis situation. If a maritime port were to become unavailable for
some reason (e.g. due to some major incident), vessels destined for that port would need to use alternative ports to carry
out operations. The paper used simulation to investigate how that re-routing process could be undertaken. The paper
considers the best alternate routes that may need to be taken given that a port is unavailable but does not consider the
time it would take for the system to recover if the disrupted port(s) become available again.
These works and other related works have demonstrated the wide range of use cases that discrete event simulation (DES)
can have in analysing port operations in the maritime domain - particularly for maritime ports. This paper expands on
this work by investigating the short and long term impacts that disruptions to crane operations will have on overall port
operations. This is done by proposing an open discrete event simulation (DES) based maritime port operations simulator
and using it to investigate the effect temporary crane unavailability has on i) ship turnaround times , ii) vessel queue
lengths and iii) port delays. The port operations model uses information on the traffic flowing through a port to estimate
the nature of port operations before, during and after disruptive events. The model can be used to model a wide variety of
ports. In this paper, the port of Valencia - a major port in the mediterranean - has been used as an illustrative example.
The port is the sixth largest port in Europe [4].
II. Port Operations Model
A port needs to undertake a wide range of operations in order to facilitate the movement of goods through the port. In
this paper, these processes will be divided into two different categories i) physical port processes and ii) port support
processes. Here, physical port operation processes refer to processes that directly facilitate the physical movement of goods
such as the unloading/loading of cargo, transporting/moving cargo within the port and transporting cargo out of the port.
Support processes are those processes that help facilitate the physical operations by providing support services such as
berth allocation planning, port planning/scheduling, stowage planning, power production and coordination services. These
support services are critical in ensuring the port operates efficiently and are usually carried out with the assistance of
various IT hardware and software (such as terminal planning software).
Figures 1 and 2 show the high level physical process flow and the support process flow respectively. This shows at a
high level what the proposed simulation is capable of considering when calculating delays regardless of the cause of the
event. In order to carry out the different tasks that need to be completed in order to run both the physical and support
processes, the maritime port would use a wide variety of assets, some of which will be IT/OT assets such as computers
(information technology) and cranes (operational technology). If any of these assets were to become unavailable due to
some incident, such as a cyber attack, then port operations could be negatively affected [5]. This paper aims to propose
an open port throughput model which can be used to estimate the impacts that would be felt if key IT/OT assets became
unavailable (or partially unavailable) for a period of time in a maritime port (for the duration of the paper we will simply
use the phrase ’port’ when referring to a maritime port). These IT/OT assets could be made unavailable by some incident,
such as a cyber-attack. In particular, this paper proposes a maritime port simulation platform and illustrates its use by
estimating the impacts that would be experienced if the maritime port’s cranes (or portion of cranes) where to become
unavailable for a certain period of time.
Ports use a wide variety of cranes for cargo handling operations including ship-to-shore (STS) cranes, rail mounted
gantry (RMG) cranes and rubber tyred gantry (RTG) cranes. STS cranes are used to load/unload cargo into and out
of the vessel and RMG/RTG cranes are used to load/unload (or move) cargo into and out of the container yard. These
crane types all have different handling capabilities and may have different OT assets attached to them for monitoring

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and/or maintenance purposes. it is therefore important for any port operation model to account for these differences when
simulating operations.
Ship Arrival Ship At Berth STS Crane
Unloading
Yard Truck
Transport RTG Unloading
Ship Departure Ship At Berth STS Crane
Loading
Yard Truck
Transport RTG loading
Train/Truck Arrival Train/Truck Wait RTG Crane
Unloading
Train/Truck Arrival Train/Truck Wait RTG Crane
Unloading
Container Yard
Fig. 1: Maritime Port Container Handling Physical Processes
Ship Arrival Berth Schedule Planning Ship Stowage Planning
Electronic Data Exchange Handling Sequence
Planning
Shipside Operation
Handling Equipment
Dispatch Plan Yard Layout Planning
Fig. 2: Maritime Port Container Handling Support Processes
In order for the model to simulate port operations, certain parameters that describe the nature of the traffic that flow
through the port have to be input into the model. This includes information characterising i) the arrival process, ii) the
average quantity of containers (in TEU) loaded/unloaded per port call, iii) the service time distribution per vessel, iv) the
proportion of input/output containers destined to be transhipped and v) the mean container dwell time. Each of these
characteristics are important, and the following subsections will go into each of these in more depth.
