www.ijecs.in
International Journal Of Engineering And Computer Science ISSN:2319-7242
Volume 4 Issue 1 January 2015, Page No. 9954-9961
Development of a Timed Coloured Petri Nets Model for Health
Centre Patient Care Flow Processes
R. A.Ganiyu1, S. O. Olabiyisi2, T. A. Badmus3, O. Y. Akingbade4
1
Department of Computer Science and Engineering,
Ladoke Akintola University of Technology, Ogbomoso, Nigeria
raganiyu@lautech.edu.ng
2
Department of Computer Science and Engineering,
Ladoke Akintola University of Technology, Ogbomoso, Nigeria
soolabiyisi@lautech.edu.ng
3
Department of Open and Distance Learning Centre,
Ladoke Akintola University of Technology, Ogbomoso, Nigeria
tabadmus@lautech.edu.ng
4
Department of Physical Science (Computer Unit)
Ajayi Crowther University, Oyo, Nigeria
akingbadeoluwatoyin@yahoo.com
Abstract:Hospital deals with human lives, which are often at risk and where everything depends on quick response to diverse medical
conditions. Thus, the need for efficient and effective management of patient care flow processes in a hospital is being one of the main leading
goals in health sector.In this paper,a Timed Coloured Petri Nets (TCPN) formalism is used to develop a simulation model forpatient care flow
processeswith emphasis on medical record area and examination room using Ladoke Akintola University of Technology Health Center,
Ogbomoso, as a case study. The developed TCPN model consists of a main model (arrival and evaluation module) and a sub model (treatment
module). The main model abstracts the arrival and operation(pre-treatment test) in the medical record area while the sub-model describesthe
operation (treatment) taking place in the examination room of the health centre.The developed TCPN model was simulated using CPN tools
while its validation was explored by comparing the simulated and actual number of patients of the health centre under study.The results obtained
from the simulation of the TCPN model revealed 34 (7 inpatients and 27 outpatients), 53 (9 inpatients and 44 outpatients), 42 (8 inpatients and
34 outpatients) and 45 (9 inpatients and 36 outpatients) as the average numbers of patients entering the health centre during the first, second,
third and fourth working days under consideration, respectively. Statistically, there were no significant differences between the simulated and
real number of patients entering the health centre at 5% level. This gave a confirmation that the developed TCPN model accurately described the
patient care flow processesof the health centre under study.The developed TCPN model could serve as a referential model for studying and
improving patient care flow processesina named health centre.
Keywords:Patient, Health, Petri Nets, Simulation-model.
1. Introduction
A health system is a pure service system that is characterized
by a high human involvement both at resource level (doctor,
nurses, paramedical staff etc.) and entity level (patient) [1]. It
is a system that can be viewed as a complex network of
medical units with a large diversity of health care professionals
(both clinical and administrative), medical equipment and
complex material flows connected through various information
systems [2]. However, appropriate coordination of these
entities is needed to provide: (i) better access, continuity and
quality of care to patients, (ii) better working conditions for
health care professionals, while (iii) compressing operating
costs and investments in new technology and infrastructures
[3].Hospital deals with human lives, which are often at risk and
where everything depends on quick response to diverse
medical conditions.Thus, the need for efficient and effective
management of patient care flow processes in a hospital is
being one of the main leading goals in health sector.Due to the
complexity of health systems, discrete event simulation has
proved to be an effective tool used for process improvement
[4], [5]. Coloured Petri nets has a discrete event simulation
modelling language can be used to describe flow of processes
in health system. Coloured Petri Nets (CPN) is an example of
high-level Petri nets which combines the strength of Petri nets
with the strength of functional programming language
Standard ML [6]. It is a graphical and mathematical tool for
describing and studying systems that are characterized as being
concurrent, synchronous, asynchronous, distributed, parallel,
deterministic, non-deterministic and/or stochastic. As a
graphical tool, Petri nets can be used as a visual
communication aid similar to flowcharts, block diagrams, and
networks. In addition, tokens are used in Petri nets to simulate
the dynamic and concurrent activities of systems. Petri nets
contain places which symbolise states or conditions that need
to be met before an action can be carried out and transitions
that may be connected by directed arcs which symbolise
actions [7]. The inclusion of time concepts into a Coloured
Petri Net model results in a model called Timed Coloured Petri
R. A.Ganiyu1 IJECS Volume 4 Issue 1 January, 2015 Page No.9954-9961
Page 9954
Net (TCPN) model [8]. Thus, with a Timed Coloured Petri
Nets, it would be possible to calculate performance measures,
such as the speed by which a system operates, mean waiting
time and throughput. Grit and Porntip [9] used petri netsmodel
tosimulate and analyse patient and their relatives flow
processesin a medical record area of an outpatient department
of a government hospital. However, the objective of this paper
is to employ a TCPN formalism to develop a simulation model
forpatient care flow processesof a named health Centre with
emphasis on operations characterizing the medical record area
and the examination room of the health centre.
