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International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 1
International Journal of Modern Innovations & Knowledge
in Information Technology (IJMIKIT)
ISSN:2971-7523
Available on-line at:www.ijmik.com
Volume 1 / Issue 1 / 2023
Priority-Based Scheduling with Diminishing Priorities Using Queueing Theory in
Marine Vessel Harbour Management
.
1Goodnews Ogboada Jaja
2Onate Egerton Taylor
3Daniel Tamuno-Iduabia Tamunodukobipi
1&2Department of Computer Science
Faculty of Science, Rivers State University.
3Department of Marine Engineering
Faculty of Engineering, Rivers State University
,
Abstract
The effective management of marine vessels at ports is crucial for minimizing wait times, reducing congestion,
and improving the overall efficiency of the shipping industry. This paper explores the use of queueing theory as a
tool for optimizing the operations in harbours. The proposed system assigns priorities to vessels based on their
type, size, and urgency, and continuously updates these priorities as vessels wait in the harbour. It leverages on
Queueing Theory to model vessel arrivals, service times, and queue lengths to optimize the allocation of resources
and minimize waiting times. The diminishing priority scheme ensures that vessels that have been waiting for longer
receive a higher priority, thereby reducing overall waiting times and increasing efficiency. The effectiveness of the
proposed system is evaluated through simulation and sensitivity analysis, which demonstrate its ability to
significantly reduce average waiting times and improve the overall management of harbours. Simulations data are
used to prove the performance of the algorithm, and the results are tested against a Gantt chart. It is found the
proposed method is well-suited for situations where priorities are the most important factor, but less suited for
situations where average waiting time is the most important factor. Thus, this research provides valuable insights
and practical solutions to port authorities and harbour operators seeking to improve their operations and advance
their service levels.
Keywords: Queueing Theory, Harbour Management, Marine Operations, Marine Vessels, Port
Management, Priority-Based Scheduling.
Corresponding Author: Ogboada Jaja, Goodnews, Department of Computer Science,
Rivers State University, Port Harcourt.
Citation: Jaja, G. O., Taylor O. E. & Tamunodukobipi D. T. (2023). Priority-Based
Scheduling with Diminishing Priorities Using Queueing Theory in Marine
Vessel Harbour Management. International Journal of Modern
Innovation & Knowledge in Information Technology, 1(1); 1 – 18.
International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 2
Introduction
Marine vessel harbour management is a critical aspect of the maritime industry, responsible for
ensuring the safe and efficient movement of boats and ships in and out of harbours, seaports,
and dockyards. One of the primary tasks of harbour management is the assignment of mooring
spaces for vessels (Rosario, 2000). This requires an understanding of the types and sizes of
vessels that will be using the harbour, as well as the capacity of the harbour to accommodate
them. Harbour managers must also take into account factors such as tide and weather conditions,
and the availability of services such as fuel and waste disposal (Udo & Daniel, 2022).
Similarly, safety is a paramount consideration in marine vessel harbour management. Harbour
managers are responsible for enforcing safety regulations, such as ensuring that all vessels are
properly equipped with safety equipment and that all crew members are trained in safety
procedures. They may also conduct regular safety inspections of vessels and the harbour itself
to identify and address any potential hazards (International Labour Office, 2018).
Maintenance of the harbour infrastructure and facilities is also an essential consideration in
harbour management. This includes tasks such as cleaning and maintaining docks, breakwaters
and other structures. Harbour managers must also plan for future development and expansion
of the harbour as needed, to accommodate the growing demands of the maritime industry
(Notteboom et al., 2021; Tamunodukobipi et al., 2022). Services to boaters and ship owners,
such as fueling, and waste disposal are other responsibility of Harbour management. They also
provide information about local weather and sea conditions, tide schedules, and other important
information to mariners (MCA, 2015).
Despite these operational responsibilities, harbour managers may also be involved in business
development and community outreach. They may work with local businesses and organizations
to promote the harbour and attract more boaters and ships. They may also provide education
and outreach programs to the public, to educate them about the importance of marine vessel
harbour management and the role it plays in maintaining a healthy and safe maritime
environment ("National Sea Grant College Program—Special Projects (DOC)," 2020).
