In hospitals, patient care service delivery is an important factor that determines the rate of quality service. Most of the existing Patient Care Service Delivery System models reported in the literature were major to improve service in the emergency department using different performance metrics. However, this research work conceptualized modelling a patient care service delivery system which is characterized by emergency, inpatient and outpatient cases using Timed Coloured Petri Nets.

In developing a Timed Coloured Petri Nets (TCPN) model for a patient care service delivery system, the medical personnel (nurses) and the three categories of the patient (emergency, inpatient and outpatient) visiting the Oyo State General Hospital, Fiditi, were used as a case study. The developed Patient Care Service Delivery System (TCPN) model consists of three sections. The first section modelled the three categories of patients and their current states. The second section modelled the Nursing station and how patients were administered by the available nurse(s), while the third section abstracted the nurse-patient service delivery. The developed TCPN model was simulated using CPN tools. The validation of the developed TCPN model was explored by carrying out the statistical analysis between the simulated and the observed average waiting times and queue length of the patients under study.

The simulation results of the developed TCPN model revealed the patient average waiting times of 14.5208, 2.9583, 0.9792 and 0.50000 minutes alongside the patient queue length of 27, 6, 5 and 1 as administered by 1, 2, 3 and 4 nurses respectively. Statistically, there was no significant difference between the simulated and the observed average waiting times and the queue lengths of patients under consideration at a 5% level.

Conclusively, this research work has been able to develop a TCPN model for studying a patient care service delivery system. Also, the developed Timed Coloured Petri Nets model, through its simulation, could help in predicting the nurse-patient ratio required for effective patient care service delivery in a named medical centre.


Title Page                                                    i

Certification                                                           ii

Dedication                                                            iii

Acknowledgements                                                iv

Abstract                                                     v

Table of Contents                                                vi

List of Figures                                                xi

List of Tables                                                                                                                                 xii  