2. Research Methodology
2.1 Overview of the Modelling Approach
In this paper, Coloured Petri Nets (CPN) and Timed Coloured
Petri Nets (TCPN) formalisms stated in (1) and (2) will be used
to model the patientcare flow processesof the health centre
under consideration.
A Coloured Petri Net and Timed Coloured Petri Nets are tuples
defined as [10];
CPN = (Σ, P, T, A, N, C, G, E, I)
(1)
Where:
(i) Σ is a finite set of non-empty types, called color sets.
(ii) P is a finite set of places.
(iii) T is a finite set of transitions.
(iv) A is a finite set of arcs such that: P ∩ T = P ∩ A = T ∩ A
= Ø.
(v) N is a node function. It is defined from A into P × T ∪ T
× P.
(vi) C is a colour function. It is defined from P into Σ.
(vii) G is a guard function. It is defined from T into
expressions such that:
∀t ∈T: [Type (G (t)) = Bool∧ Type (Var (G (t))) ⊆ Σ].
(viii) E is an arc expression function.
(ix) I is an initialization function.
A timed Coloured Petri Net is a tuple;
TCPN = (CPN, R, ro)
(2)
such that:
(i) CPN satisfying the above definition.
(ii) R is a set of time values, also called time stamps. It is
closed under + and including 0.
(iii) ro is an element of R called the start time.
2.2 Description of the Case Study
In this paper, the patients’ process flow of Ladoke Akintola
University of Technology Ogbomoso,Health Centre popularly
called LAUTECH Health Centrewill be used as a case study.
The hospital under study consist of registration, admission and
discharge unit and two inpatient areas: one for male and the
other for female withtwelve inpatient beds each. The health
centre works three (3) shifts a day with four(4) medical
attendants, four(4) nurses and three(3) doctors.Patient arriving
at the health centre follows a flow processes depicted in Figure
1.
Figure 1:Patient Care Flow processesof LAUTECH Health
Centre
The flowchart depicted in Figure 1 is based on the observation
of the processes, studying and surveying the health centre at
the current situation. The process of service started when a
patient arrives at the medical record area and ends when a
patient is admitted or discharged. On arrival, the patient goes to
the registration counter to write down his/her name and the
time he/she arrives. Then the patient goes to the waiting area
where chairs are provided for patients to sit and waiting to be
called upon by any of the available medical attendants. The
medical attendant makes an initial evaluation of the patient
temperature then refers the patient to any of the available
doctor. However, if all the doctors are busy attending to patient
then the patient will be on the queue. The doctor attends to
patient in a specified service time and the final decision about
the patient including discharge (patients in non-critical
condition) or admit (patients in critical condition) is being
taken by the doctor.
