Application of Queueing Theory in Tackling the Problem of Port Congestion at Apapa Port, Lagos, Nigeria
Chapter One
Aim and Objectives of the Study
The aim of this work is to examine the existing queuing system at Apapa Port, Lagos with a view to applying a model that would substantially improve the ports operations the objectives are:
- to establish the arrival and service distributions of ships at Apapa Port by conducting a chi-square goodness-of-fit test respectively
- to identify and apply the existing queuing model for the port‟s operations;
- to apply the appropriate queuing model in order to reduce the length of the queues and length of stay bythe ships.
- to compare the multiple queue model with the existing model
CHAPTER TWO
LITERATURE REVIEW
Review of Literature
Queuing models provide the possibilities to evaluate existing port operation and solve realistic problems in the ports by using real data obtained from the ports. These models in most cases, are used for strategic or tactical decisions.
There have been many research of immense importance in the application of queuing theory to address varying problems (theoretical and practical) in the sea ports worldwide; some of which include Lopez et al. (2012)who studied non Markovian queuing systems in container terminals of the Port of Valencia, Spain. The results of the study showed that simulation model based on queuing theory was found to be effective in replicating realistic ship traffic operations in the ports as well as in conducting capacity evaluations. Their objective was to investigate to what extent a simulation model could predict the actual container operations with a high order of accuracy. The results helped in visualizing the development of quays and understanding the system behaviors in order to evaluate the berth capacity at the port. Concluding that of very important consideration is the availability of adequate and sufficient berth capacity at the port. The simulated scenarios of each container terminal represented an important management tool for tracking progress against strategic goals and helps the port operators to maximize the number of ships serviced.
Dragovicet al. (2005) carried out the performance evaluation of ship-berth link using cost function, computational experiments are reported to evaluate the efficiency of Pusan East Container Terminal in South Korea. Their study came up with the optimum number of berths required and recommended port expansion to solve the queue congestion. The queue discipline considered was of first come first served.
Dragovicet al. (2006) on the other hand considered a queue discipline of priority service in carrying out their study of the ship-birth link in the Pusan East Container terminal in South Korea They compared results of the performance indicators obtained from simulation and analytical methodology. The study computed the optimal number of births required to reduce or eliminate queues. This requires an immense investment on the part of the port owners which is not favorable as it is a long term investment whereas a short to medium term solution is needed.
Kuoet al. (2006) studied the evolution of ship arrival and service time distribution in public and dedicated container berths in the port of Koohsiung (Taiwan) by comparing the variance in the patterns of 1400 ships in the container terminal and 7,700 ships in the entire port. The study recommended the optimum number of berths required to eliminate queues at the ports given the current traffic volumes.
Islam and Olsen (2011)examined the factors affecting seaports capacity by identifying the consequences of capacity shortage at sea ports and corresponding supply chains, offering conceptual framework to summarize the factors influencing seaport capacity using holistic approach and suggested promising research tracks on factors affecting capacity. Specifically they explored the roles of deterministic simulation and stochastic simulation as future research direction in this rapidly charging and challenging maritime domain. Their research findings were that the factors affecting seaports capacity were the container yard, which is used temporarily for container storage cranes, stressing that the performance of both on and off the ship is an important factor to support the port efficiency labour, which affects the performance of almost all of the processes rigorously from gate operations for truckers to berthing activities for shipping lines. They also considered gates and inland waterways as factors affecting seaport capacity but fell short of examining other factors like the queuing system processes in the ports.
El-Naggar (2010) determined the optimum number of berths at the seaports of Alexandria, Egypt that minimizes the total ports‟ operating costs and to be able to meet future traffic volumes. The study relied on the Erlang‟s queuing model with multiple servers (berths) and Poisson input for the analysis and came up with an optimum number of berths required. The study also used chi-square to test the goodness of fit between the observed frequency distribution and the postulated Erlang function. The aim was to avoid inadvertent over and under building. The waiting time of vessels outside the port and in queue was calculated. For economic consideration cost characteristics were also computed. The results of the study showed that the computed optimum berths proposed will be in the best interest of ship operators and port authorities. Concluding that maximum port efficient results when total port cost is minimum i.e. the cost of vacant berths over a substantial period plus the time cost of ships waiting for a berth having the same time period.
