=Paper=
{{Paper
|id=None
|storemode=property
|title=Improving Emergency Department Processes Using Coloured Petri Nets
|pdfUrl=https://ceur-ws.org/Vol-989/paper02b.pdf
|volume=Vol-989
|dblpUrl=https://dblp.org/rec/conf/apn/SalimifardHM13
}}
==Improving Emergency Department Processes Using Coloured Petri Nets==
https://ceur-ws.org/Vol-989/paper02b.pdf
Improving Emergency Department Processes Using Coloured
Petri Nets
Khodakaram Salimifard1, Seyed Yaghoub Hosseini2, Mohammad Sadegh Moradi1
1
Industrial Management Department, Persian Gulf University, Bushehr, Iran
salimifard@pgu.ac.ir, msadeghmoradi@gmail.com
2
Business Management Department, Persian Gulf University, Bushehr, Iran
hosseini@pgu.ac.ir
Abstract. With increasing demand for medical services, emergency departments (ED)
are facing problems such as overcrowding and dissatisfaction. Improving the key per-
formance indicators of EDs has been the focal point of healthcare management. This
paper addresses performance analysis of ED of a general hospital. To this aim, a dis-
crete event dynamic modeling approach is used to model the ED processes. The mod-
el employs a hierarchical timed Coloured Petri net framework in a concise and de-
tailed way to capture patient flow and care processes within the ED. The simulation
model was validated against historical data and then different types of scenarios were
used to assess, compare and improve ED key performance indicators, such as patients
waiting time, length of stay (LOS), and resource utilization rate. The proposed model
helped the hospital policy makers to configure the ED in a way to improve its effi-
ciency and staff satisfaction.
Keywords: Healthcare System, Emergency Department, Coloured Petri Net, Perfor-
mance Analysis
1 Introduction
Emergency departments (ED) are facing different problems which affect their performance.
Of these, overcrowding is a common issue around the world which provides EDs patient
with long length of stay (LOS), waiting times for receiving services and then dissatisfaction
[1]. Although most emergency departments are under growing demand, they often face
with insufficient staffing and budget constraints. One solution to this problem is to increase
capacity of ED, providing adequate facilities and manpower, but this is not the best ap-
proach for solving the problem, and perhaps not achievable [2]. Recently, the need for im-
provement in ED processes due to cost, overcrowding and safety of patients admitted to a
large extent [3].To improve the efficiency and quality of ED processes, different methods
were used which include process mapping, demand management, critical path identifica-
tion, queuing systems, statistical forecasting, balanced scorecard and computer simulation
[4].
In the last years, the use of computer simulation to help effective decision making in
health care and to improve the medical operations has been rising [5]. One of the main rea-
336 ModBE’13 – Modeling and Business Environments
sons that simulation has become a common practice in solving medical problems is its abil-
ity to dynamically analyze situations and present to the stakeholders a more realistic view
of the system [6]. The main purpose of the use of simulation studies in health care is to
reduce waiting times and length of stay for patients, better use of resources and reducing
operating cost [7]. Among the various methods for simulation in health care, discrete event
simulation is the most used method especially in EDs, and it seems to be a better alternative
with less time and cost compared to more traditional statistical methods [8].
This study is intended to present a general simulation model for studying hospital emer-
gency department. For this purpose, we used Coloured Petri Nets modeling and simulation
formalism for making a general model of emergency department of a general hospital. In
addition to internal processes, external relations between ED and other hospital wards, such
as Radiology and Laboratory, is also considered. The main objective of this paper is, hence,
to improve ED processes. The problem we are dealing with is ED overcrowding which
provide patient with long length of stay and waiting times.
The remainder of the paper is organized as follows. Section 2 covers a brief literature re-
view of the application of simulation in emergency departments. Research methodology,
simulation model, input data and variables are presented in Section 3. Section 4 focuses on
improvement scenarios and results of simulation runs. Finally, the paper is concluded in
Section 5.
