Cardiac Out-Patient Flow
Cardiac Out-Patient Flow
Abstract
Cardiac outpatients are those with heart-related diseases but are not on admission. Nieuwe Nike Air Max 2015 Dame. 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 Nike Air Max 90 Hyperfuse Heren. In this study, Nike Air Max 1, Heren 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. Nike Air Max 90 CamouflaDame. On the basis of the results obtained from the models in Table 4.7.2 and 4.82, Nike Air Max 90 VT Heren, 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
- Certification
- Dedication
- Acknowledgement
- Table of Contents
- Abstract
Chapter One:
Introduction
- 1.1 Introduction
- 1.2 Statement of the Problem
- 1.3 Objective
- 1.4 Scope of Study
- 1.5 Significance of the Study
- 1.6 Definition of Some Queuing Theory Terminologies
- 1.7 Organization of the Study
Chapter Two:
Literature Review
- 2.1 Introduction
- 2.2 Literature Review
Chapter Three:
Methodology
- 3.1 Introduction
- 3.2 Method of Data Collection
- 3.3 Measures of System Performance
- 3.4 Background of Monday Cardiology Clinic
- 3.5 Queueing Models Based on Birth-Death Process
- 3.6 The m/m/s Model
- 3.7 Priority – Discipline Queueing Models
- 3.8 A Model with State – Dependent Service Rate and/or Arrival Rate
- 3.9 Description of the Outpatient Clinic
Chapter Four:
Presentation and Analysis of Data
- 4.1 Introduction
- 4.2 Presentation of Data
- 4.2.1 Arrival Time and Service Time
- 4.3.1 Presentation of Arrival Table
- 4.3.2 Simulated Arrival Table
- 4.4.1 Presentation of Service Table
- 4.4.2 Simulated Service Table
- 4.5 Fitting the Distribution of Inter – Arrival Time
- 4.6 Fitting the Exponential Distribution to Service Time
- 4.7 NAUTH Example of m/m/s Model
- 4.7.1 Mathematical Estimation of Parameters of System Performance
- 4.7.2 Steady – State Results from the m/m/s Model for the NAUTH Hospital Nnewi
- 4.8 The NAUTH example with Priorities Model
- 4.8.1 Mathematical Estimation of Parameters of System Performance
- 4.8.2 Steady – State Results from Preemptive Priority-Discipline Model for NAUTH Nnewi
Chapter Five:
Summary, Conclusion and Recommendations
- 5.1 Introduction
- 5.2 Discussion of the main Findings
- 5.3 Conclusion
- 5.4 Recommendation
- References
- Appendix
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 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.
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:
- Improvement of patients flow to avoid congestion;
- Reducing doctor’s stress and improve patient safety from life threatening cardiac attack;
- To ameliorate patient dissatisfaction from long waits coupled with incessant bumping into the physicians.
1.4 Scope of the Study
This includes the following
- 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.
- 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.
- The mathematical estimation of measure of system performance of formulated priority – discipline queueing model will be determined on a single doctor (S = 1) or multiple doctor (S = 2).
- 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.
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
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.
- 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.
Chapter Five
Summary, Conclusions and Recommendations
5.1 Introduction
This chapter is aimed at discussing and summarizing the main findings from the study, drawing relevant conclusions and where necessary making some vital recommendations.
5.2 Discussion of the Main Findings
The aim of the study is two-fold:
Firstly, to verify the assumption that the inter-arrival time of the patients and service times lend themselves to a negative exponential distribution. Using chi-square goodness – of – fit test confirmed the description for inter-arrival time but not appropriate for service time. Thus, computer simulation can be used to verify the service time assumption again.
Secondly, because patient waiting is undesirable, limiting waiting time is an important objective hence m/m/s model and preemptive priority model are being used in measuring the queue performance system so as to reduce congestion at waiting room. On the basis of the results obtained from the mathematical model of m/m/s queue performance systems, a single doctor has utilization factor (busy) of 80% while adding a second doctor would virtually reduce it to 40%. This is better since man is not a machine. Thus reducing doctor’s stress and improving patient safety as stated in the objective has been met. Besides, the addition of a chief consultant to the existing one in morning shift will bring about relatively prompt treatment thereby reducing congestion in the waiting space provided for the patients.
