Queing Theory and Its Application to Road Traffic Congestion

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QUEUEING THEORY AND ITS APPLICATION
TO ROAD TRAFFIC CONGESTION

BY

CHIEDU NELSON CALED
PSC060774

A PROJECT WORK PRESENTED TO THE DEPARTMENT
OF MATHEMATICS, FACULTY OF PHYSICAL SCIENCE,
UNIVERSITY OF BENIN IN PARTIAL FULFILMENT OF
THE REQUIREMENT OF THE AWARD OF BACHELOR OF
SCIENCE (B.SC) (COMBINED HONOURS) DEGREE IN
STATISTICS AND COPMPUTER

NOVEMBER 2012.

CERTIFICATION
This is to certify that this project was carried out by CHIEDU NELSON CALEB of the Department of Mathematics, Faculty of Physical Sciences, and University of Benin, Benin-City, Edo State, Nigeria.

______________________ _____________________
Osagiede Francis E .U, Ph.D Prof. M.N.O Ikhile Project Supervisor Head of Department

____________________ _____________________
DateDate

DEDICATION
This project is affectionately dedicated to Jehovah God our heavenly father for his care, protection, guidance and his infinite mercy upon me. My brothers and sisters amongst who are Wisdom, Naomi, Jubilee and Happiness for their unending love. And all others too numerous to mention here for giving me their support, counsel and encouragement.

ACKNOWLEDGEMENT
Writing and publishing any book depends more on the inspiration, advice, help and interest from others. The task involved in undertaking and achieving the completion of a work of this kind is a complex one. My sincere gratitude goes to Jehovah God, who gave me the life, the knowledge and the wisdom throughout my academic pursuits I must put on record the great tolerance, understanding and assistance which I receive from my project Supervisor Dr. Osagiede Francis E .U for his patience and his pain taking in going through the manuscript of this project. I also express of heartfelt gratitude to Engr. Oche Prince Patrick and to all who contributed directly or indirectly to this project work. However, I am especially indebted to all my lectures in the department of mathematics and computer science for their moral support throughout the duration of my studies amongst who are Dr. F. Ewere and the host of others. May God grant you all you heart desires in your endeavours in life.

TABLE OF CONTENTS
Title Page----------i
Certification ---------ii
Dedication ----------iii
Acknowledgement --------iv
Table of Content ---------v
Abstract ----------viii

CHAPTER ONE
1.0Introduction --------1
1.1Background of the Study -------1
1.2Definition of Terms -------4
1.3 Poisson Distribution -------5
1.4 Exponential Distribution ------5
1.5Objectives of the Study-------8
1.6 Scope of the Study -------8
1.7Relevance of the Study -------8

CHAPTER TWO
2.0 Literature Review -------9
2.1Queue Behaviour --------17
2.2Queue Discipline --------18
2.3Priority Discipline --------21
2.4 Traffic Intensity and Idle Time -----22
2.5 Arrival and Service Patterns ------23

CHAPTER THREE
3.0 Introduction --------27
3.1 Continuous Random Variable ------27
3.2 Probability Distribution of a Continuous ----29
3.3 Cumulative Distribution Function -----30
3.4 Normal Distribution -------32
3.5 Poisson Distribution -------34
3.6 Exponential Distribution ------37
3.7 Input/ Arrival Distribution ------39
3.8 Service Components -------40
3.9 Service Facility --------40
3.10 Service Distribution -------41
3.11 Service Capacity --------41
3.12 Assumptions --------42
3.13 Notations ---------44

CHAPTER FOUR
4.0 Introduction --------51
4.1 Application of Queuing System/Case Study ----51
4.3Source of Data --------51
4.4 Data Analysis --------54

CHAPTER...
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