1.1    General Overview    1

1.2    Statement of the Problem    3

1.3    Aim and Objectives    4

1.4    Significance of  the Study    4

1.5    Scope of the Study    5

1.6    Methodology    5



2.1    History of Petri Nets    6

2.2    Definitions of Petri Nets    9

2.3    Discrete Event System    10

2.4    Division of Petri Nets    10

2.5    Properties of Petri nets    11

2.5.1Behavioral Properties    12

2.5.2Structural Properties    13

2.6    Petri Nets Basis    13

2.6.1Places, Transitions and Arcs    14

2.6.2Tokens and the Firing Rule    15

2.7Petri net Analysis and Simulation Tools    17

2.7.1  Time Petri Nets Analyzer (TINA) Tool    17

2.7.2Coloured Petri Net (CPN) Evaluation Tool    19

2.7.3Workflow Petri Nets Designer (WOPED) Tool    20

2.7.4Woflan Evaluation Tool    22

2.8    Hospital    22

2.9    Classification of Hospital    23

2.9.1Classification according to ownership/control    23

2.9.2Classification according to length of stay of patients    26

2.9.3Classification according to clinical basis    26

2.10    Types of Hospitals    26

2.10.1  General Hospitals    27

2.10.2  District Hospitals    27

2.10.3Specialized Hospitals    27

2.10.4Teaching Hospitals    28

2.10.5 Clinics    28

2.11    Departments/sections in an Hospitals    28

2.11.1Accident and Emergency    28

2.11.2Cardiology    29

2.11.3Critical Care    29

2.11.4Diagnostic Imaging    29

2.11.5General Surgery    30

2.11.6Gynecology    31

2.11.7Maternity Departments    31

2.11.8   Pharmacy    31

2.12    Functions of the Hospital    32

2.13    Service Delivery in Hospitals    33

2.13.1Factors Affecting Service Delivery in Hospitals    37

2.14    Modelling of an Hospital System    39



3.1      The Modelling Approach    41

3.2The Case Study    42

3.2.1    Description of a Patient Care Service Delivery in a Hospital Environment    42

3.2.2    Development of TCPN model for a Patient Care Service Delivery System    43

3.2.3    Declarations Used for the Model    44

3.2.4    Colorsets    48

3.2.5    Declaration of Coloured Sets and Variable in the Developed TCPN Models    49

3.3    Data Collection    50

3.4     Data Analysis    52

3.5    Simulation of the Developed TCPN Model    54

3.6     Validation of the developed TCPN Model of Patient Care Service Delivery    58



4.1    The Developed Timed Coloured Petri Nets Model of a Patient Care Service Delivery    63

4.2    Simulation Results of the Developed Timed Coloured Petri Net Model of a Patient    63

4.3    Validation Result of the developed TCPN Model of Patient Care Service Delivery    65



5.1    Conclusion    74

5.2    Contributions to Knowledge    74

5.3    Recommendations    75

               References                                               76

       Appendix                                               80   


Figure                                                Page   

2.1    Basic Petri Net Configuration                            16

2.2    Marked Nets before and after Firing the Transition                18

2.3    Some used Net Configuration                            20

3.1    CPN Tool Interface used in creating The Model                          49

3.2    Screenshot for the Declaration for the Developed TCPN Model.                           55

3.3    Simulation Page with One Nurse                                  63

3.4       Simulation Page with Two Nurses                                                        64                             

3.5    Simulation Page with Three Nurse                                    65

3.6    Simulation Page with Four Nurse                                  66

4.1       The Developed Patient Care Service Delivery System Model                 68

4.2    Simulation with One Nurse: Maximum Queue and Average Waiting Time            77

4.3       Simulation with Two Nurses Maximum Queue and Average Waiting Time         78                                                           4.4       Simulation with Three Nurses Maximum Queue and Average Waiting Time         79

4.5    Simulation with Four Nurses Maximum Queue and Average Waiting Time           80

4.6      Graph Showing Average Waiting Time and Maximum Queue                                 77          



1.1    General Overview

Hospital organization is today an essential part of the medical care scheme. Owing to the increasing complexity of medical sciences, it is very necessary that medical practitioners and specialists should be able to rely on a sound hospital service. Furthermore, there is general agreement on the active role the modern hospital has to play in health and social welfare programs, and on its influence on economic development. In the light of the rapid changes occurring in most of the countries of the world, it seems more and more urgent for them to have at hand basic information on the problem related to hospital planning and administration (WHO, 1966).

Strengthening service delivery is a key strategy to achieve the Millennium Development Goals. Thisincludes the delivery of interventions to reduce child mortality, maternal mortality, and the burden to cancer, tuberculosis, malaria and other emergency cases that claim the lives of many Nigerians. Health care Service provision or delivery is an immediate output of theinputs into the health system, such as health workforce, procurement and supplies and finances.Increased inputs should lead to improved service delivery and enhanced access to services. Ensuringavailability and access to health services is one of the main functions of a health system. SuchServices should meet a minimum quality standard (WHO, 2000).

Monitoring service delivery is not about the coverage of interventions, which is defined as the proportion of people who receive a specific intervention or service among those who need it. Coverage depends on service delivery and the utilization of theService by the target population.Monitoring service delivery has immediate relevance for the management of health services, whichdistinguishes this area from other health systems building blocks. Shortages of drugs, unevendistribution of health services, poor availability of equipment or guidelines such as patientswaiting time, length of stay, and resource utilization rate must all addressed as partof basic service management.

    As demand for improved medical care increases, hospitals are facing problems such as overcrowding and dissatisfaction. Improving the key performance indicators of emergency department has been the focal point of healthcare management.Hospital service delivery are facing different problems which affect their performance of these, overcrowding is a common issue around the world  which provide patient with long length of stay, waiting time for receiving services and then dissatisfaction. Most hospitals are under growing demand, they are often faced with insufficient staffing. One solution to the problem is to increase the capacity of hospitals by providing adequate facilities and man power, but this is not the best approach for solving the problem and perhaps not achievable. Recently, the need for improvement in hospitals process due to cost, overcrowding and safety of patient admitted to a large extent, to improving the efficiency and quality of hospital process different methods are used which include process mapping, demand management, critical part identification, queuing systems, statistical forecasting balanced scorecard and computer simulation.

