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6
International Journal of
Science and Engineering Investigations vol. 10, issue 109, February 2021
ISSN: 2251-8843
Received on February 5, 2021
Applications of Queuing Theory and Discrete Event Simulation
in Health Care Units of Pakistan
Muhammad Ahmed Kalwar1, Hussain Bux Marri2, Muhammad Ali Khan3, Sarmad Ali Khaskheli4
1Post Graduate Alumni (MUET) & Assistant Manager Production, Shafi Private Limited, Lahore, Punjab, Pakistan
2Meritorious Professor & Ex-Chairman, Department of Industrial Engineering and Management, Mehran University of
Engineering and Technology, Jamshoro, 76062, Sindh, Pakistan
3Post Graduate Student & Assistant Professor, Department of Industrial Engineering & Management, Mehran UET, Jamshoro,
76062,Sindh, Pakistan
4Assistant Manager, Karachi Shipyard & Engineering Works Limited, Karachi, Sindh, Pakistan
(1kalwar.muhammad.ahmed@gmail.com)
Abstract- In the present research, the contribution of queuing
theory and discrete event simulation in the improvement of
healthcare was discussed in detail in the light of previously
conducted research. This narrative literature review was
conducted on the available research on the problems of
healthcare in Pakistan and the analysis of evidences which are
obtained from queuing theory and discrete event simulation
(DES) research. Data was collected from the reports of world
health organization and World Bank group and it was
organized into tables by using MS excel. Mismanagement of
the resources and the queuing system was highlighted to be the
main reason for low quality of the healthcare service delivery
in public sector hospitals of Pakistan. Behavior of staff with the
arriving patients was reported to be irritating in public sector.
Moreover, delayed service, long waiting times and less
departmental capacity (at emergency, OPDs and laboratories)
are the problems faced by the patients. On the same time,
number of doctors is also less than required. When the citizens
come to the healthcare facilities, at the point of service or
distribution, overcrowding scenario is observed to an
increasing extent. Patients are delayed at the public healthcare
units long before they are served by medical staff. The delay is
the main issue and that can be obviously understood that it is
due to poor design or mismanagement of queuing system. For
all these problems, queuing theory is the best tool but
nowadays, simulation methodology has taken over the side of
queuing theory very precisely. In this regard, this review
contributes in highlighting the problems of healthcare in
Pakistan and so it focus on the solution provided by the
previous researchers as well. This review paper presents the
overall picture of healthcare delivery system of Pakistan. Since,
the issues of intensive care units (ICUs) and emergency
departments (EDs) at the hospitals have specific issues of their
own. The major limitation of this research paper is that it
doesn`t present the in-depth understanding of problems of each
facility. When the system (healthcare facility) is congested,
patients wait more in the queues and system in order to get
served. AT ICUs and EDs patients are in critical conditions and
if the patients are made to wait in that condition, anything can
happen. In this regard, it is suggested that review of problems
of ED and ICUs should also be reviewed specifically so that
the problems can highlighted for the greater good of nation.
After the deep review of literature, it was clear that none of the
literature reviews discussed the healthcare problems in the
respective country and the review of contribution of related
methodology at the same time. The contribution of present
research in highlighting the problems of healthcare delivery
system in Pakistan and review of queuing theory and queuing
simulation cannot be ignored.
Keywords- Queue, Simulation, Waiting Time, Healthcare,
Hospitals
I. INTRODUCTION
World health Organization (WHO) has defined healthcare
in its report of 2000 that “all organizations, institutions and
resources that are devoted to producing health actions”
(Musgrove et. al., 2000). Health is termed as the functional
fitness that stress on personal and social resources, as also
physical capabilities. In the race of human beings, the degree of
physical, emotional, mental and social ability of and individual
to deal with his/her surrounding environment is known as
health (Naz et. al. ,2012). Health is defined by World Health
Organization (2010) as “a state of complete physical, mental,
and social well-being, and not merely the absence of diseases
or injury” (WHO, 2010). Good health is a requirement for
respective working of any individual or society, if the health of
individuals is good then they can engage themselves in various
types of activities (Naz et. al. ,2012). But if they are injured,
distressed or ill, they may face a certain limitation in their lives
and in comparison to health other pursuits in one`s life are
meaningless (Jalal et. al., 2009). Healthier people can only be
the source for making the healthier society, therefore, the
Government should frame the policy and regulation on patient
care and also take step of developing mechanism to insure
compliance (Nasim & Janjua, 2014). Access to healthcare
services is dependent on accessibility of the service for
example, availability of doctors, healthcare centers and also
hospitals. Research has concluded that due to lack of interest of
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ISSN: 2251-8843
staff and unavailability of facilities are the main reasons of
dissatisfaction of patients in Pakistani public healthcare system
(Ahmad et. al. , 2013). It is always expected from the health
care systems to serve the medical needs of the population
effectively and efficiently. One of the major objective of health
care systems is to improve the health of the living people of the
country (Musgrove et. al., 2000), (Mashhadi et. al., 2016).
Good health is necessary for the citizens of any country; if
the people are healthy then they can contribute in the
improvement of national economy. Healthcare system is the
major sector which plays an important role in providing and
maintaining good health of citizens of country. There are two
healthcare sectors exist in Pakistan i.e. public and private. Long
before, private hospitals were in a little quantity but due to the
poor healthcare services, it attracted the people by providing
better healthcare services to them. These two healthcare sectors
were compared and it was concluded that it will be wrong to
say that the private sector is more efficient and effective in
terms of the available facilities and infrastructure; poor
healthcare services in the public sector hospitals are due to the
mismanagement of the medical personnel, which leads to
patient dissatisfaction and they cannot have the desired level of
service.
Pakistani public health care system facilitated with the
various facilities and resources which are certainly not enough
and the available facilities and resources are at the point of
mismanagement. This is the reason patients arriving at public
sector hospitals face a lot of problems. Delay is one of the
major problems, some of the patients die waiting for their turn
of service. Service is delayed when the service demand is more
than the available capacity. When there is low capacity in
comparison to the demand then the queue will form in the
system. For the analysis and study of queues, queuing theory is
used. Queuing theory was formulated by Danish Engineer A.K
Erlang in 1913. It is the mathematical tool to solve the
problems of queuing systems. The optimum solutions are
figured out by the help of queuing theory in the form of
performance measures. Unlike queuing theory, simulation is
also justified approach to detect the bottlenecks in the queuing
system or the process of service as reported by many authors.
