ABSTRACT

Queue has become a manage-mental problem in our society. However which is congestion in any of our service points. Which causes a waste of resources and good wills, even lost of time. In order to eliminate this problem, queuing system analysis has to be studied. The aim of this study is to - determine the mean arrival time in the queue, determine the mean service time, determine the mean waiting time in the queue. Thus, this project work is geared towards analyzing the queuing system an be able to come out with the expected number of customers in the queue so that if the number is too large that can scare customers away, the management of the 'U' bank will increase their service points. The analysis is also expected to come out with the expected waiting time of the customers. If the time waited in the queue is too much, the management has to improve on their service facility. All this suggestions have to improve the performance of the Banking system. The queue studied on this project work is of the type MIMII after the system has reached a steady state condition. The steady state condition is obtained when the system must have worked for a long time so that the results of arrival time, inter-arrival time, service time, waiting time, for a good number of days are similar for each of the parameter. From the analysis, it was found that the expected number of customers in the queue is 16 customers. The expected waiting time (including the service time) in the queue is 8.3 minutes which means on arriving customers will be expected to spend about 8.3 minutes in the bank.

TABLE OF CONTENTS

PAGE

TITLE PAGE i

CERTIFICATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

TABLE OF CONTENTS v

ABSTRACT vi-vii

CHAPTER ONE

1.0 INTRODUCTION 1

1.1 ORGANIZATION OF WORK 1

1.2 BACKGROUND OF STUDY .2

1.3 MOTIVATION 2

1.4 STATEMENT OF PROBLEM ..2

1.5 PURPOSE OF THE STUDY

1.6 SCOPEOFTHE STUDY 3

1.7 DATA SOURCE 3

1.8 ASSUMPTIONS 3

CHAPTER TWO

2.1 BASIC STATISTICAL TECHNIQUES .4

2.2 GOODNESS OF FIT TEST OF POISSON DISTRIBUTION 4

2.3 TESTING THE GOODNESS OF FIT OF GAMMA DISTRIBUTION. 4

ESTIMATION OF UNKNOWN PARAMETER (?) .5

ESTIMATION OF UNKNOWN PARAMETER a AND f3 6

ESTIMATION OF UNKNOWN PARAMETER ji 8

CHAPTER THREE

3.0 QUEUE 12

3.1 QUEUEING SYSTEM 12

3.2 MAJOR COMPONENT OF ANY QUEUING SYSTEM 16

3.3 DEFINITION OF TERMS .17

CHAPTER FOUR

4.1 ANALYSIS OF DATA .18

4.2 TESTING OF GOODNESS OF FIT (POISSON DISTRUBUTION). 18

4.3 TESTING OF GOODNESS OF FIT (GAMMA DISTRUBUTION).. .. 19

4.4 TESTING OF GOODNESS OF FIT (EXPONENTIAL

DESTRUBUTION) 21

4.5 EXPECTED NUMBER OF CUSTOMERS IN THE QUEUE ..24

4.6 EXPECTED WAITING TIME IN THE QUEUE . .25

CHAPTER FIVE

5.1 CONCLUSION .27

5.2 RECOMMENDATION 27

BIBLOGRAPHY

APPENDIX.