In a null shell, marine vessel harbour management is a challenging and demanding field that
requires a wide range of skills and expertise. It plays a crucial role in the maritime industry and
is essential for the safe and efficient movement of boats and ships in and out of harbours and
marinas. Due to the limited size of the harbour, it is imminent that proper arrangement is made
to optimize the use of harbour space for efficient movement of boats and ships both in and out
of the harbour (United Nations, 2021). According to Oxford (2018) queue is a line or sequence
of human or machines waiting their turns to be served or process. Queueing theory is a branch
International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 3
of mathematics that deals with the study of waiting lines, or queues (Sundarapandian, 2009). It
can be applied to a wide range of systems, including transportation systems, manufacturing
facilities, and service-based industries. In the context of marine vessel harbour management,
queueing theory can be used to model and optimize the flow of ships entering and exiting a
harbour.
The main problem in managing a seaport or vessel harbour is how to ensure that ships can enter
and exit the harbour in an efficient and timely manner. This requires balancing the needs of
different types of ships, such as cargo ships, passenger ships, and pleasure boats, while also
considering factors such as tide levels, weather conditions, and the availability of docking
facilities (Sakyi & Immurana, 2021).
Queueing theory can be used to model the flow of ships through a harbour by considering the
different types of ships as different classes of customers, and the various stages of the process
(e.g., entering the harbour, waiting to dock, loading or unloading cargo) as different servers or
stations. By using queueing models, harbour managers can make predictions about the number
of ships that will be present in the harbour at any given time, as well as the amount of time that
ships will need to spend waiting to enter or exit the harbour (Pruyn et al., 2020).
The feature of queueing theory which is best suited for marine vessel harbour management is
the concept of "priority queuing." This allows different classes of ships to be given priority over
others, based on factors such as their size, cargo, or urgency of travel. For example, cargo ships
carrying essential goods may be given priority over pleasure boats, while smaller ships may be
given priority over larger ones in order to optimize the use of limited docking facilities (Talley,
2018).
Again, the concept of "multi-channel queueing" can be implemented for marine vessel harbour
management. This can be used to model the various entrance and exit points in the harbour,
allowing ships to enter and exit through multiple channels simultaneously, and thus reducing
the overall time spent waiting in line (Nesterov, 2014).
Furthermore, simulations of queueing models can be used to illustrate, predict, and evaluate the
performance of different policies for managing the flow of ships through a harbour. This can be
useful for testing new strategies or for assessing the impact of changes to the harbour’s
infrastructure or capacity (Cahyono, 2021).
Queueing theory can be useful tool to manage marine vessel harbour. By modelling the flow of
ships as customers and different stages of ship traffic as servers, harbour managers can make
predictions and optimize the usage of harbour and evaluate the performance of different
strategies to manage the flow of ships. Priority queueing and multi-channel queueing are key
International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 4
concept that can be applied in marine vessel harbour management, and simulations can be used
to evaluate the performance of different strategies (Oyatoye et al., 2011).
Literature Review
Popov (2017) discusses the impact of the entry gate at the front of a truck cargo capacity on the
performance indicators of a cargo terminal. The researcher uses simulation modelling methods
to study this issue and develop a cargo terminal model using specialized software. The model
focuses on the processes that occur at the entry gate, including document preparation and
sending loading orders to handling zones. The capacity of the entry gates is also considered.
The model is tested using queueing theory and the results are compared to previous calculations.
The article also examines the impact of factors such as the regularity of incoming traffic flow
on the performance of the cargo terminal in the context of the relationship between the terminal
and the city.
Almeida et al. (2003) apply queuing theory models to study the traffic flow of vehicles at
waterway terminals, identifying bottlenecks and suggesting methods for traffic signal timing.
They examine data from the San Joaquim's urban waterway transport terminal.
Gates and Mccarthy (2004) consider the requirement for KC130J aircraft in the United States
Marine Corps using queuing theory and simulation, comparing them, and analysing the budget
impact of different fleet requirements, as the USMC retires its older aircraft models in favour
of newer, more capable J series aircraft.
Lin et al. (2022) propose a new approach for maritime communication networks (MCNs) using
energy harvesting space-air-sea integrated networks (EH-SASINs) to improve efficiency of
mobile edge computing (MEC) for maritime applications such as unmanned surface vehicles,
marine environment monitoring and target tracking. The optimal deployment of tethered
aerostats is determined using the K-means method and the paper studies the issue of
computation task offloading for vessels, with a focus on minimizing the process delay of ship
clearing tasks. An improved water-filling algorithm based on queuing theory is proposed to
solve the NP-hard optimization problem. Simulation results show that the proposed EH-SASINs
and algorithms can reduce about 50% of the latency compared to local computation.
