TABLE OF CONTENTS
Title Page – – – – – – – – – i
Certification – – – – – – – – ii
Dedication – – – – – – – – iii
Acknowledgement – – – – – – – iv
Table of Contents – – – – – – – v
Abstract – – – – – – – – – vii
CHAPTER ONE: INTRODUCTION
1.1 Introduction – – – – – – – 1
1.2 Statement of the Problem – – – – – 3
1.3 Objective – – – – – – – – 3
1.4 Scope of Study – – – – – – – 4
1.5 Significance of the Study – – – – – 5
1.6 Definition of Some Queuing Theory Terminologies 6
1.7 Organization of the Study – – – – – 7
CHAPTER TWO: LITERATURE REVIEW
2.1 Introduction – – – – – – – 9
2.2 Literature Review – – – – – – 9
CHAPTER THREE: METHODOLOGY
3.1 Introduction – – – – – – – 18
3.2 Method of Data Collection – – – – 18
3.3 Measures of System Performance – – – 19
3.4 Background of Monday Cardiology Clinic – – 20
3.5 Queueing Models Based on Birth-Death Process 21
3.6 The m/m/s Model – – – – – – 23
3.7 Priority – Discipline Queueing Models – – 25
3.8 A Model with State – Dependent Service Rate and/or
Arrival Rate – – – – – – – 25
3.9 Description of the Outpatient Clinic – – – 30
CHAPTER FOUR: PRESENTATION AND ANALYSIS OF
DATA
4.1 Introduction – – – – – – – 31
4.2 Presentation of Data – – – – – 31
4.2.1 Arrival Time and Service Time – – – – 32
4.3.1 Presentation of Arrival Table – – – – 33
4.3.2 Simulated Arrival Table – – – – – 33
4.4.1 Presentation of Service Table – – – – 34
4.4.2 Simulated Service Table – – – – – 35
4.5 Fitting the Distribution of Inter – Arrival Time – 36
4.6 Fitting the Exponential Distribution to Service Time 38
4.7 NAUTH Example of m/m/s Model – – – 39
4.7.1 Mathematical Estimation of Parameters of System
Performance – – – – – – – 40
4.7.2 Steady – State Results from the m/m/s Model for
the NAUTH Hospital Nnewi – – – – 46
4.8 The NAUTH example with Priorities Model – 46
4.8.1 Mathematical Estimation of Parameters of System
Performance – – – – – – – 48
4.8.2 Steady – State Results from Preemptive Priority-Discipline
Model for NAUTH Nnewi – – – – – 54
CHAPTER FIVE: SUMMARY, CONCLUSION AND
RECOMMENDATIONS
5.1 Introduction – – – – – – – 55
5.2 Discussion of the main Findings – – – 55
5.3 Conclusion – – – – – – – 58
5.4 Recommendation – – – – – – 59
References – – – – – – – 61
Appendix – – – – – – – – 63
ABSTRACT
Cardiac outpatients are those with heart-related diseases
but are not on admission. In the present study, a stochastic
approach was used for modeling the cardiac outpatient flow in
Nnamdi Azikiwe University Teaching Hospital (NAUTH) Nnewi
in a way to solving the long waiting times cardiac outpatient
experienced before they are being attended to. In this study,
Monte Carlo Simulation Method and queuing theory were used
to analyse the inter-arrival and service time of the outpatient
and measure of system performance, respectively. On the
basis of the results obtained from the models in Table 4.7.2
and 4.82, it is vividly clear that having one doctor (S = 1) in
morning shift would be inadequate for providing relatively
prompt treatment needed by patients.
1
CHAPTER ONE
INTRODUCTION
1.1 INTRODUCTION
The simple, but elusive goals in health care delivery are
“to deliver the right care, to the right patient”, “at the right
time”.
“To the right patient”, means that the health care delivery
system must be able to discriminate among patients with
different types and severities of disease so that an individual
patient is neither under-or over-treated with an appropriate
therapy.
“At the right time” means that each patient must have
access to care within a time frame that is medically
appropriate for his or her illness.
For example, long waiting times by patients seeking
consultation has been a long term complaint. Enhancing
productivity while maintaining a high level of quality has
become a challenge for healthcare managers. The major factor
for patients in terms of quality concerns waiting time which
2
has become a significant portion of determining the service
quality.
This project surveys the contributions and applications of
queueing theory in the field of healthcare processes, in which
patients arrive, wait for service, obtain service and then
depart.
Windsor star (Health Journal), of 29th June 2000,
Toronto – Canada reported that fifty-five people have died
while waiting for heart operations in Ontario in the last ten
months, a “significant” increase on previous years that has
experts worried. A new study yet to be published concludes
that “excessive waiting times” are a factor in such deaths, a
spokesman for Ontario’s Cardiac Care Network said the length
of Cardiac Surgery waiting lists in the province soared by
almost 30 percent last year.