The average time a patient spends in the queue and in the system when a single doctor is considered is 48minutes and 60minutes, respectively. This is not good for life threatening disease like cardiac problem. On the other hand, when two consultant doctors are considered the time appreciably drop to 2minutes and 14minutes, respectively.
This is fair.
Lastly, the average number of patients on the queue is 3 while on the system is 4 when a single doctor is consulting. This is in contrast when two consultant doctors are on duty. No patient will be waiting on the queue while approximately one patient will be on the system. This is an ideal situation. Incase of heart attack the sooner a patient gets medical attention the better his or her change of not only surviving, but also of minimizing heart damage following the attack. This is often referred to as the “Golden Hour”.
For the preemptive priority case, it indicates that providing a single doctor would cause critical case to wait for 10min on the average, VIP (very important patient) case to wait 11minutes and stable case to wait for 53minutes. On the other hand, when S = 2 the Wk values from table 4.72 of preemptive priority case shows that the critical case will wait for about 1.3min, VIP case about 1.4min and stable case for 2.3minutes.
The mathematical estimated values for utilization factor(r) for preemptive priority case is 80% for S = 1 and 40% for S = 2. This is the same for m/m/s model under the first – come – first – served queue discipline.
Considering the following findings:
- Inter-arrival-time lend itself to exponential distribution
- Service-time distribution deviates from the exponential form
- The queue-discipline is first-come-first-served.
- While the appropriate number of server (s) (Doctors) for morning shift for relatively prompt treatment are two.
Then, the model for the cordial out-patient flow in
(NAUTH) Nnewi is M/G/2: (¥, FCFS)
| where M | = | exponential distribution |
| G | = | non-exponential (general) distribution |
| 2 | = | Two doctors |
| ¥ = | Infinity waiting room space | |
| FCFS | = | First-Come-First-Served |
5.3 Conclusion
As long as increasing the productivity of healthcare organizations remains important, analysts will seek to apply relevant models to improve the performance of healthcare processes. The paper shows that many models for estimating waiting time and utilization are available today. However, analysts will increasingly need to consider the ways in which distinct queueing systems within an organization interact. Thus, this project surveys the contributions and application of queueing theory in the field of health care with mathematical models. The project summarizes a range of queueing theory results from m/m/s model and preemptive priority model. The fact that some of the results in Table 4.82 do not deviate substantially from those in table 4.72 reinforces the tentative conclusion that a single consultant doctor will be inadequate in a duty. Thus healthcare Managers should ensure that the mean time a customer spend waiting should be kept at minimal level by introducing a second Chief Consultant doctor on a shift since they are dealing with life and time is very precious to their existence.
5.4 Recommendation
On the basis of the result obtained from m/m/s queue model is measuring system performance, we tentatively conclude that a single doctor would be inadequate for a shift for providing the relatively prompt treatment needed in a Teaching Hospital Out-patient Cardiology Clinic.
Contrasting results of S = 1, the Wk (waiting time in the queue) values for the preemptive case with the average wait, 48minutes for all patients that was obtained in Table 4.72 under the first – come – first – severed queue discipline we observed that these values represent statistical expectations, so some patients have to wait considerably longer than the average for their priority class. This wait would not be tolerable for the critical case where a few minutes ca be vital. By contrast, the S = 2 result in table 4.82 (Preemptive Priority Case) indicates that adding a second doctor would virtually eliminate waiting drastically.
Therefore, we recommend that there by two consultant doctors on duty in the cardiac out-patient room.
Lastly, we also recommended that the state dependent service rate model should be expounded bearing in mind that it seems mean service rate does increase as the queue size increases and it provides another better representation of the real queueing system in some ways and also the service time distribution assumption should be further verified with computer simulation.
Further analysis of this kind is also recommended for comparing performance as an important direction for future research.
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