2.3 Data Collection and Analysis
Data acquisition is crucial because the results and findings of a
simulation study in the best case are as good as the input
information. In this study, different methods were used to
collect data from the health centre under consideration. These
include review of the patient admission log book at the
registration counter, direct observation and interview with the
staff in the health centre. The number of the customers and
their arrival times into the health centre for four working days
(Monday to Thursday) between the hours of 8:00am and
4:00pm were collected. These data is needed to simulate the
model to be developed. Tables 1 to 4 show the obtained interarrival time of patients coming to the health centre for the
period of four working days.
R. A.Ganiyu1 IJECS Volume 4 Issue 1 January, 2015 Page No.9954-9961
Page 9955
Table 1:Inter-arrival time of patients on Day 1
9
8:30AM
5
10
8:55AM
25
11
9:20AM
25
Patient No
Arrival time
Inter-arrival time
(minute)
1
8:00AM
-
12
9:20AM
0
2
8:02AM
2
13
9:30AM
10
9:48AM
18
3
8:05AM
3
14
4
8:35AM
30
15
9:50AM
2
5
8:38AM
3
16
9:53AM
3
6
9:00AM
22
17
9:59AM
6
18
10:10AM
11
19
20
21
10:12AM
10:12AM
10:12AM
2
0
0
22
10:12AM
0
23
10:16AM
4
24
10:18AM
2
25
10:37AM
19
26
10:42AM
5
27
10:45AM
3
28
10:45AM
0
29
10:45AM
0
30
10:50AM
5
31
11:00AM
10
32
11:19AM
19
33
11:30AM
11
34
11:42AM
12
35
11:42AM
0
36
12:00PM
18
37
12:15PM
15
38
12:29PM
14
39
12:29PM
0
40
12:30PM
1
41
12:30PM
0
42
12:31PM
1
43
12:34PM
3
44
12:34PM
0
7
9:18AM
18
8
9:29AM
8
9
9:45AM
16
10
9:51AM
6
11
10:10AM
19
12
10:12AM
2
13
10:15AM
3
14
10:28AM
13
15
10:39AM
11
16
10:58AM
19
17
11:01AM
3
18
11:07AM
6
19
11:07AM
0
20
11:10AM
3
21
11:10AM
0
22
11:12AM
2
23
11:15AM
3
24
11:24AM
9
25
12:18PM
54
26
1:00PM
42
27
1:00PM
0
28
1:06PM
6
29
1:12PM
6
30
1:36PM
24
31
2:00PM
24
32
2:35PM
35
33
2:36PM
1
34
2:39PM
3
45
12:45PM
11
35
2:40PM
1
46
12:46PM
1
47
1:00PM
14
48
1:01PM
1
49
1:48PM
47
50
1:53PM
5
51
2:40PM
47
52
53
2:56PM
2:57PM
16
1
54
3:54PM
57
Table 2:Inter-arrival time of patients on Day 2
Patient No
Arrival time
Inter-arrival time
(minutes)
1
7:30AM
-
2
7:42AM
12
3
7:58AM
16
4
7:58AM
0
5
7:58AM
0
6
8:00AM
2
7
8:20AM
20
8
8:25AM
5
Table 3:Inter-arrival time of patients on Day 3
Patient No
R. A.Ganiyu1 IJECS Volume 4 Issue 1 January, 2015 Page No.9954-9961
Arrival time
Inter-arrival time
Page 9956
1
8:15AM
(minutes)
2
8:15AM
0
-
3
8:16AM
1
8:16AM
0
2
8:29AM
9
4
3
8:33AM
4
5
8:16AM
0
4
8:35AM
2
6
8:20AM
4
8:25AM
5
5
8:57AM
22
7
6
9:13AM
16
8
9:07AM
42
7
9:24AM
11
9
9:10AM
3
8
9:32AM
8
10
9:37AM
27
9
9:35AM
3
11
9:38AM
1
10
9:50AM
15
12
9:50AM
12
11
10:01AM
11
13
10:15AM
25
12
10:02AM
1
14
10:16AM
1
13
10:20AM
18
15
10:22AM
6
14
10:39AM
19
16
10:24AM
2
10:36AM
12
15
11:14AM
35
17
16
11:26AM
12
18
10:45AM
9
17
11:27AM
1
19
10:46AM
1
10:50AM
4
18
11:27AM
0
20
19
11:54AM
27
21
11:17AM
27
20
11:59AM
5
22
11:20AM
3
11:20AM
0