II. AIMS AND OBJECTIVES
Since healthcare system problems are main problems of
any country because without healthier citizens any country will
lag behind. In this regard, aim of this research was to highlight
the problems of private and public healthcare in Pakistan and at
the same time, solutions of various problems were also
discussed in the light previously conducted research.
To identify the problems of Pakistani private and public
healthcare delivery systems
To review the applications of queuing theory and discrete
event simulation in solving the problems of healthcare
delivery systems across the globe
To suggest the space for the improvement in healthcare
delivery system
III. RESEARCH METHODOLOGY
This narrative literature review was conducted in order
gather both the problem and solution. For the analysis of
literature, narrative method of review is used. This method of
literature review on the usage of technology empowers the
broader picture of problems and controversies associated with
the use to technology (Frennert & Östlund, 2018). It helps in
the analysis of debates, results of previously conducted
research and current shortage of knowledge and at the same
time, it also helps in suggesting the future implications (Ferrari,
2015).
A. Data Collection
The data used in the present research paper was Secondary
in nature which was collected from the reports of nationally
and internationally recognized organization i.e. WHO, world
bank. The evidence from previously conducted research
(queuing theory and discrete event simulation) were collected.
Moreover, the collected data was organized in tables for the
clear understanding. The most recent literature was reviewed
so that the recent trends on the subject could be highlighted.
B. Data Analysis
All the data gathered and organized for the clear depiction
of trends and broad understanding. For data organization, MS
excel was used.
IV. LITERATURE REVIEW
In order to understand at the broad level, firstly, healthcare
system was described in the general perspective and then it was
carried out by focusing it in the context of Pakistani healthcare
system (problems and ultimate solution by using queuing
theory and discrete event simulation).
A. Healthcare system
Good health of the people is essential in order to develop
and improve the economic state of country.Health care delivery
among various service deliveries has been explained as the
kind of delivery in which there is high consumer involvement
in the process of consumption process. In whole of the process
client/patient is involved. A bad service delivery can harm the
patient and it may lead to the loss of his/her life.This is the
reason, investigating patient/client satisfaction is necessary
effort in order to bring about the improvement in the quality of
health care system(Nkrumah et. al., 2015). Patient flow in the
hospitals is particular interest of the researchers and that of
practitioners, with the assumption that on improving the patient
flow there would be significant impact on the patient
satisfaction and so on the quality (Armony et. al., 2015). The
perspective of patient satisfaction has gained serious attention
in hospital care in the recent years (Khamis & Njau, 2014).
Service quality and patient satisfaction are in a close
relationship, good service quality gives out the encouragement
to the patient to go for a strong relationship with the particular
hospital (Surydana, 2017), (Kalwar, 2020). Service quality
according to Kotler (2009) is the difference between real and
expected of customers supposed to be provided to the customer
(Surydana, 2017). Nowadays, patients bear many opinions
International Journal of Science and Engineering Investigations, Volume 10, Issue 109, February 2021
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ISSN: 2251-8843
when deciding upon to have the services of particular
healthcare provider (Yeddula, 2012). The image and patient
satisfaction are important factor for companies to influence
both tangible patient loyalty for re-coming and recommend it
to others(Juhana et. al., 2015), (Kalwar et. al., 2018).
Hospitals are one of the most important links in the
healthcare service chain and their quality directly affects
people’s lives (Dong, Yom-tov & Yom-tov, 2015). Hospital is
the major section in the view of health care settings, it is found
to have major impact on disease prevention, earlier detection,
treatment and restoration of patients (Haghighinejad et. al.,
2016). Globally, the main focus of hospitals is on occupancy
and discharge rates of patients so that the executive capacity of
the system can be figured out. Methods of Management
Sciences or Operations Research can help managers who are
involved in the activity of planning and management of
resources (Gunal, 2012). Tremendous literature is available on
the reforms of health care and many methods are debated
regarding how the reforms can be assessed? An explicit
framework is required for performance management against
which the performance can be judged and quantified (Tandon
et. al., 2002 ).
1) Healthcare System in Pakistan
In Pakistan, the distribution of healthcare facilities is unjust
in public as well as private sector, by which they are made
inaccessible to people of low income in rural areas (Naz et. al.
,2012), (Bergman, 2011). Pakistan is categorized as the country
with low income (World Bank, 2006) and according to Human
Poverty Index (HPI), it is ranked at 65th among 102 developing
countries (Watkins, 2006). However, Human development
Index (HDI) is upgraded from 0.346 as it was in 1975 to 0.539
in 2006, this is quite slow improvement and is ranked at 134th
number in 2006 United Nations Development Program
(UNDP) HDI due to its poor social and development indicators
in comparison to the countries of same level of economic
development (WHO, 2007). Health care services regulations
and coordination is still in state of evolution in the context of
structure, roles and responsibilities (WBG, 2015). Throughout
last five decades, Pakistan is improving quite slowly in health
sector as witnessed by its mentioned health indicators,
strengths and weaknesses. Therefore, the government should
take the initiative of improving it (Kurji, Premani & Mithani,
2016). Usually, public sector is regarded as providing more
reasonable and evidence-based care. After review of literature
systematically by S. Basu et al (2012), this claim is not
supported that private sector is more efficient, accountable or
more effective in terms of medical services than public sector,
however, public sector is frequently lacking in timeliness and
patient hospitality apparently (Basu, et. al., 2012). In Pakistan,
there is the existence of two parallel health care systems i.e.
public and private. The private sector was so small at the very
first until majority of the people visited there for resolution of
their medical problems and then businessmen transformed it
into the hospitals after the passage of time (Bergman, 2011). It
was indicated by the literature that people of Pakistan are not
capable enough in terms of affordability towards the private
healthcare; Because of increasing industrialization and
population, environmental pollution is increasing day by day
and the public healthcare facilities not sufficiently provided:
therefore, it was suggested to Government in that it should
focus on bringing about improvement in public healthcare
(Watkins, 2006).