Tang (1977) presents a new definition and ways to model and calculate port capacity using an
analogy to dam theory. A mathematical model is built to derive the dissipation period (time
ships wait for cargo) and storage level of the storage area. Queueing theory is used to define
capacity and actual throughput, using a GERT model to determine factors such as cycle time
and ship longest hatch time. The dependency among links is solved by using non-systematic-
tandem-queue theory, and the queueing network is analysed by decomposing it into many
International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 5
tandem queues. The proposed model can be applied to more general port cases, such as a
multipurpose terminal.
Grzelakowski (2018) focuses on the global freight market in container shipping, specifically
the mechanism for setting freight rates. The research aims to identify and analyse the
characteristics and features of the market, and the factors that determine market fluctuations
and its impact on carriers and shippers. It also evaluates the causes and effects of fluctuations
in demand and supply on freight rates and analyses the strategies and behaviour of global
container operators in different types of container markets on a global scale. The theories of
mass random service and queueing are implemented to examine the container freight market
mechanisms and presents a method of short-term forecasting freight rates as a tool for decision
making in global maritime logistics.
Grzelakowski and Karaś (2022) describe the relationship between the mechanism of reporting
and meeting the demand for terminal services and its effectiveness in terms of operational
efficiency and profitability in a bulk cargo handling terminal in the Gulf of Guinea. The study
uses the theory of mass service and queuing theory to evaluate the terminal's operational
mechanism and effectiveness in terms of costs and revenue. The results confirm that queuing
theory can be used as a useful tool to optimize the efficiency and effectiveness of bulk cargo
terminals.
Oyatoye et al. (2011) highlight the use of queueing theory in addressing port congestion in
Nigeria to improve sustainable development of the ports. Nigeria ports have been facing chronic
congestion issues which has led to the diversion of ships to other neighbouring countries and
loss of revenue. The queueing model is applied to the arrival and service patterns that cause
congestion and provide solutions. They also use the model to predict the average arrival and
service rate per ship in Tin-Can Island Port. Nonetheless, it is obvious that the number of berths
in Nigeria ports is sufficient for the traffic intensity but identified other factors leading to
congestion through interviews with stakeholders. Policy recommendations for cost-
effectiveness, attractiveness, and quick turnaround of vessels at the ports are suggested.
Lima et al. (2015) carry out an investigation that seeks to evolve a procedure that allows for
agile planning and control of transport flows in port logistics systems by coupling agent-based
simulation and queueing theory model. It focuses on transport scheduling performed by an agent
at an intermodal terminal, considering data acquired from remote points in the system. The
results indicate the importance of considering transit time and waiting times in transport
planning and control of port logistics systems.
International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 6
Tuzenko et al. (2020) describe a mathematical model of the maritime grain terminal operations
using queueing theory. Its simulation model is developed using Any Logic software and allows
for analysis of the terminal's operation and individual units such as automobile and railway
unloading stations, conveyor belts, and ship loaders by setting parameters such as warehouse
length, arrival rates, unloading rates, percentage of defective vehicles, etc.
Thus, this research aims at developing a priority based scheduling algorithm that utilizes the
M/M/1 queueing model while applying graceful segregation to high priority vessel with extra
service to reduce starvation of vessel with lower priority. And as such improving the efficiency
of the harbour management in servicing marine vessel.
Materials and Methods
Queueing Models
The M/M/1/GD/∞ system has M as its inter-arrival and service time, which is exponential
service and arrival time, one server. M/M/1/GD/C/∞ the above system has exponential inter-
arrival and exponential service time, with rate and respectively. The system has maximum
capacity of C. which implies that when ever arrival is denied for any new
customer.
M/M/s/GD/∞/∞ the system has an exponential inter-arrival and service time with rate and
respectively, but with s server. Here are serving customers from a single line.
And if customers exist at the point in time in the system and every customer is being
served but if then customers are waiting in the system.
M/G/∞/GD/∞/∞ in this system there exist no waiting customer, because there exist an infinite
number of servers in the system. At all times such that there is a server for each
process. j is never greater than s in this system. So at any given time t in the system.
M/M/R/GD/K/K this system has exponential inter-arrival and service time and R number of
servers. And the maximum number of populations allowed in the system = the size of customer
population = K. this model can explain situation where there exist K numbers of humans that
can get sick at rate and R doctors who can each threat them at rate . This implies that and
are dependent on either how many customers are there in the queue or how many servers are
in service.