A. Ship Arrival Time Distribution
A maritime port has the primary purpose of facilitating intermodal transport by loading, unloading, processing and storing
cargo that is brought in and out of the port using some vehicle, such as a ship, train or truck. The points in time at
which vessels arrive in a real port are not deterministic but rather follow some random probability distribution. It can
be shown that if an arrival process is characterised by i) each time instant being independent of every other time instant
and ii) each time instant having equal likelihood of corresponding to an arrival then the arrival process will be poisson.
If the number of vessel arrivals is λa year, then this means ships arrive at a rate of λ/n per unit time, where unit time
here is defined as being 1/n years. If nis chosen such that the probability that more than one ship arrive in a unit interval
is small (i.e. nis large), then the probability that one ship arrives in any interval is p=λ/n. The probability that kships
arrive in nintervals is thus

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P(X=k) = 󰀕n
k, (n−k)󰀖pk(1 −p)n−k
=󰀕n
k, (n−k)󰀖·λk
nk󰀕1−λ
n󰀖n−k
which evaluates to the expression for the poisson distribution (equation 1) if nis large [6] [7]. Where the poisson distribution
is defined as being the distribution shown in the equation 1.
P(X=k) = λke−λ
k!(1)
Let Abe an n-bit array that is used to record whether there has been an arrival in each of the nintervals in a year. In
addition to this, let ‘1’ in the ith bit of Arepresent an arrival and let a ‘0’ represent no arrival. If there are karrivals
then there are 󰀃n
k󰀄different unique arrival patterns that could correspond to this particular scenario. Given that each
of these arrival patterns have a likelihood of occurring of pk(1 −p)n−k, the probability that there are karrivals is the
sum of all these 󰀃n
k󰀄arrival patterns, which [6] shows evaluates to the equation outlined in equation 1. It is generally
considered that the long term arrival distribution of ships approximates to a poisson distribution [8]. Following from this,
the inter-arrival time distribution (the time between successive arrivals if the arrival time distribution is poisson) will then
be the exponential distribution.
A key assumption to note when utilising the poisson distribution to model arrivals is that the distribution, when
parameterised using mean arrivals per year, models each time instant having equal likelihood of corresponding to an
arrival. This is appropriate where the arrivals are approximately equally distributed throughout the period of simulation
or when the mean arrivals in different time sub-intervals (e.g mean arrivals per month) are not known. If the mean
arrivals varies widely depending on the month of year, then the arrival distribution should be considered separately for
each specific month if the aim of the analysis is to estimate the impact that would be felt in a specific month. UNCTAD,
in it’s port design and development handbook, has made the argument that the exponential distribution is the best way
to describe the inter-arrival times of break bulk ships [8] but does not state that this extends to container ship arrivals
as well. Here break-bulk is defined as cargo that can be broken into individual, countable units. Research work in [9]
shows that the result extends to general cargo vessel arrivals and to container vessels in cases where there are multiple
shipping liners using the port’s terminals. If the mean number of arrivals of ships in a particular time period is the only
key piece of arrival information known, then the inter-arrival time distribution can thus then be taken to be exponential.
An exponential inter-arrival time distribution corresponds (i.e. is equivalent) to the arrival time distribution following a
poisson distribution.
B. Container Arrival Process
Quayside containerised cargo arrives and departs the port via vessels. The vessels, as outlined in subsection II-A, are
modelled as having an arrival distribution pattern that corresponds to the poisson distribution. Each of these vessels
would need to serviced at port by unloading and/or loading containers onto them. The specific number of containers that
need to be loaded and unloaded into each vessel will typically vary by vessel. The average number of containers unloaded
and/or loaded per call can be computed using the total number of containers unloaded (or loaded) in a year and the
number of calls in that particular year.
The number of containers that need to be unloaded or loaded by each vessel can thus be estimated as being equal to
the average number of containers unloaded or loaded on each call. Let ¯
QUand ¯
QLbe the average number of containers
unloaded and loaded per call respectively. If there are currently nvessels in port, the estimation above estimates the
number of containers that need to be unloaded and loaded to be n¯
QUand n¯
QLrespectively.
C. Handling Operations
The time a ship spends in port will depend on the time it takes for all ship side operations and related support operations
to take place. Ship turnaround times are an important cost factor and are an important measure of port efficiency. Due
to this fact, ports will always try and reduce these times as much as possible [10]. This can be done by improving the
service times in the port (and is so doing improving the throughput). The service time experienced by a ship will depend
on a number of factors such as the type and amount of cargo that needs to be unloaded and loaded. In 2018, UNCTAD

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estimated that the median time a ship spends at a port was 23.5 hours, this varies by type of cargo with container ships
averaging 0.7 days (0.73 days in the UK and 0.65 days in Spain) whilst dry bulk carriers averaging over 2 days [11].