21
12:04PM
5
23
22
12:10PM
6
24
11:55AM
35
23
12:12PM
2
25
11:55AM
0
24
12:16PM
4
26
11:56AM
1
25
12:26PM
10
27
12:01PM
5
26
12:26PM
0
28
12:17PM
16
27
12:37PM
11
29
12:18PM
1
12:19PM
1
28
12:45PM
18
30
29
1:08PM
23
31
12:21PM
2
30
1:16PM
12
32
12:25PM
4
31
1:54PM
38
33
12:30PM
5
32
1:55PM
1
34
12:43PM
13
33
2:21PM
26
35
1:15PM
32
34
2:25PM
4
36
2:13PM
58
35
2:25PM
0
37
2:35PM
22
36
2:37PM
12
38
2:50PM
15
37
2:38PM
1
39
2:55PM
5
38
2:45PM
7
40
3:02PM
7
39
2:45PM
0
41
3:14PM
12
40
3:10PM
25
42
3:15PM
1
41
3:18PM
8
42
3:42PM
24
43
3:25PM
10
43
3:48PM
6
44
3:48PM
23
45
3:49PM
1
Table 4:Inter-arrival time of patients on Day 4
Patient No
Arrival time
Inter-arrival time
(minutes)
1
8:15AM
-
However, the collected data were analyzed using the Input
Analyzer in the ARENA Simulation software to determine the
statistical distribution of the collected data (that is, the interarrival time (Tables 1 to 4) of patients entering the health
centre). The input analyzer in the ARENA allows user to enter
raw data and obtain the appropriate statistical distribution for
input to the model.After employing the Input Analyzer in the
R. A.Ganiyu1 IJECS Volume 4 Issue 1 January, 2015 Page No.9954-9961
Page 9957
ARENA simulation software, the analysis of the inter-arrival
times of patients entering the health centre to receive care
between Monday and Thursday are depicted in Figures 2 to 5.
These statistical distributions are summarized in Table 5.
Figure 2:Patients Arrival Distribution on Day 1
Figure 3:Patients Arrival Distribution on Day 2
Figure 4:Patients Arrival Distribution on Day 3
Day
Distribution
1
Lognormal/Weibull
distribution
Arena’s Expression/Time
(minutes)
-0.5 + LOGN(14, 27.3) or
-0.5 + WEIB(11.7, 0.923)
2
Beta distribution
-0.5 + 58 * BETA(0.51, 1.93)
3
Beta distribution
-0.5 + 39 * BETA(0.723, 1.56)
4
Lognormal/Weibull
distribution
-0.5 + LOGN(12.4, 27.9) or
-0.5 + WEIB(9.75, 0.832)
According to the interview conducted with the medical
attendants and the doctors in the examination room, the time
the medical attendant takes to carry outan initial evaluation of
the patient temperature in the medical record area is 5 minutes.
On the other hand, the time it takes the doctor to service the
patient in the examination room is between 5 and 15 minutes
(uniform distribution: uniform(5.0, 15.0)). Patients entering
into the health centre are classified into: critical patient and
non-critical patient. The critical patient will be admitted into
the health centre while the non-critical patient will be
discharged after treatment. Based on the information obtained
from the medical staff in the health centre, the ratio of the
critical patient to non-critical is currently 1:4.The model to be
developed will contain resources such as medical attendants
and doctors. At the time of this study, there are four (4)
medical attendants and three (3) doctors in the health centre.