M/G/s/GD/s/∞ in this system there is no waiting customer, arrival is close when . In this
system no queue is ever form this implies . If is the arrival rate and
is the
mean service time, then
International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 7
The Proposed Model
Generating Signal for the Proposed Model
To characterize the proposed queue the probabilistic properties of the queue must be identified
which are the incoming flow, service time, length of queue, service discipline, waiting time,
number of vessels in the queue and number of servers. The arrival of new vessels can be
characterized by the distribution of the inter arrival time denoted by , that is:
The service time is the time taken to service a vessel and is denoted by . It is expressed as:
Let traffic density be denoted by
If the queue has an arrival intensity which is reciprocal of the mean inter-arrival time, and let
the mean service denote by
. Then
If then the queue is overloaded since the request arrive faster than as they are served. In
this case the M/M/s model will be applied but if then M/M/1 model will be used.
Since the system is a time schedule system, let denote the event when the server is
idle at time T. then the utilization of the server at time T is defined by
Where T is a long interval of time. As , the utilization of the server can be denoted as
which holds the following relationship with the probability of 1
Where is the steady state probability that the server is idle. denote the mean busy period
and denotes the mean idle period s. The steady state distribution for the proposed system can
be obtained in the form
Consider the system at the moments of arrival and departure, respectively. Let , denote
the state of the system at the instant of arrival and departure, respectively, and let
stand for their distributions. By applying the
Bayles’s theorem it is easy to see that
International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 8
Similarly,
Since
thus,
From equation (10), it can be interpreted that in steady state the arrival and departure of vessels
in the system are the same. Furthermore, it should be adequately noted that this does not imply
that it is equal to the steady state distribution at a random point. It is essential to note that by
further observation the mean arrival of vessels in the system is equal to the departure of vessels
from the system at steady state which can be expressed as:
In this research the M/M/1 Queue is used since the arrival of the vessels to the queue are
independent and the service time are also independent. It implies that the vessels arrive at a
Poisson distribution with rate and the inter-arrival time of the vessels are exponentially
distributed randomly with parameter . With this the service time (the time taken to serve a
vessels) is assumed to be independent and exponentially distributed with parameter . All
random variables are therefore independent of each other.
Let denote the number of vessels in the system at time . It is then said that the system is
at state if , since all the random variables in the system are exponentially distributed
therefore, they have no history of their past (independent of their past). So, the variables are
memoryless. Hence, is a continuous time Markov chain with state space 0, 1,…..
The transition probabilities of h can be seen in
Using independent assumption, the first term is the probability that during one vessel has
arrived, and no vessel has been served. Then, the summation term is the probability that during
at least 2 vessels have arrived and at least 1 has been served. It can then be deduced that the
second term o(h) with relation to the Poisson process is
International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 9
In the same vein, the transition probability from state to state during can be deduce
as
For non-neighbouring states, it is
In conclusion, the introduced random process is the arrival and departure process with
rates,
That is all the arrival rates are while all the departure rate of vessels is . To deduce the steady-
state distribution, these rates are inserted into equation (14) to generate the proposed system,
Using the normalization condition, the geometric sum is convergent if and only if
and
Where
. Thus which is a modified geometric distribution
with success parameter .
Modelling the Proposed System without Priority
Mean number of vessels in the system
Variance
International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 10
Mean number of waiting vessels, mean queue length
Variance
Vessels service utilization
Modelling the Proposed System with Priorities
Considering the proposed system which uses First in first out (FIFO), and the queue is M/M/1
systems with priorities. This implied that each vessel is associated with a priority. So, there are
classes of vessels and each arrives according to a Poisson distribution with parameter
respectively, and the vessels are independent of each other. The Servicing
time for each class are assumed to be exponentially distributed with parameter . The system is
stable if and only if
where is number of classes and
Note that implies that has the highest priority.
Modelling the Proposed System with Priorities and Pre-emption
This is effective only when more than one vessel has the same departure time. Class will pre-
empt This implies that if a class lower than the current class emerges in the system, it
automatically interrupts the system and start using it. It remains engaged, until it finishes, or a
lower class arrives to pre-empt, or cause its class to increase.
Let denote the number of priorities vessels in the system and let denote the response time
of the priority vessels. To calculate the and for since always
preempt and it is independent of number of vessels in the system.
