operation research at medical emergency at AIIMS

Introduction
 Accident and Emergency services are rightly considered as the
“shop window” of a hospital and because of the real or perceived
“emergency”; everyone demands prompt action. Hence it is of
utmost importance that doctors posted in the casualty should be
calm and composed, and give their best effort as quickly as
possible. The objective of this department is to provide medical
care to the patient as quickly as possible; thus increasing the
patient’s chances of survival.
 However with the escalation of the ED Waiting line strength , a
need for study was perceived to get a scientific approach towards
the causes of such waiting line build ups and also to assess the
most suitable alternative and to formulate the most efficient one
to tackle the emergency queue .

Aim :
To evaluate the waiting time of an emergency patient in
a seeking emergency healthcare at a tertiary care
hospital.
Objectives :
 To study the process flow of emergency department.
 To study the various time consuming parametres
which are generated during emergency healthcare
services delivery.
 To study the arrival rate , service rate and queue
capacity and number of servers.

Methodology :
 Study Area- New Emergency Department , AIIMS
 Study Period – 15th May -30th June 2012
 Study Type- Descriptive (Observational), Cross Sectional
 Study Population- All patients who come to seek eergency
healthcare services.
 Sample Size – 500 ( observation ) , 100 ( questionnaire ) and
13,200 for studying the arrival pattern.
 Sampling Method- Simple Random Selection
 Study Tool- 1. observation form 2. CHECKLIST
 Inclusion Criteria
All the Patients who seek emergency healthcare services
at New Emergency.
 Exclusion criteria
EHS (Employee Health Scheme) Patients of AIIMS were excluded from
the study and staff peronnels or their kins , and also who were referred to
opd after triage without start of nursing care were excluded from the study.

 Sample size :
The sample size was calculated by the formula
E = zσ/√n
Where , z = area under the graph within the specified confidence interval
σ is the standard deviation obtained under the pilot study.
n = number of samlple to be collected
E = expected margin of error.
Thus , for study , it was assumed that within 95 % of confidence interval with a
expected margin of error of 5 % and σ = 0.57 ( as got by the pilot study of 25
patients ) ,
Therefore , the sample size came out to be = 499.254 patients , rounding off the
value gives a total of 500 patients .
For the questionnaire , with the same method , it was calculated that the sample
size came out to be 99.57 patients . With σ coming out to be 1.02 .
The arrival rate was calculated by studying the arrival pattern of patients during
the study period ( = 13,200 patients )

Casuality department
The hospital consists of 5 emergency departments, dedicate to various types, viz.
eye, pediatrics, surgical , medicine and trauma emergency department. However a
broad look on all the departments have reflected that the medicine emergency
was regularly suffering from the build up queues in front of the ED Gate , so the
New Emergency Department have been set up to undertake the study .
The department is located on ground floor in front of the surgical emergency (
main emergency ) in the AB Wing . The department serves for the medical
emergency needs of emergency patients in their acute health.

New Emergency Department
The medical emergency locared in the AB wing of Main
AIIMS is serving a total of approx 7000 to 10,000 patient per
month . The patients coming here are of variety types and
from various demographies . The emergency serves these
patient round the clock with the help of a 19 doctors
including 3 CMO’s working in 3 shifts and 45 nurses divided
in 4 grades and working in 3 shifts round the clock .
Although the above personnels seem to be efficient in
maintaining the emergency but many a times it has been
seen that a long waiting line of patients seeking emergency
care is build up in front of the medical emergency door .

Working Procedure
The working procedure of the emergency department is
as follows :

Waiting Line Model
One of the most important managerial applications of random processes
is the prediction of congestion is a system, as measured by delays caused
by waiting in line for a service. Patients arriving at a bank, a checkout
counter in a clothing store, a theater ticket office, a fast food drive-
through, a supermarket checkout, or at emergency services of a hospital
etc. may perceive that they are wasting their time when they have to wait
in line for service. Repeated and excessive delays may ultimately influence
the patients’ perception about the brand and experience.
The medical emergency of AIIMS hospital is overwhelmed with the rush
of patients throughout the day , to overcome the same , the AIIMS
Adminstration has deployed the maximum staff as compared to the other
emergency services . a total of 19 Junior Doctors and 45 nurses divided in
3 shifts work tirelessly to tackle the patient line but still many a times
waiting lines can be seen outside the medical emergency gate . The study
was undertaken to find the true picture and to find the possible ways to
tackle the problem .

 The Number of Waiting Lines
AIIMS New Emergency has a three waiting line of patients viz . the general
waiting line , the staff waiting line and the emergency waiting line .
 Number of phase
AIIMS New Emergency has a 2 phase system , i.e , in the first phase the doctors
are the servers whereas in the next phase the nurses are the servers .
 The Number of Servers
AIIMS New Emergency is a multiserver system as a total of 4 junior resident
doctors ( servers ) are deployed to tackle the waiting line of the patients . Also in
the second phase , 4 nurses are assigned for the job to start the new emergency
arrivals.
Thus for the AIIMS New Emergency Department is a multiphase , multi
server and single line system with “emergency first” criteria.

Arrival Pattern
 Waiting line models that assess the performance of
service systems usually assume that patients arrive
according to a Poisson probability distribution, and
service times are described by an exponential
distribution. The Poisson distribution specifies the
probability that a certain number of patients will arrive
in a given time period (such as per hour). The
exponential distribution describes the service times as
the probability that a particular service time will be
less than or equal to a given amount of time.