2.4 Development of the TCPN Simulation Model forthe
Patient Care Flow Processes
CPN Tools (version 4.0.0) was used in constructing a
Timedcoloured petri nets simulation model for the considered
patient care flow processes.The proposed TCPN simulation
model consists of 14 places and 10 transitions. In TCPN
simulation model, places are draw as ovals while transitions
are drawn as rectangle. Places and transitions are connected
with directed arcs which model the relations among the
individual elements of the developed model. The arcs with
their arc expressions define the flows of tokens in the net. The
descriptions of the major places and transitions in the proposed
TCPN simulation model are stated in Tables 6 and 7
respectively.
Table 6:Description of Major Places in the TCPN Model
Place
Description
Nextpatient
busy
Model entry of new patient
Model list of patient waiting to be
served by the medical attendants
Number of attendant(s) busy
waitingpatients
Figure 5:Patients Arrival Distribution on Day 4
free
Number of attendant(s) free
pwfdasse
Treatment
room
Doctor
Patient waiting for doctor
Number of doctor(s) available
end
Indicate end of treatment
Admit
Indicate inpatient
discharge
Indicate outpatient
Patient in the treatment room
Table 5:Summary of appropriate statistical distribution
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Page 9958
Table 7:Description of Major Transitions in the Model
Table 8: Number of patient of the actual system
Transition
Description
Day
Patient
Arrivalpatient
Execution of this transition models
arrival of new patient
Number of actual
inpatient (IP)
Number of actual
outpatient (OP)
startservice
Execution of this transition models start
of service by medical attendant (s)
1
2
35
54
7
11
28
43
Execution of this transition models end
of service by medical attendant
3
43
9
34
finished
4
45
9
36
EXAMINATION
ROOM
A substitution transition
Start
Assessing
Execution of this transition models start
of service by doctor (s)
EndTreatment
Execution of this transition models of
end of service by the doctor (s)
Critical
patient
NonCritical
Patient
Execution of this transition models of
list of critical patients
Execution of this transition models of
list of non-critical patients
The color sets, variables, initial parameters and functions that
are needed in developing the TCPN simulation model of the
patient care flow processes are depicted in Figure 6.
3. Results and Discussion
Figure7(a) shows the developed TCPN simulation model of
patient care flow processes of the health centre under
consideration. This figure depicts the main page which models
the arrival of patients and process at the medical record area of
the case study. Figure 7(b) depicts a subnet layer
(TREATMENT sub-module) of the main model (Figure
7(a)).It models operation in the examination room of the health
centre under study.
Figure 7(a):The Main Page of the Developed TCPN Model
Figure 6:Color sets, variables, initial parameters and functions
declarations used in the developed TCPN Model
The simulation of the proposed TCPN model was carried out
using CPN tools. Due to the fact that the simulation model is
stochastic, it is necessary to execute several simulation runs
with the proposed model in order to compute mean value.
Hence, several replications were run for each day and average
of each was calculated.Besides, validation is important for the
correctness and credibility of the model [11]. Validation is to
determine the model which will be a representation of the real
system [12]. Thus, the proposed Timed Coloured Petri Net
model was validated by comparing the output of the simulation
model (i.e. number of inpatients and number of outpatients) for
four consecutive days with the number of inpatients and of
outpatients (Table 8) of the actual system.
Figure 7(b):The Sub-net TREATMRNT of the Developed
TCPN Model
From Figure 7(a), entry of each patient to the health centre is
modelled by a token on the place Nextpatient (Figure 7a). This
place has the color set UNIT and the color set UNIT is defined
to be equal to unit timed type as depicted in the declarations
block (Figure 6) of the developed model. The color set UNIT is
used to model arrival time of patient based on the time stamp
such as @++Day1AT() attached to the arc that runs from
transition Init to place Nextpatient(Figure 7(a)). Based on the
evaluation of the distribution expression: ~0.5 + weibull(11.7,
0.923), function Day1AT() is used to generate the arrival time
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Page 9959
Figure 8:Screenshot of the Simulation of the Developed TCPN
Model for Day 1
Table 9:Simulation Output of the Developed TCPN Model
Day
Number of
Simulated
Inpatient (i.e. IP)
1
2
7
9
Number of
Simulated
Outpatient (i.e. OP)
27
44
3
8
34
4
9
36
Figure 9 shows the results of the validation. Furthermore,
statistical analysis of the results shown in Figure 9was carried
out usingSPSS (Statistical Package for the Social Sciences)
software, version 17.0. The result (Figure 10) of the statistical
analysis shows that there were no significant differences
between the outputs of the simulation and the actual data at 5%
significance level. Hence, the developed TCPN model is valid
and accurately represents the actual system.