2 Literature review
In the literature, the main focal point of discrete-event simulation models that are used
for analysis of hospital emergency department is improving the flow of patients to reduce
waiting times. Examples of this include studying patient flow and forecasting ED over-
crowding using simulation by Hoot et al. [9], defining buffer concept to reduce waiting
times and increase throughput, and comparing amount of improvement gain by buffers by
Kolb et al. [10], and Khandekar et al. [11] paper on rearranging sequence of activities of
care process in order to reduce waiting times. Another area of ED simulations study focus
is on capacity estimation which determines the optimum number of personnel and physical
resources such as bed [12], [13] and also ED layout [14]. Improving quality of services and
ED processes is another area of study [5], [15].
Although the use of Petri nets in the health sector is less than other fields such as com-
puter networks and production system, but it can be a useful method in this area. Here some
related works in this area are presented. Xiong et al. [16], apply petri nets for modeling and
analysis of health care process. They used a Petri net model to examine the effect of chang-
es in arrival pattern and resources on performance metrics such as waiting times and re-
source utilization. Chockalingam et al [17] used Petri nets to model patient and resource
flow in a hospital system. Using the Petri net model they obtained a stochastic representa-
tion of a metric termed distance to divert which measure the proximity of a hospital to a
divert state. Dotoli et al. [18] focused on pulmonology department workflow and drug dis-
tribution system and used simulation as a decision support system. They employed a timed
Petri net (TPN) framework to describe the workflow in the department. Another example
is the work done by Ronny Man et al [19] of using process mining and Petri nets for pre
hospital stroke care. In the paper, process mining is used to extract process related infor-
mation e.g. timing information. Jorgensen et al [20] have used CPN for implementing a
new Electronic Patient Record Workflow System at two stages. The first CPN model is
K. Salimifard et al.: Improving Emergency Department Processes 337
used as an execution engine for a graphical animation called EUC and the second CPN
model is a Coloured Workflow Net (CWN). Together, the EUC and the CWN are used to
close the gap between the given requirements specification and the realization of these re-
quirements with the help of an IT system.
In this paper, care processes of ED are modeled using hierarchical timed CPN. The main
focus of the model is on patient flows. The model also concentrates on the inter-department
care processes. It is aimed to find a suitable operating scenario to improve some perfor-
mance metrics of the department. Similar to [17], this paper has considered the relationship
between different departments (Labs, Radiology) of the hospital. Performance metrics in-
cluding waiting time, patient length of stay, and resource utilization are calculated under
different operating scenarios. Compared to existing literature, this paper puts more empha-
sis on using features of CPN (color, time, and hierarchy) to capture the complex nature of
the system.
3 Research methodology
In this paper, CPN Tools is utilized to create the Coloured Petri net model of the system
and to simulate the model to produce desired outputs. CPN Tools [21] is a powerful soft-
ware tool for modeling and simulation of discrete event systems modeled in CPN. Our
choice of using CPNs to model ED patient flow stems from the fact that PNs capture struc-
tural properties of the underlying system which we can study and use. Petri nets provide the
foundation of the graphical notation and the basic primitives for modeling concurrency and
synchronization, conditions which are common in our model. After reviewing a wide range
of related literature, an initial model was prepared. Based on the initial model, the generic
conceptual model was developed. The generic model aimed to capture the characteristics of
an emergency department of a general hospital in Iran. Information required for the model-
ing and simulation of processes were collected using hospital information system, sampling
in ward, and also open interview with employees. In order to simulate the model under
different configurations, different types of improvement scenarios were defined and com-
pared against performance criteria. Please note that here the term “Generic” as Gunal and
Pidd [22] mentioned means that the model has a defined structure with probability distribu-
tions that can be parameterized by the user.
The hospital under study is a general hospital in the city of Yazd of Iran. The emergency
department of the hospital consists of one triage room, one primary visit room, admission
and discharge unit, CPR room, and two inpatient areas with 24 inpatient bed. It works 3
shifts a day with 1 triage nurse, 1 general practitioner (GP), 1 emergency medicine special-
ist (SP), 1 admission staff and 6 nurses.