Similarly in Novaeset al. (2010),a short survey on mathematical approach of queuing models applied to container terminals planning has been presented. In addition, they described some approximate methods for more complex queuing models based on approximate formulae to estimate mean waiting times. The result of their work is quite suitable at the planning stage to determine the number of berths to be constructed based on the estimated expected traffic volume.
CHAPTER THREE
METHODOLOGY
Chi-Square Goodness-of-fit-tests
To determine if the arrival distribution was Poisson andif the services was exponentially distributed, chi-square criteria goodness of fit test on month by month analysis was employed.
The test involves the statistical comparison between actual observed frequencies and computed expected frequencies of the random variables.
For this test the Null Hypothesis,H0 =The arrivals of ships were Poisson distributed; While the alternative H1 = The arrivals were not Poisson distributed. We fail to reject the Null hypothesis if the chi-square statistics calculated is less than the chi-square value obtained at 0.05, and r-1 degrees of freedom, while we reject the null hypothesis otherwise. Similarly, the null hypothesis for service times is H0 = Services rendered to ships are exponentially distributed while the alternative hypothesis H1= the services rendered by the Apapa ports to ships is not exponentially distributed. We fail to reject the null hypothesis if the chi-square calculated is less than chi-square from the table.
Inter-arrivals are exponentially distributed
Ships arrive randomly and independently. We have assumed that they arrive according to a Poisson process i.e. the number of ships arriving until any specific time has a Poisson distribution. The pattern of arrival in a times period t follows Poisson distribution which assumes that arrival is completely independent of other arrivals i.e. arrivals are completely random.
CHAPTER FOUR
RESULTS AND DISCUSSION
Goodness of fit test
Arrivals of ships into the queue at Apapa Port
The null hypothesis for the respective arrivals for all the months H0: Arrivals are Poisson distributed, while the alternative hypothesis H1: Arrivals are not Poisson distributed
CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMENDATIONS
Summary
The study examined the application of a multi-queue multi-berth model to the arrival and departure of ship operations at Apapa Port of the Nigeria Ports Authority in Lagos.
The existing single queue multi-berth operations of the port was also reviewed.
Since it is not possible to obtain solutions for multi-server models in closed form or by solving a set of equations the study therefore relied on simulation using the WINQSB software for the computation of the number of ships on the queue Lq.
The data obtained was for five months and the results clearly showed that the queue length for the system and in the queue was shorter for a multiple queue than for the single queue presently in operation.
Similarly it was observed that the time a ship will spend on the queue and in the system is much shorter for a multiple queue than for a single queue.
Conclusion
The application of queuing theory modeling to analyze various aspects of port operations was shown to be very useful for understanding and meeting challenges encountered in port activities.
In this study we showed from results obtained that for a multi queue multi berth very important variables like the number of ships on queue and in the system were fewer than in a single queue multi berth model.
Likewise other variables supported the proposed model over the existing model since the mean time ships spent on the queue and in the system were relatively shorter in the proposed multi queue model than in the single queue model.
Therefore the proposed model should be of great interest to the port owners and the port users alike since the port would become attractive with the reduced turnaround time and which will make the port busier and generate more revenue for the port owner while the shorter time means less expenditure by the port user. The implementation of the multiple queue model is the more attractive as it involves no additional cost by the port owners in contrast to the previous works ofOyatoyeet al.(2011).
Recommendations
Recommendations arising from the study includes that research students could explore unequal berth numbers andother queuing models‟ application to various port operations.
A student of queuing theory could also examine the inter relationships between various port operations like dockyard activities, materials handling, warehousing, gate operations.
The result of this study could also generate interest in looking at various modes of arrivals and even distribution-less arrivals and services as in the deterministic queuing models.
It is also recommended that other queuing disciplines and behaviours different from the blocked customer first in first out could be another area of research interest.
Finally it is strongly recommended that the multiple queue model should be adopted for the containerized general goods operations of the port.
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