In Pakistani public sector hospitals, the quality of the
healthcare service delivery is highly ignored and
inconsistencies of the process are not perceived as the main
problem in health care facilities (Sajid et. al., 2008). The
patient`s visits to the hospitals are observed to be increasing
with the increasing population because in the context of
relationship between health and development Pakistan is at
main intersection being the 6th highly populated country with
the population of 191.71 million with growth rate of 1.91%
(Mashhadi et. al., 2016). Therefore, due to continuously
increasing population, health care services also need to be
enhanced and improved so that the people can be provided
better health care by the Government. Hospitals are the one of
essential connections in the chain of health care service and the
lives of the people are directly affected by the quality of
healthcare (Gunal, 2012).
a) Problems of Healthcare in Pakistan
Public healthcare system in Pakistan is large and dispersed
and is given in access to people with trained doctors, staff and
medicines; but there was the problem of unavailability
medicines and doctors due to the unavailability of doctors; It
was concluded in the study that these both problems were due
to managerial constraints not because of financial constraints
(Callen et. al., 2013). An empirical study conducted to expose
the problems faced by the patients in public health care
hospitals. Study showed that 36.4% patients were poor who
visited the hospital, 41.8% patients reported that staff is
frustrated towards the patients; furthermore, 72.7%
respondents had common opinion that poor patients are not
well treated, whereas, 96.4% of patients reported about the
preference of doctors to relatives and known patients (Ahmad
et. al. , 2013). Another study was conducted on public sector
hospitals of Pakistan, and it was revealed that mostly poor
people visited the public hospital for their health issues and
they faced variety of problems there in terms of treatment and
facilities. The picture of public healthcare service delivery
represents an even distribution of resources between urban and
rural region. The poor in the rural areas are at obvious
disadvantage in the context of primary and tertiary public
healthcare facilities and they also fail to take advantage of
immunization of their children from the public programs
(Afzal & Yusuf, 2013). Due to poor health services patients
especially children and women are suffering a lot. It be seen in
the table 1 that the health indicators are poorly decreasing;
after the period of two decades, infant mortality is decreased
from 95/1000 lives to 60/1000 lives. Same case is with the
maternal mortality rate, it has decreased from 490 -260 lives
per 100,000 lives. Children mortality under five years is
decreased from 122 – 74 in two decades.
There is greater number of children which are affected
because of not being provided the proper vaccines. However,
the report of World Bank Group 2015, shows that infant
mortality rate is 69/1000 live births. It seems to be increased
than that was reported by World Health Organization in 2013
i.e. 60.
International Journal of Science and Engineering Investigations, Volume 10, Issue 109, February 2021
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ISSN: 2251-8843
TABLE I. HEALTH INDICATORS OF COUNTRIES OF SOUTH ASIA
Health Indicators
Pakistan
Bangladesh
India
Sri Lanka
Nepal
1990
2010
1990
2010
1990
2010
1990
2010
1990
2010
Infant mortality rate (per 1,000 live births)
95
60
97
39
81
49
24
11
94
41
Maternal mortality rate (per 1,000 live births)
490
260
800
240
600
200
85
35
770
170
Under-five mortality rate (per 1,000 live births)
122
74
139
49
114
63
29
13
135
50
Immunization (DPT)* among 1-year old (%)
54
86
69
95
90
72
86
99
43
82
Immunization (measles) among 1-year old (%)
50
82
65
94
56
74
88
99
57
86
Total fertility rate (births per woman)
-
3.4
-
2.2
-
2.6
-
2.3
-
2.7
Life expectancy at birth (years)
-
65.2
-
68.6
-
65.1
-
74.7
-
68.4
Source: World Health Organization (2013) (Breu, Guggenbichler & Wollmann, 2013)
This data is an accurate and proper reflection of poor health
care services of public health sector of Pakistan. These issues
must be resolved so that the existing healthcare system can be
improved and vulnerable people can be provided better access
to public healthcare facilities and service. The reasons behind
poor health services at public hospitals are limited
governmental funding, lack of governmental interest in
launching new healthcare projects and over-burdened public
hospitals (Ahmad et. al. , 2013).
TABLE II. HEALTH INDICATORS OF COUNTRIES OF SOUTH ASIA
Infant mortality rate (per 1,000 live births)
Malnutrition prevalence, (% of children under age 5)
Maternal mortality rate (per 1,000 live births)
Country/Year
2013
2004-11
2013
Afghanistan
70
-
400
Bangladesh
33
42
170
India
41
48
190
Nepal
32
41
190
Pakistan
69
43
170
Sri Lanka
8
19
29
Source: The world Bank Group (2015) (WBG, 2015)
It was suggested in the research that the Government
should focus on health care in terms of proper medical
equipment and infrastructure maintain check and balance, in
this way the problems can be reduced (Naz et. al. ,2012). The
human resources for healthcare are gradually increasing in
Pakistan year by year. As reported by International Finance
Corporation (IFC) in its report of 2011 that, 5000 medical
graduates are produced by different universities and colleges.
The present ratio of doctor to person is 1:1,183, which is quite
below than the standard recommended by World Health
Organization (WHO) i.e. 1:1000 (Bergman, 2011). The
requirement of medical personnel i.e. doctors almost complete;
it is quite near to the standard recommended by World Health
Organization. Now, dynamic leadership and governance is
needed desperately for designing and enforcing evidence-based
policies, programs and the way to take care of the system
(Kumar & Bano, 2017).
Besides above mentioned problems the patients in the
public sector hospitals face too many problems and delay is
one of those major problem. Patients wait too long in order to
get served in hospitals, it’s a potential threat to healthcare
services and is observed to an increasing extent (Obulor & E.
B.O, 2016). Healthcare sector is facing the problem of delays.
All of us wait for an appointment regarding health issue at
hospitals and after arriving the facility we are supposed to wait
even more to see the doctor. Delay is not unusual in hospitals,
we always find may people awaiting at different stages in the
hospitals i.e. patients waiting for surgery, Diagnostic tests,
OPDs, Emergencies etc. (Green, 2006).
2) Problems of Hospitals
Nowadays, the big problems of the hospitals is congestion
of patients at receptions, out-patient departments (OPDs),
emergency departments, intensive care unit (ICU) and waiting
areas. This is because of inaccuracy of planned queuing system
in the various areas of hospitals. Queue is the common
occurrence in daily life (Kembe et. al., 2012)–(Yusuff,
2015)e.g. at Hospitals. When the numbers of patients exceed
the number of doctors then the queue is formed. Outdoor
patient department (OPDs), emergency department (EDs) are
the most visited departments at any hospital and are the initial
confrontation of a patient with staff of hospital to get
service(Wang et. al., 2009). Highlighted problem that the
patients face is long queues which causes delay for patients to
consult the doctor. Most of the patients die until their turn to
get the service. OPDs and EDs play an important role in the
healthcare services. In the past ten years, developed countries
have stressed on the EDs in terms of overcrowding crisis and
their impact on service time and on the same time great
attention was paid on the ability of the hospital to meet medical
emergency needs (Haghighinejad et. al., 2016). Due to
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ISSN: 2251-8843
lacking in the control over the customer services, the capacity
planning of the particular department can complicated by the
service demands (Uriarte et. al., 2015).Delay is the difference
between service demand and the available capacity to meet the
demand (Green, 2011). Long waiting experience of the
patients in the queue usually have negative impact on the
satisfaction of the patient (Obamiro, 2010). Which incurs cost
to organizations, which is termed as cost of customer
dissatisfaction (Kembe et. al., 2012), (Agyei, Darko, and
Odilon, 2015). Poor health services are acting as obstacles
against the overall development of Pakistan (Mustafa, 2015).