3.1 Process flow chart
Fig.1. depicts an overall patient flow of Emergency Department of the hospital. This flow
chart is depicted based on researcher observation of the process and also domain expert
opinion. The process diagram was drawn in such a way that in addition to our hospital it
could also be used in other Iranian hospitals. Patients are triaged on arrival at the emergen-
cy department. The triage nurse makes an initial evaluation of patient symptoms. Then,
according to Emergency Severity Index (ESI), she classifies the patient in one of the 5 lev-
els of emergency. A patient in level 1 is with more acuity while a patient in level 5 is in fact
338 ModBE’13 – Modeling and Business Environments
an outpatient with less acuity. After this stage, patient is referred to the GP. The GP deter-
mines whether or not the patient requires other care services. Usually, patients with acuity
level 5 will leave the ED as soon as the payment cleared. Other patients who need more
medical services, such as diagnostic tests, need to be registered and will be directed through
the other processes. The final decision about the patient including discharge, inpatient at
ED, or being referred to other wards is taken by SP.
3.2 Performance variables
For each process improvement project, establishing quantitative measures to implement
changes and develop monitoring system for continuous improvement is crucial. In this
paper, we investigate three key performance metrics including patients waiting times,
length of stay, and ED resource utilization.
• Waiting times [min]. It is the mean duration a patient need to spend in the ED waiting
room.
• Length of stay (LOS) [min]. The total time of staying at ED, from arrival to the time of
final decision made by SP.
• Resource utilization [%]. Represents the total busy time of resources compared with total
working time.
3.3 Data collection
Model inputs are distribution functions of ED activities. Random sampling was used to
estimate required data for patient’s arrival times and service time for all resources. All
distributions determined from the data and used in the model were validated by using Kol-
mogorov Smirnov goodness of fit test with a 5% significance level. Using statistical good-
ness of fit method, the distribution of processing time of different activities have been de-
fined.
K. Salimifard et al.: Improving Emergency Department Processes 339
Fig. 1. Process flow of emergency department
Table 1. Simulation input distribution functions
Input parameter Distribution
Patients inter arrival pattern Exponential , expel(9)
Triage time Lognormal , 0.21 + LOGN(0.875, 0.613)
GP visit time Gamma , 1 + GAMM(0.732, 2.2)
admission Lognormal , 0.16 + LOGN(1.11,0.729)
SP visit time Triangular (1,2,3)
CPR time Triangular (5,15,30)
ED outpatient surgery(OR) Triangular (10,20,30)
In cases where there was no possibility of sampling, based on information available in the
hospital information system and also hospital staff experience, minimum, average and max-
imum duration of each activity were chosen as the statistical distribution.
340 ModBE’13 – Modeling and Business Environments
3.4 The Hierarchical Timed Petri Net Model of the ED
We used Color Petri-nets (CPNs) to model patient flow in an emergency department of a
hospital. A PN consists of a set of places, and a set of transitions and arcs that connect
place(s) to a transition and vice-versa. Non-negative integers assigned to every place in the
net are known as tokens.