Let an Erlang distribution with a shape parameter of kbe defined as an Erlang-kdistribution. The service time distribution
at ports has been shown to approximately follow an Erlang-2 distribution (with a particular port specific mean value
parameterising the distribution) [8]. In the case of break-bulk ships, UNCTAD recommends the use of this distribution
when modelling the service time distribution for port operational planning purposes [8]. This is also the service distribution
used in this paper. The Erlang-1 distribution is the exponential distribution and the Erlang-2 distribution is defined as
being the the distribution followed by the sum of two Erlang-1 distributions. In this paper the unload and load time is
taken to follow Erlang-1 (exponential) distributions leading to a service time distribution which is Erlang-2 distributed.
Another important factor that affects how a port operates both during normal operation and during disruptions is the
berth occupancy ratio. The berth occupancy ratio can be estimated by evaluating the ratio of the number of vessels
serviced a year to the maximum number of vessels.
Berth Occupancy Ratio ≈Vessels Handled per Year
max Vessels that can be Handled per Year
=Vessels Handled per Year
(max Vessels per Year per Berth) ×NB
(2)
where NBequals number of discrete berths available at the port. The maximum number of vessels that can be handled
by a berth in a year can be estimated by dividing the number of days in a year by the average ship turn around time.
D. Incidents At The Port
Incidents at a maritime port could occur for a number of different reasons, such as due to the compromise of IT/OT
equipment via a cyber attack or due to congestion, logistics errors and/or mechanical errors. Cyber attacks in particular
are an emerging but increasingly concerning disruption factor. This problem is ever growing because of port’s increased
use of technology in a wide range of operations [12]. In this paper, we investigate how the throughput and average ship
turnaround times experienced in a port change as the proportion of available cranes (both STS and RTG) changes over
time. Let the proportion of ship-to-shore cranes available at time tbe denoted as αSTS(t), the proportion of RTG/RMG
cranes available at time tbe αRTG(t) and the service time experienced by a ship completing service at time point tbe
denoted as Ts(t) (the average number of containers a ship unloads and loads is denoted as ¯
QLTEU).
The average throughput (number of TEUs unloaded/loaded per unit time) will thus be defined as ¯
QTEU/Ts(t). The
quantities αSTS(t) and αRTG(t) take the value of 1 if all cranes are operational and take the values of v1and v2if the
proportion of operational STS and RTG cranes is v1and v2respectively. The graph in figure 3 shows a graph of αSTS(t)
against time (t). The graph illustrates a situation where all cranes are non-operational in some time interval (between t1
and t2), in all other points in time all STS cranes are fully operational.
Fig. 3: A graph illustrating αSTS(t) versus time (t)
In this paper, we will illustrate the use of the model by looking at the case where a proportion of cranes become unavailable
for a particular period of time. This analysis being for the containerised portion of the port. If cranes stop operating then
the flow of containers will also be affected. In a port, the exact level of disruption will depend on the location of the

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unavailable cranes and also on other factors such as the current berth utilisation ratio. If the proportion of operational
STS cranes falls from 1 to p1at the time period between t1and t2, then the unload/loading capacity is modelled as
having had fallen by a factor of p1. If the berth utilisation is high and p1is low then the port will be less able to handle
the containers flowing through the port (on the quayside) during the period of disruption. If the disruption persists for
long enough, this will lead to container ships waiting to berth and thus increase ship turnaround times.
III. Implementation, Results and Evaluation
The simulation models a port as a queuing model and implemented on the MATLAB platform using the simevents and
simulink packages [13]. The simulation takes in a number of parameters that characterise the traffic flowing through the
port. The parameters used in the implementation instance are outlined in table 4. The parameters have been taken to
closely align with the traffic statistics seen at the port of Valencia in 2019, information of which is openly available in
[14] [15]. This is just one example of a port that can be simulated. As we were able to discuss and adjust parameters as
necessarily through discussions with the port, and it is a key EU container port, this was an ideal demonstration case.
Parameters have been sourced from Valencia port statistics [14] [15], in instances where a parameter value is unavailable,
then a parameter value is set to being equal to the average value of that parameter for similar ports. The maximum
number of median sized container vessels that can simultaneously unload and/or load at a given time will depend on a
number of factors with the most important factor being the number as how many berths are available for container vessels
at the port.