B. Application of queuing theory for the improvement of
healthcare operations
Hospitals are known as complex systems which are
included with some societal benefits and bulk incurred costs.
Those costs are made to be incurred more because of
inefficacies of processes which occur due to congestion and
delays in the patients care systems. Literature indicates that
prediction of level of congestion and needed capacity is
impossible to be figured out without the help of queuing
models (Green, 2006). Therefore, in order to study and
improve patients flow, it is suitable to look at the facility with
the lens queuing network (Armony et. al., 2015). Queuing
models are required to be put in a little data and results can be
calculated by the help of simple formulae in terms of
performance measures; this is an easier way to figure out the
optimum solutions instead of estimating the performance of the
system in the provided context (Green, 2006).
The most practical approach to solve these sort of issues is
queuing theory or waiting line theory (Olorunsola et. al., 2014).
It was developed by renowned Danish telephone engineer
AgnerKrarupErlang in 1913 (Bastani, 2009),(Kissani & Rifai,
2015),(Green, 2011), (Mustafa & Nisa, 2015)–(Varma, 2016).
He was the first scientist in 20th century who treated the
congestion problem in the context of telephone
exchange(Mwangi & Ombuni, 2015). The major elements in
waiting line theory involve people getting services, entrance
process, queue formation, discipline of the queues and the
service mechanisms in the service industries like as hospitals,
waiting times of the customers/patients must be predicted at the
different levels of the service (Fitzsimmons, Fitzsimmons &
Bordoli, 2008). Queue or waiting line at hospitals are
associated with waiting cost of patients, when they are made to
wait in the hospitals (Kembe et. al., 2012)(Khaskheli et. al.,
2020). These problems are solved and simplified by using the
queuing theory. In which waiting time and service times are
calculated and also the optimum service level and waiting time
of the patient can be calculated (Varma, 2016). The study of
queue deals with quantifying the phenomenon of waiting in
lines using representative measures of performance, such as
average queue length, average waiting time in queue and
system respectively and average facility utilization(Adaora,
2013).Queuing models are used to study queue systematically
(Bastani, 2009), (Kandemir & Cavas, 2007). Due to dealing
with the overcrowded scenarios, queuing theory is also known
as the theory of overcrowding(Adaora, 2013). It is widely used
in service organizations for waiting lines to be analyzed and
their processes to be modeled (Olorunsola et. al., 2014).
Aggressive driving behavior has become prevalent (Kalwar et.
al., 2020), (Khaskheli et. al., 2018). In recent years it has been
the teething concern in health care services (Ikwunne &
Onyesolu, 2016). It is required to increase the customer
satisfaction by reducing the queue and making service delivery
efficient (Fomundam & Herrmann, 2007).The analytical
approach i.e. queuing formulae and its solutions are only
possible when the hospital already exists, then the data would
be collected after the collection of data, the optimum queuing
system can be suggested. What if the actual system is not
installed and the scenario which is not real but the computer`s
manipulated calculations are taken out by different software,
which are considered as the replica of real world systems. This
method is called as simulation, now a days most of the
decisions are made on the basis of simulation. Suppose we are
taking the simulation model of radiology department of the
hospital, it can be used for the better understanding of the
impact of new machine that it may have on the service quality
of hospital (Gunal, 2012). Simulation is more effective as
compared to analytical solutions because in case simulation
analysis of complex models, the conditions can be changed and
the behavior of model can be judged (Haghighinejad et. al.,
2016).
1) Related Research Work
Mustafa &Nisa, 2015 used applications of queuing theory
in healthcare were mainly focused. Different departments i.e.
patient’s registration department, outpatients department
(OPD) and pharmacy were under consideration: on the same
time, different processes in in the queuing system were also
kept on the observation. Exponential and poison distribution
were used for the service and arrival of patients respectively.
Single server M/M/1 and multiple server queuing models
M/M/2 were used for the calculation of performance measures
and for analysis simulation was used. Furthermore, correlation
among performance measures was also calculated (Mustafa &
Nisa, 2015).
Olorunsola et al., 2014 modelled Patients` flow in his
research; Queuing theory was used and the performance
measures were calculated so that optimum bed count could be
determined. For the analysis of queuing system multi-server
queuing model was used. As per its assumptions, it was
assumed that the arrival and service of patients followed the
poison and exponential distribution respectively. Reneging
logic was used for the analysis of customers`/patients` waiting
times at Emergency and Accident Department of the respective
hospital. On the same time, its impact on the number of beds
was investigated in different departments (Olorunsola et. al.,
2014).
Odunukwe, 2013 conducted study with the aim of
determining the average time of customers they spent in queue
and their time to get served by the service channel; then impact
of wasted time could be investigated on the cost associated.
Data were collected by considering the arrival pattern and
service pattern of customers. Birth and death Markovian
process was used; furthermore, chi-square test was used to
confirm the arrival and service distributions if they were
Poisson and exponential distributions. After this confirmation
the data could be analyzed by using Markovian birth and death
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process. The results indicated service rate is 0.1521 and arrival
rate was 0.2157, the probability of servers to remain idle was
0.2786 (27%) and the waiting cost was calculated to be
N938.597. In last, management was suggested to increase the
number of servers to three so that the waiting time of patients
and the associated cost could be minimized(Adaora, 2013).
Bastani, 2009 estimated the number of required beds at the
hospital. This was accomplished by the use an adequate model
by the help of which patient flow could be analyzed in and
between the various departments of the hospital. Stream of
emergency patients was only focused and the network was
developed in which the interaction between the intensive care
unit (ICU) and the monitor unit (MU) was modelled, which
was meant to be causing a main proportion of the congestion in
the emergency department (ED). MATLAB was used to
develop and simulate the model. It was concluded that the
approximate number of beds was 14 in the Intensive care unit
ICU and 208 beds in the MU for the new hospital setup which
was under consideration(Bastani, 2009).
McManus et al., 2004 developed a mathematical model for
the patient flow. Data of the patients i.e., admission and
discharge of the patients in ICUs. By using queuing theory
application a mathematical model of patient flow was
developed. The actual/real scenario was compared with the
results of the model. After the validation the model was proved
to be accurate(McManus et. al., 2004).