Overview of Colored Petri Nets. Coloured Petri nets are a discrete-event modeling lan-
guage combining the capabilities of Petri nets with the capabilities of a high-level pro-
gramming language. Petri nets are directed, bipartite graphs that can be used to model dis-
crete distributed systems. A CPN as defined by [23] is a nine-tuple
𝐶𝑃𝑁 = (𝑃, 𝑇, 𝐴, Σ, 𝑉, 𝐶, 𝐺, 𝐸, 𝐼), where 𝑃 is a finite set of place 𝑇 , is a finite set of transitions 𝑇
such that 𝑃 ∩ 𝑇 = ∅, 𝐴 ⊆ 𝑃×𝑇 ∪ 𝑇×𝑃 is a set of directed arcs, Σ is a finite set of non-empty
color sets, 𝑉 is a finite set of typed variables such that type [𝑣]𝜖Σ for all variable 𝑣𝜖𝑉 s,
𝐶: 𝑃 → Σ is a color set function that assigns a color set to each place, 𝐺: 𝑇 → 𝐸𝑋𝑃𝑅! is a
guard function that assigns a guard to each transition 𝑡 such that type 𝐺 𝑡 = 𝐵𝑜𝑜𝑙 ,
𝐸: 𝐴 → 𝐸𝑋𝑃𝑅! is an arc expression function that assigns an arc expression to each arc 𝛼 such
that type, 𝐸 𝑎 = 𝑐(𝑝)!" where 𝑝 is the place connected to the arc 𝛼, 𝐼: 𝑃 → 𝐸𝑋𝑃𝑅! is an
initialization function that assigns an initialization expression to each place 𝑝 such that
type. 𝐼 𝑝 = 𝑐(𝑝)!" . A CP-net has a distinguished initial marking, denoted by 𝑀! , and
obtained by evaluating the initialization expressions. The marking can be viewed as a
‘snapshot’ of how tokens are distributed in the PN [24].
The simulation model of ED. Fig.2. shows the key structures of the model. The top layer
of the ED model is illustrated in this figure. This layer is the core part of the model. In the
model each place (circle) represents the state where patients may to be exposed there (table
2). Entry of each patient to the ED is modeled by a token on the place New Patient
(Fig.2). This place has the color set PAT, whose elements are 5-tuples (ESI, at,
qtr., wt, pt) consisting of patient Emergency Severity Index (ESI=1,...,5),
patient arrival time to the ED (at), an intermediate variable for Calculating wait time (qt),
patient wait time for receiving services (wt) and activities process time (pt). In the initial
marking, the New Patient has a random integer ESI number Between 1 to 5, an arrival
time based on an exponential distribution with mean 9, qt is equal to at and wt and pt are
equal to 0. In the ED layer (Fig.2) there are 8 transitions (the rectangles) with tag beside
them which called substitution transitions. Each of this transition has a subnet page belong
to it that corresponds to one of the considered tasks in the process. To know about the mod-
el mechanism in each subnet consider GP visit subnet page as an example (Fig.3).The oc-
currence of the transition Start visit models the situation where a general Practitioner
(resource) changes from being ready to being busy until the transition End visit occurs.
Patients wait to seize GP and after stochastic delay (GP visit time) and receiving GP orders,
they release that resource and come back to top layer to carry on rest of the process. The
other page is as the illustrated mechanism.
K. Salimifard et al.: Improving Emergency Department Processes 341
Table 2. Place Description of the ED core layer
Place description
P1 State for non urgent patient
P2 State for urgent patient (CPR needed)
P3 Patients visited and need extra services
P4 Patients visited and will be discharge
P5 Patients admitted
P6 Patients admitted and need surgery
P7 Number of patients waiting for radiology
P8 Number of patients waiting for laboratory
P9 Patients have done radiology test
P10 Patients have done radiology and also need lab test
P11 Surgery result with success
P12& P13 Patients with their Lab test result
P14 Patients have done radiology and do not need Lab
The model contains resources (shown in Table 3) like nurses; physicians etc. in the form of
tokens, and patients use these resources according to model logic to receive care. These
resource tokens are held by the patients until they move to the next stage. The delay in
availability of a resource is represented as non-availability of tokens to advance the patient
tokens through the net. This delay increases the number of patient tokens in the system
waiting for a resource. Also Sets of variables used on the transitions in Fig. 2 are showed in
Table 4.
