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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 University Of Port-Harcourt Teaching Hospital (UPTH) 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.
TABLE OF CONTENTS
TITLE PAGE i
COVER PAGE…………………………………..………………………..ii
DECLARATION iii
CERTIFICATION iv
DEDICATION v
ACKNOWLEDGEMENTS vi
ABSTRACT viii
TABLE OF CONTENTS ix
CHAPTER ONE 12
1.1 INTRODUCTION 12
1.2 STATEMENT OF THE PROBLEM 3
1.3 AIMS OF STUDY 3
1.4 OBJECTIVE OF STUDY 4
1.4 SCOPE OF THE STUDY 4
1.5 SIGNIFICANCE OF THE STUDY 5
1.6 DEFINITION OF SOME QUEUEING THEORY TERMINOLOGIES 6
1.7 ORGANIZATION OF THE STUDY 7
CHAPTER TWO 9
2.2LITERATURE REVIEW 9
CHAPTER THREE 18
METHODOLOGY 18
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 RATEAND/OR ARRIVAL RATE……………………………………..25
3.9 DESCRIPTION OF THE OUT-PATIENT CLINIC 40
CHAPTER FOUR 31
PRESENTATION OF DATA 31
INTRODUCTION…………………………….…………………………31
4.2 PRESENTATION OF DATA………………………….………….31
4.2.1 ARRIVAL TIME AND SERVICE TIME 32
4.3.1 PRESENTATION OF ARRIVAL TABLE 43
4.3.2 SIMULATED ARRIVAL 34
4.4.1PRESENTATION OF SERVICE TABLE 36
4.4.2SIMULATED SERVICE TABLE 37
4.6 FITTING THE DISTRIBUTION OF INTER – ARRIVAL
TIME………………………………………………………………………38
3.8 UPTH EXAMPLE OF M/M/S MODEL 39
3.9 MATHEMATICAL ESTIMATION OF PARAMETERS OF
SYSTEM PERFORMANCE 40
4.7.2 STEADY – STATE RESULTS FROM THE M/M/S MODEL FOR THE UPTH HOSPITAL CHOBA………………………..……..46
4.2 THE UPTH EXAMPLE WITH PRIORITY MODEL 46
4.8.1MATHEMATICAL ESTIMATION OF PARAMETERS OF 48
4.8.2 STEADY – STATE RESULTS FROM PREEMPTIVE
PRIORITY – DISCIPLINE MODEL FOR UPTH CHOBA 54
CHAPTER FIVE 55
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 55
5.1 INTRODUCTION 55
5.2 DISCUSSION OF THE MAIN FINDINGS 55
5.3 CONCLUSION 58
5.4 RECOMMENDATION 59
REFERENCES 61
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 whichhas become a significant portion of determining the servicequality.
This project surveys the contributions and applications of queuing 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.
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 AIMS OF STUDY
These are
(a) Improvement of patients flow to avoid congestion
(b) Reducing doctor’s stress and improve patient safety from life threatening cardiac attack;
(c) To ameliorate patient dissatisfaction from long waits coupled with incessant bumping into the physicians.
1.4 OBJECTIVE OF STUDY
(a) Using Monte Carlo Simulation Method Reducing doctor’s stress and improve patient safety from life threatening cardiac attack.
(b) Using Queuing Model for the Improvement of patients flow to avoid congestion.
1.4 SCOPE OF THE STUDY
This includes the following
(a) Queuing theory is to be used in modeling cardiac outpatient flow in UPTH. 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 queuing
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 tohealth care managers who take decisions in hospitalmanagement without the help of quantitative model – basedanalyses, but will now have queuing theory to model a healthcare process at their disposal.
1.6 DEFINITION OF SOME QUEUEING THEORY TERMINOLOGIES
(a) Balking: This is where customers decide not to join thequeue.
(b) Blocking: Blocking occurs when a queuing systemplaces 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 thequeue leaves it afterward without being served.
(e) Steady State: This is the state of the system in the longrun. 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
1.7 ORGANIZATION OF THE STUDY
The study is aimed at modeling cardiac outpatient flow inUPTH – 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 thischapter include: the statement of the problem, the objectivesof the study, the scope and significance of the study, somequeuing theory terminologies and the organization of thestudy.In chapter two, the related literature are reviewed as toascertaining what various scholars had said. In this chapter,the following are considered: variable arrival rate, priorityqueuing discipline and appointment systems.In chapter three the methodology used in the study isdescribed as to enhance the understanding of the study. Themethod of data collection and method of data analysis areclearly stated.The chapter four of this study shows the presentationand the analysis of data. The data collected are presented inTable 4.1, and to enhance the achievement of primaryobjective of the study the m/m/s model table, and the prioritypreemptive model would be presented for comparison andcontrast for proper understanding of the cardiac outpatientflow.
In chapter five, the discussion of the findings would bedone coupled with the conclusions and recommendations.