Obamiro, 2010 used multi-server queuing model to carry
out the study. In this research pregnant women arrival was
focused in the hospital. Data was collected for the month. The
frequency of the pregnant women and their waiting times were
evaluated in the different weeks of the month. For data analysis
TORA software was used(Obamiro, 2010).
Kembe et al., 2012 conducted his research at Riverside
hospital. In this study multi-server model was used to calculate
the waiting cost, service cost and opportunity cost and total
system cost by using the performance measures of the queuing
system. TORA software was used to analyze the data. In
conclusion it was suggested that management of the hospital
should increase the number of doctors from 10 to 12(Kembe et.
al., 2012).
Puoza&Hoggar, 2014 used multi-server queuing model to
resolve the issue of long waiting times of patients in the queue
and over utilization of doctors. QM software was used to
calculate the all performance measures and parameters of the
queuing system (Puoza & Hoggar, 2014).
Mensah &Asamoah, 2014 used single server queuing
model to analyze the data. Two hospitals i.e., Nkawie
Government Hospital and Aniwaa Medical Centre which is
fully private owned were compared in terms of traffic intensity
and utilization factor. The data was analyzed in QM software
version 2.2(Mensah & Asamoah, 2014).
Armony et al., 2015 studied the flow at Israeli hospital
through the exploratory data analysis. There were certain
questions that were raised by exploratory data analysis (EDA)
i.e. 1) Can a simple queuing model usefully capture the
complex operational reality of the emergency department
(ED)? 2) What time scales and operational regiems are relevant
for modeling patient length of stay in the internal ward (IWs)?
3) How do protocols of patient transfer between the ED and
IWs influence patient delay, workload division and fairness?
Relating bottlenecks from ED to IW physician protocols were
also given importance(Armony et. al., 2015).
Varma, 2016 aimed to reduce the waiting time of patients,
they spent while in remaining in the clinic. Single server
queuing model was used to calculate the waiting time of
patients, traffic intensity, and average number of individuals in
the system. Poison arrival of patients based on first come first
served discipline and exponential distribution service rate were
the assumptions(Varma, 2016).
Ikwunne&Onyesolu, 2016 used multi server queuing model
to find the optimum service level. The author has suggested the
optimum number of doctors, so that the waiting time of
patients can be minimized. Production management and
operations management (POM QM) and queuing theory
calculator was used to analyze the data(Ikwunne & Onyesolu,
2016).
Khaskheli et al., 2020 conducted their research to suggest
the optimum number of receptionists and doctors at the study
areas in order to optimize the performance of existing queuing
systems at the out-patient departments (OPDs). The most
congested OPD i.e. medical OPD was selected for the study at
the case hospital 1 and then same OPD was selected in another
public sector hospital (case hospital 2). Both hospitals were the
tertiary care hospitals of the different districts of Sindh
Pakistan. Data was collected for two weeks: data collection
parameters were; arrival rate, service rate of patients, number
of servers, salaries of the servers and associated waiting cost of
patients. Arrival and service distribution of the patients were
verified as per assumptions of the multi-server queuing model
(M/M/c) by using input analyzer of Rockwell Arena 14.5.
Performance measures of the queuing system were calculated
by using TORA optimization software. For cost calculation and
graph plots MS excel was used. According to the results, one
receptionist and doctor was suggested to be increased at both of
the OPDs for the minimization of congestion of patients and
their waiting times (Khaskheli et. al., 2020).
Unlike queuing theory, the simulation approach is more
simple and detailed. Simulation leads to the clear
understanding of where bottlenecks exist in the queuing
system. Simulation is a mimic of reality that exists or is
contemplated. Simulation is most effectively used as a stage in
queuing analysis. The simulation is run for patients coming to
department, the pertinent parameters like waiting time, service
time, waiting time-service time ratio (Lade, Choriwar &
Sawaitul, 2013). It is an analytical tool used for creation,
maintenance, evaluation or improvement of a system or
process. In fifties it was firstly used in the healthcare
operations, it was used in order to increase the efficiency of
healthcare operations and after that it has been used as
powerful tool for improving and analyzing the healthcare
systems (Uriarte et. al., 2015).
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C. Application of modeling and simulation for the
improvement of healthcare operations
Real world is represented quantitatively by the help of
discrete event simulation (DES), by which its dynamics is
simulated on an event-by-event basis, and detailed performance
report is generated (Babulak & Wang, 2010). There are three
most common computer simulations i.e. discrete event
simulation (DES), system dynamic simulation (SDS), and
Monte Carlo simulation (MCS) used in health care: the most
popular method is discrete event simulation(Hong et. al.,
2013). Queuing models for systems are inflexible unless
numbers of simplifying assumptions are made. Because of
these reasons, queuing systems are complex and cannot be
analyzed typically by using mathematical models. Instead,
discrete-event simulation is used, in which the values and
expressions of different probability distributions i.e. arrival and
service distribution and on the same time it keeps track of
relevant statistics, which is used to analyze such systems and
calculate the performance metrics (Chan & Green, 2013). In
different clinical settings, researchers of operations research
use queuing theory and discrete event simulation techniques
and use them for deciding the different appointment strategies.
(Priyan, 2017). In the early duration of its development,
discrete event simulation was used greatly in the manufacturing
sector: a basic structure i.e. active and dead stage is followed
by these models where the customers move from an activity to
the queue and usually changing between these two
components. (Swinerd & McNaught, 2014). Organizations are
needed to improve their processes and practices at the advent
of new technology in the market (Kalwar & Khan, 2020)–
(Arain, Khan & Kalwar, 2020). Technologies of discrete event
simulation (DEs) have been greatly used by industry as well as
academia in order to deal with different industrial problems
(Babulak & Wang, 2010). It has greatly grown out of modeling
manufacturing systems, nowadays it has increasingly been
applied in the service sector (Swinerd & McNaught, 2014). A
research was conducted in the 1970s in which DES was used)
to improve flow of patients in emergency rooms and office
doctor (Roberts, 2015). This technique allows end users (i.e.
hospital administrator, clinic manager) to assess the efficiency
of existing health care delivery system(Aeenparast et. al.,
2013).
