CHAPTER ONE

INTRODUCTION

1.1            BACKGROUND OF STUDY

Queue is a common sight in banks especially on Mondays and Fridays. The

word queue comes via French and the Latin Cauda.Customersmeani waiting in line to receive services in any service system is inevitable and that is

why queue management has been where the manager faces huge challenge.

Hence, queuing theory is suitable to be applied in the banking system. Since it is associated with queue or waiting line where customers who cannot be served immediately have to queue (wait) for service for a long time and time being a resource ought to be managed effectively and efficiently because time is money. Queuing theory as the mathematical study of waiting lines or queues. It is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide service (Wikipedia, 2008).

Queuing theory is also known as the theory of overcrowding; it is the branch of operational research that explores the relationship between the demand on a service system and the delays suffered by the users of that system (A.K. Sharma, 2013)

Queuing theory is a major topic for applied mathematics that deals with phenomenon of waiting and arises from the use of powerful mathematical analysis to describe production processes (M. Masurdi, 2011).

The study of queues deals with quantifying the phenomenon of waiting in lines using representative measures of performance, such as average queue length, average waiting time in queue and average facility utilization (H.A. Taha 2002)

Queueing theory can also be applied to a variety of operational situations where it is not possible to accurately predict the arrival rate (or time) of customers and service rate (or time)) of service facility of facilities. Queuing theory permits the derivation and calculation of several performance measures including the average waiting time in the queue or the system, the expected number waiting or receiving service and the probability of encountering the system in certain states, such as empty, full or having an available server or having to wait a certain time to be served.(Biju, M.K (2011)

queuing models provide the analyst with a powerful tool for evaluating the performance of queuing systems( Bank, Carson, Nelson & Nicol, 2001)

1.2            STATEMENT OF PROBLEM

This study is required to investigate the expected waiting time of customers and the actual waiting time in banks, where the gap between the actual and expected

waiting time can be analyzed to know how to improve on the efficiency and

effectiveness of their bank. Such problems are

·        How poor service facilities has affected the overall bank performance.

·        How poor service pattern affects queue discipline.

·        How service facilities has affected the time of customers

·        How poor service delivery impacts on time.

·        How   poor   service’s   delivery   has   aff

1.3         AIMS AND OBJECTIVES OF THE STUDY

The aim of this study is to determine the amount of average time customers spend on a queue and actual time of service delivery. Therefore the objectives of this study are as follows:-

·        To examine the impact of time wasting on the weak performance.

·        To improve on the efficiency and effectiveness of their operations.

·        To help bank mangers improve custo management.

·        To improve on time management which is a resource.

1.4              SIGNIFICANCE OF STUDY

This study when completed will be significant to many people and organisations especially banks in Nigeria. First of all, it will add to the literature on queuing theory and management which will be accessed by lecturers and scholars.

Most importantly, Bank Managers will benefit a lot from this study as they will apply this theory in their various banks, thereby reducing the amount of time

spent on queues which mightandimproveleadon to their overall efficiency and effectiveness.

1.5.  RESEARCH QUESTIONS

In terms of the analysis of queuing situations, the type of questions in which we are interested in are typically concerned with measures of system performance which includes

·        To what extent does the service time differ from the actual time that customers have to wait before being served?

·        To what extent does poor service pattern affect queue discipline?

·        To   what   extent   do   service   facilitie

·        To what extent does the average service time affect the overall performance of the bank?

·        How   does   poor   service   delivery   affe

1.6           SCOPE AND LIMITATIONS OF STUDY

In this paper, we will be studying one bank and our concern is the single queue multiple service point because of lack of time and resources to embark on large scale study on majority of banks. One bank to our mind is fair judgement. The queue discipline is first in first out (FIFO) and the arrival is strictly random.

We also consider a Poisson distributed arrival times and exponentially distributed service times.

1.6.1  PROBLEM DEFINITION

Single-channel queuing system with multi where S>1) are operated by banks with the hope of giving customers maximum satisfaction and also make their profit, the problem arises when these objectives

are not reached.

1.7            DEFINITIONS OF TERMS ASSOCIATED WITH QUEUING MODELS

We now look at the definition of terms associated with queuing theory

Queue –A queue can be defined as an aggregation of items waiting for a service function.

Queuing theory –This is the construction of mathematical model of varying forms of queuing systems.

Arrival –This element is concerned with the rate of entry by customers into the system.

Queuing discipline –This element is concerned with what goes on between the arrival time of a customer and when service is rendered to him/her.

Server –An operation fed by a queue

Phase –A queue and its connected servers, or router to a server.

Arrival pattern –This is the manner in which customers arrive in the system for service.

Service pattern –This is the rate in which the service channel renders service to a customer.

Balking –This is the refusal of a customer to join the queue if the queue is long.

Reneging –This is the withdrawal of a customer from the queue because of the length of the waiting line.

Jockeying –When a customer withdraws from a queue to join another one because the new queue is shorter.

Arrivalmeanratenumber of(λ):arrivalper unit time.

Service rate (µ): Mean number of customers that can be served at 100% utilization by each individual server per unit time (usually per hour a day)