1.0 Introduction

As the size of the world’s population increased so the number of queues and their queue length. In the business world, more customers mean more business transactions. Out of the many ways to attract customers, an efficient queuing system plays an important role as it reduces a customers waiting time. As a result, the shorter waiting time makes customer happy, and one thing for sure is that a happy customer will come back for business again. Queuing as the mathematical study of waiting times or queues. They study endless mathematical analysis of several related processes, including the arrival of the queue, waiting in the queue and being served by servers at the front of the queue.

Due to the advent of computer system over the years, has brought considerable changes to many areas of human endeavor. This technology has led to speed and accuracy of information that are processed with it. With the introduction of computer in almost all spheres of life, cumbersome jobs are now done with a little time and energy. Our present day computers can be used in airlines reservation, transportation, and patient diagnosis, as an aid to the handicapped and in providing hospital information systems effectively.

Computer system described as an electronic device that accepts data as input, process the data and brings, output as information.. Its uses are not overlooked in the area of simulation. Simulation, which is the process of experimenting or using a model and noting the results, which occur, It is used in a technique referred to as the computer assisted instructions. This has made computers to be continuously ground with scientists, engineers, medical expert, and businessmen and in transportation, industries, science and education. Developing a simulation is often a highly complex mathematical process. Initially a set of rules, relationship and operating procedures are specified along with other variables, Example identifying the objectives of the simulation, identifying the input variables. Distinguish between controlled and non-controlled variables etc. the interactions of these event new rules, which further evolved as the simulation procedures. Simulation implementation ranges from paper and pencil and board game production of situations to complex computer aided interactive systems. As a technique for instructions, simulation allows students to deal in realistic way with vital concern. The use of computers can be employed in simulation of queuing system. Simulation involves representing aspect of business that can be manipulated by a computer by trying various alternatives on the simulation model. With the computer results in the real world can be accurately determined. For instance if a simulation model for investment practices has been developed various investment strategies can be tried to ascertain, which has the likelihood of success.

The term queue as line up of individual, waiting to be served is found in transport like people waiting to purchase tickets for their journey, in banks, supermarkets, hospitals, offices, restaurants etc. this constitutes one important and particular application of the queuing theory. By analyzing these situations to find average waiting-times, arrival rates etc. help can be obtained for making decisions available at particular times of day in order to process customers faster or whether more queuing spaces are needed.

Imo Transport Company (ITC) has several terminals; their processes are not computerized. Tickets are issued to customers on payment, job are done manually. Their queuing system can be stimulated; this is with the help of models that are computerized. This will go a long way to facilitating efficiency and aid at proper satisfaction to its customers.

1.1 Statement Of The Problem

There are many factors that lead to the investigation or study of this system, queuing is an important issue that need to be resolved in Imo state transport company’s operation. Some of the problems that motivate the research to study of this system include:

Time wasting
Idle time at service facility
Dissatisfaction encounter in the company as a result of queue
To allocate resources according to encourage customers satisfaction

1.2 Objective Of The Study

Basically simulation is the imitation representation of the behavior of a dynamic system (capture expostulation) by that of another system namely a computer base mode.

Therefore the objective of this study include amongst others:

To test hypothesis and to design or experiment with system that may not yet be available for direct observation or experiment
By applying digital simulation to help find solutions to problems relating resources allocations to production schedule.
To achieve an economic balance between the cost of service and the cost associated with the wait required for the service.
To provide adequate but not excessive service facility. This is because if too much facility is provided, the service facility will be often idle. And if too little service is provided, it will lead to excessive waiting cost. Which shall lead to customer’s frustration and loss of goodwill.

1.3 Significance Of The Study

The significance of this study cannot be overemphasized owing to the various areas in which it is applied. The study of stimulation by the use of model in getting results in the world, which can be more accurately determined, Its significance can also be seen in the following reasons:

The study will go a long way to understand complex interaction of physical or social environmental factors.
The flexibility of the study is provided because it is easier, less costly and safer to change a representative of a system than to change the system itself.
One of the major significance of this study is to provide an adequate but not excessive service faculty. This is because if too service facility is provided, the service facility will often be idle and if too little service is provided it will lead to excessive waiting costs in terms of customers frustration and less of good will
This study will save cost in terms of time and money
With the use of simulation model, the risk involved in working on the real system is avoided.
The complexity of the real life system demands a representative model will ease the understanding of the model

1.4 Scope And Limitation

The research is basically limited to the case study of Imo state transport company. The simulation of queuing system in this aspect is limited to queuing in transportation. Manipulation of a simulation system concerns the acceptance of input and generation of output.

1.5 Background Of The Case Study

Imo state transport company formally called Imo Transport Corporation is a limited liability company incorporated under the companies Act of 1968, the company commenced transport business in August 1988, the same month it was commissioned.

On inception in August 1988, the company’s “fleet” size was 20 vehicles made up of 10 nos 0365, 42 seater Mercedes Benz buses and 10 nos. 17 seater J-5 buses distributed over nine operational routes. The main objective of the company is to provide transport and allied services in the stave and beyond at an affordable rate.

1.6 Background Of The Study

The research is faced with the basis of transportation. The company is an establishment with over fourthy two (42) branches Andover two hundred (200) buses serving as the background of the study. The research is faced towards different services as well as effective use of the available resources.

1.7 Definition Of Terms

Simulation: Simulation is the process of experimenting or using a model and noting the results, which occur. It can also be defined as the imitation of some real things, state of affairs or process.

Model: a model is any representation (physical or abstract) of a real thing, event or circumstance.

Queuing: Queuing is the mathematical study of waiting times or queues. Queuing System

Input Process: this is the manner in which units arrive at the queuing system.

Calling Population: this is the probability distribution of time between successive arrivals

Service Facility: this describes how customers are served and how they leave the queue system.

First Come First Serve: (FCFS) services are rendered to customers in the order in which they joined the queue. Queuing System

Last Come Last Serve: (LCFS) services are rendered to customers in the reverse order in which they enter the queue. Queuing System

Random: there is no order in which customers are served. Queuing System

Computer Stimulation: this is an attempt to model a real life or hypothetical situations on a computer so that it can be studied to show how the system works. Queuing System

Computer: computer is an electronic device that accepts data as input and processes it to give information as its output. It has been describe by several authors to mean several thing example:

Ndukwe (2005) windows based application packages described computer as a robot, an idiot, a magic machine etc. the author defined computer as an electronic device operating under stored-programme concept that accept data as input, processes the data and produces result as output.

Okafor (2006) file design, organization and management said that efficient file/data management requires the use of a computer database, which implies that computer is needed in this research work for record of the system. Queuing System

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