To compute the s for
International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 11
For :
For
Thus,
Hence,
Similarly, for
Hence,
Generally, it can be rewritten as:
Also, to compute the s for
For
For
Using Little’s law yields
Similarly, for
International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 12
Generally,
Table 1 Data Table for Simulation
SN
Page
Priority
Schedule Date
Extra
Service
Process
Time
Process Time +
Extra
1
4
5
10:00:00 AM
2
20
30
2
3
6
7:15:00 AM
15
15
3
2
4
10:00:00 AM
10
10
4
1
5
12:00:00 PM
5
5
5
7
6
12:15:00 PM
3
35
50
6
2
6
7:00:00 PM
10
10
7
1
1
12:15:00 PM
5
5
8
2
2
1:00:00 PM
10
10
9
4
4
1:40:00 PM
1
20
25
10
5
3
1:40:00 PM
25
25
11
2
5
1:45:00 PM
10
10
12
3
2
1:45:00 PM
15
15
13
1
6
2:15:00 PM
1
5
10
14
4
1
2:15:00 PM
20
20
15
3
7
2:45:00 PM
15
15
16
5
2
2:45:00 PM
25
25
17
3
3
3:15:00 PM
15
15
18
1
4
3:30:00 PM
5
5
19
2
6
3:45:00 PM
1
10
15
20
5
1
3:45:00 PM
25
25
Total
60
3.95
300
340
RESULTS
International Journal of Modern Innovations & Knowledge in Information Technology (IJMIKIT)
13
Figure 1 Wait Time of the Simulation (Time in minutes vs Processes)
SN1 SN2 SN3 SN4 SN5 SN6 SN7 SN8 SN9 SN10 SN11 SN12 SN13 SN14 SN15 SN16 SN17 SN18 SN19 SN20
FIFO 0 0 30 0 0 0 50 10 025 45 55 40 50 40 55 50 50 40 55
SJF 10 0 0 0 5 0 0 10 025 45 55 40 50 40 55 50 50 40 55
ROUND ROBIN 10 010 015 010 065 70 15 65 25 70 60 95 70 30 50 55
PRIORITY BASED 10 0 0 0 15 0 0 0 100 0150 0130 0125 0 0 40 50 0
PRIORITY BASED WITH DIMISHINIG PRIORITY 10 0 0 0 15 0 0 0 130 0150 0140 0125 0 0 10 60 0
0
20
40
60
80
100
120
140
160
Time in minutes
Processes
WAIT TIME
FIFO SJF ROUND ROBIN PRIORITY BASED PRIORITY BASED WITH DIMISHINIG PRIORITY
p5
p5
p4
p6
p6
p1
p2
p4
p3
p5
p2
p6
p1
p7
p2
p3
p4 p6 p1
p6
The p implied their
priorities
International Journal of Modern Innovations & Knowledge in Information Technology (IJMIKIT)
14
Figure 2 Total time in the system of the Simulation (Time in minutes vs Processes)
SN1 SN2 SN3 SN4 SN5 SN6 SN7 SN8 SN9 SN10 SN11 SN12 SN13 SN14 SN15 SN16 SN17 SN18 SN19 SN20
FIFO 30 15 40 550 10 55 20 25 50 55 70 50 70 55 80 65 55 55 80
SJF 40 15 10 555 10 520 25 50 55 70 50 70 55 80 65 55 55 80
ROUND ROBIN 40 15 20 565 10 15 10 90 95 25 80 35 90 75 120 85 35 65 80
PRIORITY BASED 40 15 10 565 10 510 125 25 160 15 140 20 140 25 15 45 65 25
PRIORITY BASED WITH DIMISHINIG PRIORITY 40 15 10 565 10 510 155 25 160 15 150 20 140 25 15 15 75 25
0
20
40
60
80
100
120
140
160
180
Time in Minutes
Processes
TOTAL TIME IN SYSTEM
FIFO SJF ROUND ROBIN PRIORITY BASED PRIORITY BASED WITH DIMISHINIG PRIORITY
p5
p6
p4
p5
p6
p6
p1
p2
p4
p3
p5 p6
p1
p7
p2
p3
p4 p6
p1
p2
The p implied their
priorities
International Journal of Modern Innovations & Knowledge in Information Technology (IJMIKIT)
15
Figure 3 The Sum of Waiting time and Total time of processes in the system (Time in minutes vs Scheduling Methods)
FIFO SJF ROUND ROBIN PRIORITY BASED PRIORITY BASED WITH
DIMISHINIG PRIORITY
TOTAL WATING TIME 595 530 715 620 640
TOTAL TIME IN SYSTEM 935 870 1055 960 980
595 530
715
620 640
935 870
1055
960 980
0
200
400
600
800
1000
1200
Time in minutes
Scheduling methods
TIME IN SYSTEM AND WAIT TIME
TOTAL WATING TIME TOTAL TIME IN SYSTEM
International Journal of Modern Innovations & Knowledge in Information
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DISCUSSION
Figure 1 shows a comparison between all the scheduling methods in respect to their waiting time.