Table 3. Initial resource-token distribution
resources places tokens
Triage nurse 1
GP Doc 1
admission 1
SP Doctor 1
Radiology staff 6
Laboratory staff 12
CPR equipment 1
342 ModBE’13 – Modeling and Business Environments
Table 4. Model variables and description
variable description
Represent each patient and carry five attribute: ESI, arrival
p
time, qt, wait time, process time which are assigned to them
l determine that patient need laboratory test or not
r determine that patient need radiology test or not
LR Laboratory result
RR Radiology result
gp General Practitioner (resource)
sp Emergency medicine specialist (resource)
K. Salimifard et al.: Improving Emergency Department Processes 343
p@+expTime(9)
1`(1,0,0,0,0)@0
p new NewPatient
(p)
Triage Arrival next
patient patient
Triage
p PAT PAT
p p
p2
p1
PAT
PAT
p
p
GP
visit p4 p
p GP
Visit
gp
PAT
1`gp@0 ((p,l,r),or)
GP
Doc OPAR p3
GP
gp
((p,l,r),or)
CPR
[r=need]
CPR p (p,l,r) (p,l,r)
P_HIGH p6 Admission p5 t1
PAT Admission
(p,l,r) PAT1 (p,l,r)
sp
p p7 PAT1
[r=notneed] t2
(p,l) (p,l,r)
p8 PAT4 Radiology
ED
OR
sp p Radiology
OR
(p,l) (p,l,RR)
p11
PAT (p,l,RR) (p,l,RR) t (p,l,RR)
LAB p10 p9
3 PAT2
p LAB
p p PAT2 [l=Y]
[result=bernoulli(0.4)] (p,LR) (p,LR,RR) (p,l,RR)
t5
p12
PAT5 p13 [l=N] t4
PAT6
if
result=0
then
1`p
(p,LR)
else
empty (p,RR)
(p,LR,RR)
1`sp@0
SP
sp SP
visit p14
Doctor (p,RR)
SP
visit
SP PAT3
if
result=1
then
1`p
p p p
else
empty
p
p t
dead inpatient refer discharge
PAT 6
PAT
PAT PAT
Fig. 2. Core page of ED simulation model using Coloured Petri net (top layer)
In Fig.3 the function on output arc from end visit transition determines whether pa-
tients need diagnostic tests (laboratory or radiology) or surgery or to be discharged. In SP
visit subnet page shown in Fig.4, the SP Doctor place is a common resource that is shared
by three activities in the page. Patients with Lab result, Radiology result or both of them are
coming to SP, because SP should decide about them. Patients may need to be inpatient in
ED. So go to the ED inpatient place or maybe it is necessary to go to other hospital ward
for special care, then go to the refer place. Finally, patient after visit by SP may be dis-
charged, so they go to discharge place in SP visit page.
Model validation. We validate final results of the simulation model at first by interviewing
ED senior managers and nursing staff in order to validate the final results of the simulation
model. Secondly output of the simulation model is compared with real performance indica-
tors (Table 5) and it shows the validation of our model
344 ModBE’13 – Modeling and Business Environments
1`gp@0
gp GP gp
Doc
I/O
GP
p start upd_p@+proctime visit (esi,at,qt,wt,pt) end
p1 visit room visit
In
PAT PAT
input
(p);
output
(upd_p,proctime); (((esi,at,qt,wt,pt),labNEEd(),radNEEd()),OrNEed())
action
startGPVisit(p);
visit
((p,l,r),or) ed
((p,l,r),or)
PAT0
[l=N,r=notneed,or=no] t1 t2
p
((p,l,r),or)
p4 p3
Out Out
OPAR
PAT
Fig. 3. GP visit page of substitution transition GP visit in ED page (subnet layer)
Finally we also used CPN Tools state space graph to investigate whether the model works
truly or not. The state space tools are used to calculate state spaces and to generate state
space reports. Because our graph is very large, it is not possible to show it here.
Table 5. Comparison between simulated and real data.
Simulation
Performance criteria
real data
output
Wait for GP visit
3.2 2.9
Wait for Admission
5.12 5.5
Wait for SP visit
1.15 1
ESI 1&2 LOS
38.2 37.5
ESI 3 LOS
185 187
ESI 4 LOS
140 136
ESI 5 LOS
11.5 12
The performance metrics are investigated using 5 different replications with 95% confi-
dence interval. In each case the system is simulated by a long simulation run of 3 years.