1) Related Research Work
Kalwar et al., 2020 aimed to suggest the optimum number
and schedule of doctors at the OPD (Out-Patient Department)
of Gastrology of a hospital in Pakistan. In order to achieve this
aim, the discrete event simulation model is developed to
minimize waiting time of patients. Data is collected for one
week from the OPD; Data collection variables are arrival and
service rate of patients, their salaries/income, patient‘s OPD
fee, doctor’s charges/patient, service time of patients at each of
service channel i.e. reception, triage and doctors’ cabin. Stop
watch is used for recording the service time of patients. Input
analyzer is used to reveal the distribution of the data. Rockwell
arena software version 14.5 is used to model and simulate the
queuing system of the outpatient department. Scenario analysis
is conducted in four scenarios; in each of the scenario doctors
were assumed to be seated for one additional hour. During the
period of data collection, it is observed that most of the patients
are coming with an appointment of doctors therefore, it is not
justified to suggest the hiring of new doctor; especially when
patients are coming for the particular doctor; therefore, already
available doctors are suggested to be seated longer in the OPD;
that is the way to serve the maximum number of patients in the
virtual queue of patients that has been kept waiting for having
an appointment and for their turn to see the doctor(Kalwar,
2020).
Roumani, 2013developed discrete event simulation model
with the help of Arena software version 13.0. The model was
simulated for 10000 days with the exercise 50000 days. The
period which is called warm-up period is necessary because it
ensures that whether the system has reached to the steady state
or not before any statistics is recorded. It was executed twice,
at the first execution the Markovin arrival and service were
assumed. Secondly it was assumed generally and exponentially
distributed service was assumed. For validation of simulation
model, the actual flow of patients was compared with the
simulation results of the model (Roumani, 2013).
Connelly & Bair, 2004explored the potential of discrete
event simulation (DES) methods to advance system level
investigation of emergency department operations.
Development and operation of emergency department
simulation was described new platform for computer
simulation activity at a level 1 trauma center. The extend DES
modeling package was used to develop the model. The inputs
of the model were staffing level, facility characteristics and
patient data drawn from the electronic databases. The accuracy
of the model was tested by comparing predicted and known
patients service times(Connelly & Bair, 2004).
Lade et al., 2013conducted his research with the objective
of minimization of patient waiting times in different sections of
radiation therapy and oncology department. In order to achieve
the set objectives, simulation was carried out by focusing 59
patients. Analysis revealed that the doctors should be increased
from 4 – 5; After the increment of one doctor the average
waiting time of patients decreased from 7.20 to 4.25
minutes(Lade, Choriwar & Sawaitul, 2013).
Uriarte et al., 2015conducted his research based on discrete
event simulation based at Swedish Emergency department by
applying Multi-Objective Optimization simulation technique in
order to study the system improvement analysis. Number of
solution were provided to the decision makers after the analysis
was done, in which the length of stay and waiting times of
patients were reduced for Emergency department. Multi-
Objective Optimization simulation technique was proved to be
useful technique for improving healthcare processes(Uriarte et.
al., 2015).
Dawei, 2009conducted simulation to analyze the process of
outpatient service, simulation as conducted by using the Arena
simulation software. The current process of services was
compared with the simulated process so that bottlenecks can be
identified. It was revealed that patients were spending 7.2% of
their total times in the OPD uselessly. This problem was due to
the saturation of medical resources. Therefore, it was suggested
that the outpatient resources should be reasonably coordinated
in order to improve the outpatient flow(Dawei, 2009).
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Wang et al., 2009constructed a model for emergency
services by using ARIS and Arena software. Two assumed
scenarios were tested in these software. The model was
constructed in order to rectify the bottlenecks in the system and
optimally allocated the resources at the different stages of
services(Wang et. al., 2009).
Haghighinejad et al., 2016aimed to reduce the waiting time
of the patients they wait in the queue and emergency
department of Iranian hospital. Arena version 14 was used for
the simulation of results. There was the issue of bed capacity in
the emergency department, and because of that reason patients
waited too long to get served. Therefore, it was suggested in
the study that number of beds should be increased from 81 to
179. Classification of patients was defined in terms of priority;
First priority was given to patients with the high degree of
illness(Haghighinejad et. al., 2016).
Kanagarajah et al., 2008presented architecture of complex
systems and an agent based modeling framework for studding
the improvements in healthcare system and their influence on
patient safety, workloads and economics. The application of a
safety dynamics model proposed by Cook and Rasmussen is
demonstrated in order to study and analyze the healthcare
system by using simulation of an emergency department
hypothetically. By means of simulation, complexities of
healthcare system and its nonlinear behaviors of is
demonstrated in this paper; this model in various aspects of
healthcare was evaluated with the question of how it can be
used in healthcare setting. Its societal, organizational and
operational consequences were evaluated in assumed scenario
of its application in healthcare setting(Kanagarajah et. al.,
2008).
Kittipittayakorn& Ying, 2016integrated discrete event
simulation and agent based simulation so that the waiting time
of patients could be minimized. Patient`s behavior was
modelled from the collected data and also were incorporated in
the agent based simulation. Proposed approach was an aid for
the analysis and modification of processes of orthopedic
department and it provides the more reliable results by
considering more details. After the implementation of proposed
approach, the total waiting time of patients at orthopedic
department reduced from 1246.39 minutes to 847.21
minutes(Kittipittayakorn & Ying, 2016).
Nunez-Perez et al., 2017designed operational strategies and
pretested for better care delivery at emergency department by
the use of discrete event simulation. At the very first, input
analysis of was carried out. Then the simulation model was
developed and validated in order to reveal that whether it
coincided with the real world or not. After the development of
model, performance indicators were calculated and their
analysis was conducted. In last the strategies for the
improvement were suggested after the evaluation through the
modeling, simulation and statistical analysis. It was
demonstrated by the results that waiting time of patients could
be meaningfully reduced based on the suggested approaches in
this research(Nunez-Perez et. al., 2017).
Shakoor et al., 2017improved the healthcare delivery at
MRI by utilizing the Arena Simulation software. Radiology
department of public hospital was selected for the conduction
of this research. This was model based research and the main
criteria used for the development of simulation model was
service quality, medical needs of patients and the service cost.
Data of arrival and process time was collected for the duration
of one year. Model was developed in Arena simulation
software. Results indicated that the resources at the research
site were exhausted(Shakoor et. al., 2017).
Al-Araidah et al., 2012developed discrete event simulation
model at local hospital. Data was collected form the
ophthalmology outpatient clinic. Total time spent by them in
the system was recorded along with the service time of patients
then was fed in the discrete event simulation model. The
developed model was compared statistically with the real
scenario. Many alternative improvements were suggested after
investigating through the discrete event simulation model. Key
performance measures i.e. expected waiting time, expected
visit length were traced in the model. Number of alternatives
were found to be causing the waiting time reduction up to 29%
and length of visit up to 19% after implementation(Al-Araidah,
Boran & Wahsheh, 2012).