It is observed that SN11 in priority-based, with diminishing priority has the highest singular
waiting time at 150 minutes having level 5 priority. This indicates that FIFO, SJF and Round
Robin has better average waiting time considering the high wait time experience by SN11,
SN13, SN7 and SN9. Round robin having it highest peak waiting time in SN16 at 95 minutes
but with priority of 2. Process rated at level 2 should be treated as emergency because it shows
it downside in SN17, SN20, SN14, SN10 and SN7. This implies that Round Robin is not the
best choice when it comes to systems that require some cases to be treated as emergency and
others as normal tasks. For instance, it will be counter effective in an Engineering firm where
systems are meant to queue information and dispatch to different department based on priority.
Round robin will delay prioritize vessel or service if their arrival time is late and will not render
the full service at once since time slice will be allocated to each segment. The result also shows
the same for SJF as SN12, SN14, SN16, SN17, SN18 and SN20. This shows that if a process is
an emergency but has a larger process time the execution will be delay. In such system, if an
emergency process will utilize, more resources when compared to other less urgent processes
but lesser resource utilization, the former is denied and kept waiting till lower utilization
processes are completed. The result shows that processes with the highest priority which are 1
and 2 are kept in queue for lower priorities processes to be executed due to process time.
Consequently, FIFO has almost the same flaws as SJF since processes are treated by their arrival
time rather than their priorities that will explain the rise of wait time in SN7, SN12, SN14,
SN16, SN17 and SN20
Figure 2 shows the total time spent in the system by each process is relative to
the wait time. Here, the result shows that SN2, SN4 and SN6 all scheduling algorithm has a flat
rate when waiting time is equal to 0. Figure 3 show the total waiting time of the system. The
result depicts that SJF has the best average waiting time at 530 minutes which is followed by
FIFO, then Round Robin. The least is the Priority-based with diminishing priorities. This is
gotten from the summation of wait time of all processes while the total time in the system is
gotten from the summation of all time spent in the system.
CONCLUSION
The aim of this research is to develop a new marine vessel harbour scheduling algorithm that
has no latency and utilize the pre-emptive nature of the algorithm to give fast service to priorities
vessel and to reduce starvation by graceful increment of starve vessel with low priority. The
International Journal of Modern Innovations & Knowledge in Information
Technology (IJMIKIT) 17
algorithm is developed using the M/M/1/GD/∞ queueing system, while the scheduling method
used is Priority-based. The latter reduces resource starvation. Priorities reduction is introduced
to prolong or over-time vessels as to allow vessels with lower priorities a chance to be served.
Also, Round robin is used for vessels that has the same priorities and scheduling time. The
algorithm has been proven efficient in dispatching jobs to vessels with higher priorities making
it suited for situation where priorities is the most important factor but is not best suited for
situation where average waiting time of the system is the most important factor. The scheduling
algorithm can be used in health care, Oil firm or any system where there is queue, and priorities
are considered as one of the most important factors.
Correlations with simulation data are carried out to prove the algorithm in section 3. The results
are tested against Gantt chart to prove their validity. It is concluded that the algorithm is efficient
in system where priorities is of great important and resource starvation is to be reduced.
Further work should be carried out to reduce the average waiting time of the priority based with
diminishing priorities. Also, investigation should be conducted to determine if SJF or FIFO will
be a suitable choice to used when two processes have the same scheduling time and priorities.
Further work can also be carried to test the Simulation when there no scheduling time just arrival
time.
The major contributions to knowledge are the:
• formulation of optimal algorithm that minimizes the resources needed for scheduling
marine vessel in a single server environment;
• development of models that can assist software developers and engineering get higher
performance in utilizing schedulers; and
• evolution of a new queueing model that can be used in any field that require a pre-
emptive nature and reduce latency in service nodes in the queue.
References
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Cahyono, R. T. (2021). Multi-agent Based Modeling of Container Terminal Operations. Journal
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Gates, W. R., & Mccarthy, M. J. (2004). United states marine corps aerial refueling
requirements: Queuing theory and simulation analysis. Defense & Security Analysis, 20,
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Grzelakowski, A. S. (2018). Freight Markets in the Global Container Shipping – Their
Dynamics and Its Impact on the Freight Rates Quoting Mechanism. TransNav:
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