K. Salimifard et al.: Improving Emergency Department Processes 345
1`sp@0
SP
Doctor SP
I/O
sp sp
p12 PAT5 p13 PAT6 p14 PAT3
In In In
sp (p,RR)
(p,LR) (p,LR,RR)
input
(p,LR); input
(p,LR,RR); input
(p,RR);
output
(upd_p,proctime); start output
(upd_p,proctime); start start output
(upd_p,proctime);
action visit1 action visit2 sp visit3 action
startSPVisit1(p,LR); startSPVisit2(p,LR,RR); startSPVisit3(p,RR);
(upd_p,LR)@+proctime (upd_p,LR,RR)@+proctime (upd_p,RR)@+proctime
sp
p1 PAT5 p2 p3
PAT6 PAT3
((esi,at,qt,wt,pt),LR) sp ((esi,at,qt,wt,pt),LR,RR) ((esi,at,qt,wt,pt),RR)
end end end
visit1 visit2 visit3
((esi,at,qt,wt,pt),LR)
((esi,at,qt,wt,pt),LR,RR) ((esi,at,qt,wt,pt),RR)
PAT6
p4 PAT5 p5 p6 PAT3
(p,LR) (p,LR) (p,RR) (p,RR)
(p,LR,RR) (p,LR,RR) (p,LR,RR)
[LR=natural] [RR=notok]
[LR=unnatural] t1 t2 t3 t4 t5 t6 t7 [RR=ok]
p
p p [LR=natural
andalso
RR=ok
]
p
p
p
p
[LR=unnatural
andalso
RR=notok
]
[LR=unnatural
andalso
RR=ok
orelse refer inpatient PAT dicharge
PAT
LR=natural
andalso
RR=notok
] Out Out Out
PAT
Fig. 4. SP visit page of substitution transition SP visit in ED page (subnet layer)
4 Improvement scenarios
In order to improve processes in terms of system performance metrics, four types of scenar-
ios were defined. These alternate scenarios are validated with domain experts and then were
implemented in simulation model. They are as fallow:
• Current scenario (benchmark):
A – Current state of the ED as a basis for comparisons.
• Increase or decrease scenarios. It is, in fact, the most common type of scenario associ-
ated with simulation studies. In this scenarios (increase or decrease) number of re-
sources, the number of emergency room doctors, nurses, beds and other physical re-
sources will be changed. In this view, one scenario is defined here:
B – Increase an emergency medicine specialist (SP)
• Displacement Scenarios. In these scenarios, if possible, an alternative resource will be
replaced with available resource.
C – Putting in place an emergency medicine specialist instead of GP
346 ModBE’13 – Modeling and Business Environments
• Structural scenarios. The purpose of these scenarios is change of the process activities
and even delete or add new activities as part of the process.
D – Remove triage unit and refer patients for triage and visit to GP
• Hybrid scenarios. These scenarios are defined as a combination of two or more than
two of the above scenarios. For example, displacement scenarios, and a structural sce-
nario combined to make a hybrid one.
E – Replace GP visit and triage activities with a substitute emergency medicine
specialist who does these two.
In scenario B, we have added 1 specialist to SP Doctor place and then run the simula-
tion model. To implement scenarios D and E, we have to change our basic model. In these
scenarios triage and visit is done simultaneously by a substitute doctor (GP or SP). The
difference is on the time of visit done by each of them. It’s less for SP than GP.
The results of running simulation model with scenarios A to E alongside with their im-
provement are shown in Table 6. We ran each of the improvement options individually as
separate scenario for this purpose.