Maull et al., 2009analyzed the influence of fast track
strategy (FTS) on patient waiting time in emergency
department at the hospital. Discrete Event Simulation (DES)
was used to develop the simulation model in order to predict
output in a various categories of triage and comparison
between these and post-implementation results was also
conducted. Results indicated a significant reduction in waiting
time of patients: 13.2% of the population was waiting more
than four hours before implementation and it was compared
with 1.4% after the implementation(Maull et. al., 2009).
Montgomery & Davis, 2013conducted his study by using
discrete event simulation (DES), by the help of which the range
of possible variables could be forecasted. Discrete event
simulation (DES) permitted the incorporation of multi-layered
variation by the help of probability distributions in the hospital;
which helped in the determination of attributes of patient and
their actions flowing through the system. Various scenarios
were designed in order to determine the influence of closing or
opening beds and changing policy of flow on the average daily
census and number of beds occupied in the different sections
and for the hospital. The results of this research indicated that
how the decisions of information leaders might influence the
system wholly and the long-term consequences of policy
changes. The model of patient flow at the hospital was
successful in creating virtual environment and permitting it to
experimentation and therefore, mitigating the risk of investing
resources in non-value added policy(Montgomery & Davis,
2013).
Mistakes or flaws cannot be overcome or improved until
and unless they are detected. Simulation is a practical and
justified approach to detect the bottlenecks in the queuing
system and after the problems are detected they can be
simplified. So in the context of public healthcare facilities of
Pakistan it is highly required to investigate the queuing system
of public sector hospitals, so that the patients may not face so
many problems which are caused by the mismanagement and
misallocation of medical resources.
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V. SUMMARY OF LITERATURE
In the number of healthcare facilities, application of
queuing theory and discrete event simulation were found to be
used for the improvement. Literature indicates that queuing
theory was used for the calculation of expected service cost,
expected waiting cost, bed capacity at ED, ICU and MU etc.
(see table 3). Table 3 shows the research which has been
conducted in the field of health care operations and the
improvements carried out in them.
TABLE III. SUMMARY OF LITERATURE REVIEW
Author(s)
Healthcare Facility
Analysis/Finding
Mustafa &Nisa, 2015
Reception, OPD and Pharmacy
Correlation analysis was conducted among the performance measures of queuing system by using
M/M/1 and M/M/2 queuing models
Olorunsola et al., 2014
Emergency and accidents
departments
Optimum number of beds was calculated and its effects on the other departments was also calculated
Odunukwe, 2013
OPD
Waiting time and cost of patients was minimized by increasing the number of servers at the facility.
Bastani, 2009
Intensive care unit and monitor
unit
Number of beds were estimated for ICU and MU section for new setup of the hospital by the
development of simulation model in MATLAB.
McManus et al., 2004
ICU
Mathematical model was developed for the patients` flow (admission and discharge) at the ICU.
Obamiro, 2010
OPD
Waiting time of pregnant women was analyzed by using multi-server queuing model in TORA
optimization software.
Kembe et al., 2012
OPD
Patients` service cost and opportunity cost were calculated by using multi-server queuing model in
TORA optimization software. In order to minimize the waiting cost of patients, the number of servers
were increased.
Puoza&Hoggar, 2014
OPD
Long queues and utilization of doctors were studied and for analysis, QM software was used.
Mensah &Asamoah,
2014
Hospital
Traffic intensity and utilization factor of two hospitals were compared by using single server queuing
model.
Armony et al., 2015
Emergency department (ED)
and internal wards (IW)
The delay of patients transferred from ED to IW was analyzed and bottlenecks were highlighted by
using the technique of exploratory data analysis.
Varma, 2016
Clinic
Patients waiting time, traffic intensity and average number patients were calculated by using single
server queuing model. Moreover, he minimized the patients` waiting time at the facility.
Ikwunne&Onyesolu,
2016
Clinic
Optimum service level was calculated by using multi-server queuing model in Production
management and operations management (POM QM) software
Khaskheli et al., 2020
Hospital
Compared the performance measures of two public sector hospitals (calculated by using multi-server
queuing model in TORA optimization software). Waiting time of patients was also minimized by
increasing the number of doctors.
Kalwar et al., 2020
OPD
Conducted discrete event simulation (DES) for the minimization of virtual queue of patients awaiting
for healthcare service by using Rockwell Arena software.
Lade et al., 2013
Section of radiation therapy
and oncology department
Waiting time of patients was minimized by increasing one doctor.
Dawei, 2009
OPD
The existing service of OPD and results of simulation were compared and it was revealed that the
patients were spending extra useless time at the OPD.
Wang et al., 2009
ED
Optimal allocation of resources at the various level was determined by using ARIS and Arena
software.
Haghighinejad et al.,
2016
ED
Waiting time of patients was focused to be minimized at ED and it was highlighted that patients were
waiting more at ED because of bed capacity problem.
Kanagarajah et al., 2008
ED
Simulation modelling framework was developed in order to study the advancements in the healthcare
systems and their impact on the economics, workload and safety of patients.
Kittipittayakorn& Ying,
2016
Orthopedic department
DES and agent based simulation (ABS) were integrated for the purpose of minimization of patients`
waiting time. In order to fulfil the purpose of the study, behavior of patients was modelled in ABS
model.
Nunez-Perez et al., 2017
ED
DES was used to design the operational strategies and conducted a pretest health care delivery system
in context of ED.
Shakoor et al., 2017
Radiology Department
DES was used to improve the healthcare delivery system at MRI. After the data collection and
analysis, it was indicated that resources were exhausted.
Al-Araidah et al., 2012
ophthalmology outpatient
clinic
DES model was developed in which expected waiting time and expected visiting time of patients was
traced and numerous alternatives were found by the help of which patients` waiting time could be
minimized.
Maull et al., 2009
ED
DES model was developed for the analysis of fast tract strategy in the patients` waiting time at ED.
Results indicated a significant minimization of waiting time.
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Since, ED, ICU and OPD are the facilities which were
carried out in the previous research for the improvement in
terms of their queuing systems. Since, the waiting time of
patients is a factor worth working for because significant
amount of cost is associated with it. Most of the researchers
have calculated and worked on the patients waiting time at
different healthcare facilities.