Given the mean calls per year and the TEUs unloaded in a year, the average TEUs unloaded per port call can be calculated
by evaluating the value in equation 3. The level of activity within a port varies by time of year, with some times being
more busy than others. It is therefore likely that some periods of time might experience activity which can be much less
or much more than the average, whilst some periods of time will oscillate around the average. The cumulative number
of TEU’s handled to date by month for the port of Valencia can be seen in the port’s annual statistical report [14]. It is
thus important that the average TEU per call used as a parameter in the simulation and the number of port calls align
closely the number seen in the particular period of interest. In this paper, we will look at estimated impact faced when
a proportion of STS cranes become unavailable for a period of time. The number of port calls and the average TEU per
call are taken to equal their year long averages. The period of time being simulated here being 40 working days. We will
look at the case where all STS cranes become unavailable for a period of time.
Average TEUs unloaded per port call = TEUs Unloaded per year
Mean Calls Per Year (3)
Parameter Value
Inter-Arrival Time Distribution Exponential
Service Time Distribution Erlang, parameter k= 2
Unload Time Distribution Exponential
Load Time Distribution Exponential
Mean Calls Per Year (Est. Valencia Port) ≃2325
Mean Turn Around Time (hrs) 23.5
TEUs Unloaded per year 5386309
TEUs Transhipped 2385286
Proportion Land Traffic Truck 90%
Proportion Land Traffic Train 10%
Maximum Unloading / loading Container Berths (nBERTH) 7-9
Fig. 4: Parameter Table
When a container ship arrives, it can be allocated to one of nBERTH different berths. If there is no berth free berth, the
ship will need to wait in a queue to be served. This waiting time does not contribute to the expected service time but it
contributes to the ship turn around time. Ships arrive (with the inter-arrival time following a exponential distribution)
and then are served for some duration of time. The average service time is a port specific parameter that specifies the
average of ship service times. The set of ship service times are generally considered to follow an Erlang distribution with a
parameter value of 2 [8]. The port operations model thus models the service time of following an Erlang distribution with
a mean value λand a parameter k, where k= 2 and λis the mean service time. In this paper we will use this model to
estimate how the throughput and the average service time changes during periods where Quay cranes periodically become

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unavailable. The model allows us to investigate both the transient and steady state responses of the model to changes in
crane availability.
The servicing of a ship consists of a number of distinct stages such the the unloading/loading of cargo (both Quay and
Yard side), and transporting the cargo within the port. Quay side load/unload operations involve the loading of cargo to
and from the vessel whilst yard side unload/load operation involve loading and/or unloading cargo from the container yard
to some form of transport. The total service time is taken to be carried out over a duration of tshours, where tsfollows
an Erlang-2 distribution and each of the distinct nssub-stages are taken to take place over a duration of ts/nshours.
Given that the mean calls per day, λDay, is 6.37 (= 2325/Days In Year = λDay) and the arrival distribution is poisson,
the probability that the number of ships that arrive in any particular day is xis taken to be P(X=x) = e−λDay (λDay)x
x!.
The theoretical maximum capacity of the port is here defined as being equal to the maximum number of TEUs a port
can move in a given time frame. This maximum capacity is dependent of the number of Quay cranes at the port and
the maximum number of container moves (or TEU moves) each crane achieves in an hour. The instantaneous capacity
(maximum throughput possible at any given point in time) is hard to evaluate and depends on the current lengths of the
vessels seeking to berth, geometrical constraints of the port and maximum throughput that can be supported by port
cranes, personnel and support systems at that given point in time.
The capacity and the berth utilisation rate plays a massive role in the traffic dynamics of a maritime port, the modelling
in this paper will thus analyse the transient and steady state behaviour of maritime ports given different berth utilisation
rates. Let the annual vessel handling capacity of a port, C, be defined as being the maximum number of vessels a maritime
port can service if the average berthing time (in days) of those vessels is ts. Further to this, let NBbe the number of
berths at the port and twbe the number of days the port of operational in a year. Given the above, the capacity Ccan
be estimated as shown in equation 4. The long term berth occupancy, U, can then be estimated as shown in equation 5
where nCalls is the number of vessel calls a year.
C=󰀕Working Days A Year
Average Berthing Time (in days)󰀖×Number of Berths
C=󰀕tw
ts󰀖NB(4)
U≈Vessels Serviced In A Year
max Vessels Serviceable In A Year
=nCalls
C
=tsnCalls
twNB
(5)
The paper uses the discrete event simulator to look at the case of full crane disruption. Here, the number of operational
days in a year (tw) is 365, the vessel service time (ts) is 1 day and for berth occupancies of 92% and 72%. These occupancies
are consistent with the number of equivalent discretised berths being 7 and