Table 6. Improvement rate of each scenario considering its resources
Resources Improvement rate (%)
Resource utilization rate
Wait for Admission
(%)
Admission Staff
ESI 1&2 LOS
Scenarios
Wait for GP
Wait for SP
ESI 3 LOS
ESI 4 LOS
ESI 5 LOS
Admission Staff
GP
SP
GP
SP
A 1 1 1 62 63.7 58 3.2 5.12 1.1 38 185 140 11.5
B 1 2 1 +9.67 -10.5 0 0 +23 0 +5.2 +2.7 +2.65
0
C - 2 1 +7.25 -1.8 - - -21 -7.2 +5.2 +0.5 +1 +8.7
D 1 1 1 +8 -0.3 +14.5 -65 +0.3 -81 +8.6 +1 +1.42 +19.1
E - 2 1 +11.3 -0.3 - - -2 -81 +9.2 +1.35 +2.15 +21.7
Benchmark scenario, A, represent current situation in terms of three performance
measures. Waiting time is one of the effective measures of patient satisfaction. Here are
three main areas of patients waiting for service. Current scenario has the lowest waiting for
GP. Scenario B and C reduce SP waiting by about 45% and 0.4%. Scenario B reduces
admission waiting by 10%. Patients’ length of stay is a measure of ED efficiency and very
important in hospital performance evaluation. We compare LOS for patients with different
ESI level. ESI 1 and 2 include those patients who need CPR and then go to inpatient. In this
level, E has 9.2% improvement. D reduces LOS by about 8.6% and B and C by about 5.2%.
Patients with ESI 3 are patients who need two diagnostic tests here include Laboratory and
K. Salimifard et al.: Improving Emergency Department Processes 347
Radiology. In this level B, C, D and E reduced LOS by about 2.7%, 0.5%, 1% and 1.35%.
Patients with ESI 4 just need one diagnostic test, laboratory or radiology. In this level B, C,
D and E reduced LOS by about 2.65%, 1%, 1.42% and 2.15%. Finally, patients with ESI 5
are outpatient and leave ED after GP visit. In this level B, C, D and E reduced LOS by
about 0%, 8.7%, 19.1% and 21.7%. Resource utilization represents total busy time of re-
sources to available working time under the simulated conditions.it is a good measure for
ED manager in the allocation of resources. Scenario A improves GP utilization by 18%.
Scenario B, C, D and E improve admission staff utilization by about 9.67%, 7.25%, 8% and
11.3%. Scenario A has the most SP utilization and other scenarios reduced it. Substituted
SP utilization for scenario E is more than C by about 2.1 minute. Also ED staff reaction to
our work was positive and they helped us through the work but due to the reluctance of ED
managers, we failed to implement the proposed changes in reality.
5 Conclusions and future work
In this research a CPN model was developed to analyze the performance of an emergency
department. To evaluate the system under different conditions and improve processes, im-
provement scenarios were defined. These scenarios may not greatly improve the perfor-
mance of the model parameters, but could be considered as an existing and potential alter-
native. We compare 5 scenarios by three variables.
In table 7, improvement rate of each scenario, considering its resources, presented.
To have a better analysis in choosing scenarios, it is necessary to see cost and benefit of
each scenario simultaneously. Another option which should be considered is ED’s mission,
saving patients with high acuity (ESI 1&2), and scenarios that aim to facilitate this pur-
pose even if they cost more than other, are selected. Among defined scenarios, E and D
have more improvement especially about patient with ESI 1&2. Although the cost of sce-
nario E to scenario D is some more, but given the purpose of the improvements resulting
from the scenario E, this scenario is selected as major one. In the next stage scenario D due
to lower cost and also more overall improvement than the other two scenarios have been
chosen as the second better scenario.
Based on the model proposed in this paper, it is possible to translate the flow diagram
into a Generalized Stochastic Petri net. It would be interesting to compare the results of the
two modeling approaches. That is, the exact values of different performance indices can be
compared with the simulated values. Because of the hierarchical nature of the model and
that every activity has a separate page belong to it; acceptance and use of this model in
various conditions may seem easy and by just few change it could be localized. Using Col-
oured Petri net, we were able to assign different attributes to patients entered into the ED
and therefore, the model traces them to calculate performance metrics. The tools and fea-
tures that are available for simulating CPN models in CPN Tools e.g. hierarchy, functions,
guards, state space analysis etc. made it a useful option in simulating complex systems
specially healthcare. Future development to this work would be to add other attributes to
tokens color such as cost of each activity in the process and engage other wards. Also, it
would be of value to consider other resources including beds, facilities and equipment.
348 ModBE’13 – Modeling and Business Environments
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