VI. DISCUSSION
To improve population`s health status is the purpose of
health care services(Lavanya & Ahmed, 2015). The activities
or practices which are used for determination of health, health
care delivery system (HCDS) is societal response to those
activities. It is combination of people, agencies, organizations
and number of resources by which healthcare system render its
services by the help of them (Kumar & Bano, 2017),
(Musgrove et. al., 2000). The efficient allocation of resources
and channels are extremely necessary in order to provide quick
and timely healthcare service to the patients at the every stage
at healthcare facility. This is the reason, healthcare delivery
systems has gained the attention of researchers since so long.
Present research paper was aimed to present the broader and
clear picture of healthcare problems in Pakistan and the various
solutions are also discusses which are given by the researcher
across the globe.
Delay occurs when there is less available capacity to meet
the service demand (Green, 2011). When patients experience
long waiting lines at the healthcare facility, it result in the
dissatisfaction of patients (Obamiro, 2010). In this regard, the
patients` waiting time to see the doctor must be minimized by
making the procedure of hospital simpler and at the same time,
they should be provided guidance by signboards for various
departments (Lavanya & Ahmed, 2015). In patient flow is
considered to be major element for the improvement of
efficiency of healthcare services (Olorunsola et. al., 2014).
There are certain frameworks which provide understanding for
quantitative analysis of patient flow at emergency department,
their waiting time, serving time and it also provides the
analysis tools for analysis of factors which have an impact on
mentioned outcomes (Connelly & Bair, 2004). There is another
famous technique which has been used for the solving the
problems of waiting lines known as queuing theory. A little
data is supposed to be put into queuing models and in the form
of performance measures they give result about the
performance of the unit and accordingly, the optimal solution is
calculated (Green, 2006). Queuing models are used for
modelling process (which include waiting line) at the
engineering industries (McManus et. al., 2004).
Mensah et al., 2014 conducted their research on the
comparison of queuing systems of two hospitals i.e. Nkawie
Government Hospital and Aniwaa Medical Centre (Private
hospital). Government hospital was indicated to be with greater
waiting times of patients in the comparison of private hospital
although the figures of waiting times were same for both
hospitals but on the basis of OPD cases government hospital
(5040) and private hospital (8991). After such traffic at the
private hospital, the traffic intensity and utilization factor were
calculated to be the same for both hospitals. At the same time,
it was also noted that waiting time of patients at government
hospital was growing longer as compared to the private
hospital. It was finally indicated that longer patients` waiting
times at government hospital were because of inadequacies in
supervision at the different levels of the services (Mensah &
Asamoah, 2014). Kembe et al., 2012 analyzed three costs
(service cost, waiting cost and total system cost) in order
increase the number of doctors at riversite hospital. Where the
total system cost was minimum he suggested to increase the
number of doctors from 10 to 12 and the solution was counted
to be optimum (Kembe et. al., 2012). Since, ICU is the critical
care unit of any hospital; one of the researchers reported the
array of factors that have an impact on ICU occupancy i.e.
weekly and monthly variations in patients; moreover, he also
reported the unit level factors i.e. patient case mix, size of unit
and throughput of unit; in the factors which are considered as
external factors i.e. size of the hospital, step down facilities at
the hospital, models of care and practices for bed management
(Tierney & Conroy, 2013). McManus et al., 2004 used the
queuing model in his analysis and the model was proved to be
accurate. The model was found useful for the prediction of
monthly responsiveness to the varying demand. He conducted
the correlation analysis among the various performance
measures of the model (McManus et. al., 2004). Mustafa and
Nisa, 2015 used queuing models and simulation in three
departments of government hospital of Rawalpindi. They used
both single server and multi-server queuing models and greater
waiting time of patients was indicated by the model at
pharmacy in the comparison of other departments. It was
observed that waiting time of patients could be minimized by
the help of multi-server queuing model.
VII. CONCLUSION
Mismanagement of the resources and the queuing system
was highlighted to be the main reason for low quality of the
healthcare service delivery in public sector hospitals of
Pakistan. Behavior of staff with the arriving patients was
reported to be irritating in public sector. Moreover, delayed
service, long waiting times and less departmental capacity (at
emergency, OPDs and laboratories) are the problems faced by
the patients. On the same time, number of doctors is also less
than required. Applications of queuing theory can bring a big
improvement in the healthcare system. Problems related to the
queuing system (i.e. patients` waiting time in the queue,
delayed service at the end of hospital, bed capacity in wards,
overall patients` flow/congestion) can be solved by the help of
queuing theory (i.e. single server queuing model, multi-server
queuing model by using TORA and POM software). Most
importantly, there is another technique for mentioned problem.
It is called discrete event simulation (DES). Simulation is
replica of reality in which the existing systems can be modelled
and analyzed by changing the various parameters
simultaneously.Occurrence of waiting lines will always be
prevalent in the systems (Brahma, 2013) and because of long
waiting lines, doctors are prone to the stressful situation of
examining patients in such a greater number and they strive to
get free without examining them in deep. (Obamiro,
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2010),(Yusuff, 2015), (Puoza & Hoggar, 2014), (Albert, 2007).
In this situation, public health will certainly be put to an
alarming condition; so to get rid of this situation, it is highly
need to manage the queuing system in the most possible way.
If the queuing system is aligned as optimum, no resources will
be stuck in the system. Therefore, queuing simplification is the
optimum solution in order to get out of congestion and waiting
line problems.
VIII. RESEARCH GAP
After the deep review of literature, it was clear that none of
the literature reviews discussed the healthcare problems in the
respective country and the review of contribution of related
methodology at the same time. The contribution of present
research in highlighting the problems of healthcare delivery
system in Pakistan and review of queuing theory and queuing
simulation cannot be ignored.
IX. FUTURE IMPLICATIONS
When the system (healthcare facility) is congested, patients
wait more in the queues and system in order to get served. AT
ICUs and EDs patients are in critical conditions and if the
patients are made to wait in that condition, anything can
happen. In this regard, it is suggested that review of problems
of ED and ICUs should also be reviewed specifically so that
the problems can highlighted for the greater good of nation.
X. ACKNOWLEDGEMENT
We thank our teachers for their supervision and ultimate
help in carrying out this research paper.
XI. CONFLICT OF INTERESTS
There are no conflicts of interest among the authors of
present research paper.
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How to Cite this Article:
Kalwar, M. A., Marri, H. B., Khan, M. A. & Khaskheli,
S. A. (2021). Applications of Queuing Theory and
Discrete Event Simulation in Health Care Units of
Pakistan. International Journal of Science and
Engineering Investigations (IJSEI), 10(109), 6-18.
http://www.ijsei.com/papers/ijsei-1010921-02.pdf