50
40
No of Patient
of new patient into the system. From Figure 6, color set
PatientType is used to represent types of patient entering the
health centre. It is enumerated type of CP (critical patient) and
NCP (non-critical patient). The place waitingpatients has the
color set Patients defined to be set of list Patient. The color set
Patients is used to model the queue of patients to be attended
to. The color set Patient models a patient as a record consisting
of two fields. The first field denoted with patientType is of
type PatientType and represents type of the patient. Second
field is denoted with the title AT is of type real and represents
arrival time of a patient. The color set AttendantxPatient is a
product color set defined as product Attendant*Patient timed.
This color set is used to represent the attendant when he/she is
busy serving patient. Also, the color set DoctorxPatient is to
represent the doctor when he/she is busy treating patient.The
function Day1AT() uses weibull distribution with the
expression: ~0.5 + weibull(11.7, 0.923) to generate arrival
times of patients for day 1. This distribution is used instead of
lognormal distribution because currently CPN Tools (Version
4.0.0) does not support lognormal distribution. The place
waitingpatientsand the place pwfdasse are used to model the
queue of patients at the registration counter unit and
examination room respectively. The single token on each of the
places waitingpatientsand the place pwfdasse represents the
queue of patients. In the initial marking the lists are empty. The
places free and busy are used to represent the status of the
medical attendant. A token on the place free indicates that the
medical attendant is not serving a patient at that time. The
parameter globrefnum_of_attendants = 4; and function fun
initAttendants() = (!num_of_attendants)`attendant in Figure 6,
show that there are 4 tokens on the place free in the initial
marking. A token on the place busy indicates that the medical
attendant is busy attending to a patient, and the value of the
token indicates which patient is being processed. The initial
marking of busy is empty. The medical attendant can start
attending to patient (transition startservice), if the medical
attendant is free and if there is at least one patient in the queue
of patients (patient::patients on the arc from place
waitingpatients to transition startservice).From Figure 7(b),
after treatment, the doctor would decide whether to admit the
patient (crical patient) or to discharge the patient (non-critical
patient). The decision will depend on the outcome of the
treatment. The guard functions [# patientType patient = CP]on
transition CriticalPatientand [# patientType patient = NCP]on
transition NonCriticalPatient were used to achieve this goal.
SimulatedIP
30
ActualIP
20
SimulatedOP
10
ActualOP
0
Day 1 Day 2 Day 3 Day 4
Figure 9:ValidationResult
Figure 8 depicts the screenshot of the simulation of the
developed TCPN model.Table 9 shows the simulated number
of patient (critical and non-critical) coming into the hospital.
Figure 10:Statistical analysis of the validationresult
4. Conclusion
In this paper, we have been able to develop a Timed Coloured
Petri Net (TCPNs) simulation model forpatient care flow
processes with emphasis on medical record area and
examination room using Ladoke Akintola University of
Technology Health Center, Ogbomoso, as a case study.The
developed Timed Coloured Petri Net simulation model reveals
valid representation of the patient care flow processes of the
considered health centre. This is evident from the result of the
statistical analysis, which shows that there were no
significance differences between the simulated and real
R. A.Ganiyu1 IJECS Volume 4 Issue 1 January, 2015 Page No.9954-9961
Page 9960
number of patients entering the health centre at 5% level. Thus,
the developed TCPN simulation model could accurately
describe the patient care flow processes of the health centre
under study or any other related healthflow processes.
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R. A.Ganiyu1 IJECS Volume 4 Issue 1 January, 2015 Page No.9954-9961
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