Right now, waits at peak hours are long, sometimes more
then six hours, said John Greenaway, the Antonio Deluca
hospital’s chief of staff. “Our patients don’t like that, our staff
doesn’t like that, and our board doesn’t like that” reported by
Brain Cross, Star Health/Science Reporter.
Therefore excessive waiting time by patents has become
everybody’s headache in Health care institution and all hands
must be on deck to tame this monster.
3
1.2 STATEMENT OF THE PROBLEM
In the outpatient department, long waiting times for
treatment followed by short consultations have long been
complaints of patients. The Windsor Star-Health Journal in
Canada, reported that some Canadian doctors believe that
hospital emergency departments are being hit with fallout of
increased waiting times; the longer patients wait, the worse
their illness becomes, and the more likely they are to end up
in emergency. Thus, Health Managers have a number of very
good reasons to be concerned with waiting lines. Chief among
these reasons are the following:
The cost to provide waiting space;
A possible loss of goodwill and health deterioration;
A possible reduction in customer satisfaction;
The resulting congestion may disrupt other business
operation and/or customers.
1.3 OBJECTIVES
These are:
(a) Improvement of patients flow to avoid congestion;
(b) Reducing doctor’s stress and improve patient safety from
life threatening cardiac attack;
4
(c) To ameliorate patient dissatisfaction from long waits
coupled with incessant bumping into the physicians.
1.4 SCOPE OF THE STUDY
This includes the following
(a) Queueing theory is to be used in modeling cardiac
outpatient flow in NAUTH. The outpatient flow involves
the arrival and service time of the patient that follows
exponential distribution by assumption. This assumption
has to be verified.
(b) The mathematical estimation of measure of system
performance (i.e. , P0, Ls, Lq, Ws, Wq) of M/M/S model
will be determined on a single server (S = 1) or multiple
server (S = 2). By implication, the two alternative being
considered are to continue to having just one Chief
consultant doctor on clinic day or add a second doctor.
(c) The mathematical estimation of measure of system
performance of formulated priority – discipline queueing
5
model will be determined on a single doctor (S = 1) or
multiple doctor (S = 2).
(d) Lastly, given that the mean service rate does increase as
the queue size increases, it is desirable to develop a
theoretical model (state – dependent service rate) that
seems to describe the pattern by which it increases. This
model not only should bed a reasonable approximation of
the actual pattern but also should be simple enough to
be practical for implementation.
1.5 SIGNIFICANCE OF THE STUDY
The significance of this work cannot be overemphasized.
This study, when completed will be of tremendous relevance to
Health care managers who take decisions in hospital
management without the help of quantitative model – based
analyses, but will now have queueing theory to model a health
care process at their disposal.
6
1.6 DEFINITION OF SOME QUEUEING THEORY TERMINOLOGIES
(a) Balking: This is where customers decide not to join the
queue.
(b) Blocking: Blocking occurs when a queueing system
places a limit on queue length. In a hospital, patients
who find all beds occupied are refused admissions.
(c) Queue Length: This is the number of customers
(patients) waiting in the queue.
(d) Reneging: This is when a customer (patient) joining the
queue leaves it afterward without being served.
(e) Steady State: This is the state of the system in the long
run. This is, when there is stability in its component
parts – the arrival rate, the service facilities and service
rate.
(f) Transient State: This is the opposite of a steady state. It
describes a situation whereby the component parts of the
queuing system change. Also the probability of a given
number of customers (patients) in the system at any
point in time changes from time to time.
(g) FCFS: first – come, first – served
(h) PS: Priority served
7
1.7 ORGANIZATION OF THE STUDY
The study is aimed at modeling cardiac outpatient flow in
NAUTH – an application of queuing theory.
The work is organized in five systematic chapters.
Chapter one is made up of the introduction to the study,
including its background. Other sub-topics considered in this
chapter include: the statement of the problem, the objectives
of the study, the scope and significance of the study, some
queueing theory terminologies and the organization of the
study.
In chapter two, the related literature are reviewed as to
ascertaining what various scholars had said. In this chapter,
the following are considered: variable arrival rate, priority
queuing discipline and appointment systems.
In chapter three the methodology used in the study is
described as to enhance the understanding of the study. The
method of data collection and method of data analysis are
clearly stated.
8
The chapter four of this study shows the presentation
and the analysis of data. The data collected are presented in
Table 4.1, and to enhance the achievement of primary
objective of the study the m/m/s model table, and the priority
preemptive model would be presented for comparison and
contrast for proper understanding of the cardiac outpatient
flow.
In chapter five, the discussion of the findings would be
done coupled with the conclusions and recommendations.
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