Modelling is a universal technique that can be used across many of the activities in system development. Many modelling languages have been suggested, and many are being used for system development but Petri Nets have been proving to be a powerful modelling tool for various kinds of discreet systems (Murata, 1989; Peterson, 1981), and its formalism provides a clear means for presenting simulation and control logic. Hence, Petri Nets formalism becomes a right candidate for modelling hospital service delivery system.

Coloured Petri nets (CPN) is a graphical oriented language for modelling and validation of systems in which communication, synchronization and resource sharing and resources allocation in needed. It is an example of high level Petri nets which combines the strength of Petri nets with the strength of programming languages. That is, Petri nets provide the primitives for describing synchronization of concurrent processes, while programming languages provide the primitive for definition of data types and manipulation of their data values. The inclusion of time concepts into a Coloured Petri Net model results in a model called Timed Coloured Petri Nets (TCPN) model (Ganiyu et al., 2011a). Thus, with a Timed Coloured Petri Nets, it would be possible to calculate length of stay of patients on the queue, and the amount of time it takes nurses to attend to patients with different cases.

1.2    Statement of the Problem

    In hospitals, direct service delivery is offered by medical practitioners, which involves attending to different cases from different patients. As the demand for quality service delivery in healthcare increases (which includes the minimum length of stay on the service queue), it becomes very important that many health service services providers (hospitals) require an optimal number of personnel/ staff to help them. Emergency patients often expect to receive treatment with minimum delay and in a timely manner. Lack of resource capacity, such as beds, doctors and nurses will hamper the care process and reduce health care quality, as well as increasing the potential of medical errors and long waiting times. This scenario is inherently difficult because, in hospital, capacity decision is a major determinant for providing services over a specified time interval (Norazura, 2012).

The previous areas of research focused on the modelling and simulation of emergency department capacity estimation, which determines the optimum number of personnel and physical resources as well as emergency department planning (Nagula,2006).  This research work employed Timed Coloured Petri Nets formalism to model and simulate a patient care service delivery system which is characterized by emergency, inpatient and outpatient cases using Oyo State General Hospital, Fiditi, as a case study.

1.3    Aim and Objectives

    The aim of this research work is to model and simulate a patient care service delivery system using Timed Coloured Petri Nets.

 The specific objectives are to:

i.    develop a Timed Coloured Petri Net (TCPN) model for a patient care service delivery         system using Oyo State General Hospital, Fiditi, as a case study;

ii.    simulate the developed model using CPN tools;

iii.    validate the developed model on the basis of the simulated and the measured patient        queue and average waiting time;

1.4    Significance of the Study

 In this field of study, a concept is not studied directly but through a model of the system. By the manipulation of the representation, it is hoped that new knowledge about the modelled system can be obtained without the danger, cost or inconvenience of manipulating the real system itself. Thus, the developed Timed Coloured Petri Nets model through its simulation could help in studying and improving the patient care service delivery system of a named hospital.  

1.5    Scope of the Study

In this project work, Timed Coloured Petri nuts were mainly used to model hospital service delivery with the use of CPN tools to simulate the model. Also, statistical analysis was carried out to validate the model.

1.6    Methodology

    The methods of the study employed in this research work are as follows:

i.    Establishment of a theoretical foundation for the research through a sound literature review.

ii.    Distribution and administration of Questionnaires.

iii.    Identification of Patient service delivery process.

iv.    Development of a model for the process.

v.    The use of Timed Coloured Petri Nets tools to simulate the developed model.



2.1    History of Petri nets

    Modelling is a central part of all activities that lead up to the design, implementation, and deployment of systems. Models are built for a better understanding of the system being developed. Models enable us to communicate the desired structure and the behaviour of our system and provide a basis for designing high-performance systems (Naraharis, 1999). Since some systems are too expensive to handle or too dangerous to handle, it is important to derive the model of the system in question so as to know the way and manner of its operations.  This phenomenon leads to the development of several modelling tools suitable for analyzing systems. Carl Adam Petri (1962) presented an architectural construction in the first world computer conference in Munich. With the thought of this experiment, Petri intends to show that asynchronous systems are more powerful than synchronous systems. From this insight, the consequence that a general theory of information processing must start out with asynchronous, locally limited operations is deduced.



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