The arrival pattern at main aiims new emergency
department strictly follows the negative exponential
distribution or poisson distribution as the the spacing
between the arrivals , inter arrival time does not occur
uniformly . for example , having a look over the data
collected from the registration counter of the casuality
department , between 9 am to 10 am on Monday 4 june ,
2012 , we see that ,

Queue Discipline
It refers to the order in which the customers are processed . the AIIMS New Emergency
delivers the healthcare services to the patients on first come first serve basis for the general
patients and emergency first for the overall patient population .
Thus in a nut shell , the queing model classification for the services delivered in the
emergency department are as follows :
 A: Specification of arrival process :
M : negative exponential or poisson distribution
 B. specification of service process :
M : negative exponential or poisson distribution
 C : Specification of number of servers( here doctors serving in the New Emergency
Department )
= 4
 D. Specification of the queue :
= infinity as there is an unlimited queuing capacity.
 E. Specification of patients :
= except eye , paediatrics , surgical and trauma emergency , all other
emergency can seek emergency healthcare services at New
Emergency.
Thus the New Emergency will be described by M/M/4 , and as the last two specification are
unlimited , hence will be omitted .

5
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Tuesday

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Wednesday

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Thursday

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Friday

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Sunday

Percentage utilization of the servers :
80%
69%
53%
61% 62%
60%
64%
88%
79%
73%
62%
81%
73%
66%
68%
53%
51%
47%
60%
52% 53%
28%
23%
17%
25%
31%
25% 25%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Monday Tuesday wednesday Thursday Friday Saturday Sunday
7 am to 1 pm 1 pm to 7 pm 7 pm to 1 am 1 am to 7 am

Inference
We can infer by the graph that the on Monday, the physicians
were drained highest of their efficiency especially in the
morning hours, however on all days, the time at which opd
closes also views the highest efficiency utilization of the
servers (between 1 pm to 2 pm). Also, the weekend days show
a continuous stable utilization of the servers as the opds are
closed on these days.
According to facts, the OPD reroute 10 % of its patients daily
towards the emergency admission, which can be clearly seen
in the above graph as the non opd hours have got slightly
lesser utilization coefficient than the opd working days.

8
4
1
2 2 2
3
18
7
5
2
8
5
3
1 1 1 0 1 1 1
0 0 0 0 0 0 0
0
2
4
6
8
10
12
14
16
18
20
Waiting Line

Inference
Thus it can be clearly visualized about the correct picture of
waiting line conditions in emergency department, also, it can
be inferred by the graph that the highest waiting time is that
of Monday that too just after the opd closing time that is
between 1 pm to 2 pm, the other higher side can be visualized
by seeing the waiting time conditions of all the weekdays
between 9 am to 1 pm (as the peak hours). The weekend days
however show a very minimal time spent in the queue, the
most probable cause for this seems to be the closing day for
opds, and also the most equalized and continuous arrival of
patients without any ups and downs in the arrival pattern of
the patients.

Probability of getting an empty system :
3%
5%
11%
8% 8% 8% 7%
1%
3% 4%
8%
3% 4%
6%6%
11% 13%
15%
8%
12% 12%
32%
40%
50%
37%
29%
37% 36%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%

Probability of having to wait for seeking
the emergency healthcare
60%
41%
21%
29%
31%
29%
34%
75%
57%
47%
31%
61%
48%
37%
40%
21%
18%
14%
28%
19% 20%
3%
1% 1% 2%
4%
2% 2%
0%
10%
20%
30%
40%
50%
60%
70%
80%

Traffic Intensity
3.2
2.8
2.1
2.4 2.5
2.4
2.5
3.5
3.1
2.9
2.5
3.2
2.9
2.6
2.7
2.1
2.0
1.9
2.4
2.1 2.1
1.1
0.9
0.7
1.0
1.2
1.0 1.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0

Age Group
23%
32%
26%
19%
0%
20%
40%
60%
80%
100%
0 - 20 20 - 40 40 - 60 > 60
Age Group Break Up
Age Group Break Up

Monthly Income Of Family
0%
20%
40%
60%
80%
100%
< 10,000 10,000 -
25000
25,000 -
50,000
> 50,000
52%
28%
18%
2%
monthly income of family

Visit(s)
0%
20%
40%
60%
80%
100%
new revisit
78%
22%
visit

Approach
22%
68%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
direct referred
Approach

Referre
consultant / rmp
32%
public body
38%
private body
30%
referee

Getting the order of preference
brand name, 35%
cost of hospital, 23%
location of
hospital, 12%
experienced staff, 19%
higher
facilities, 11%

Unique Selling Point of the hospital
free service, 21%
reknowned doctors, 28%
ease of documentaion, 9%
quality, 18%
higher facilities, 24%

Factor Analysis
The questionnaire was also composed of a 5 point likert scale asking the patients
satisfaction towards the promptness of the delivery of in following aspects :
 Ease of locating the emergency department
 Availability of patient assistance
 Ease of documentation
 Availability of doctors
 Prompt investigation reports
 Availability of nurses to start treatment
The likert scale used to assess the patient satisfaction was as follows :
 Highly satisfied
 Partially Satisfied
 Neutral
 Partially dissatisfied
 Highly dissatisfied

Sampling adequacy
KMO and Bartlett's Test was showing the following
results :
Kaiser-Meyer-Olkin Measure of Sampling Adequacy.
.652
Bartlett's Test of Sphericity Approx. Chi-Square
81.685
df
15
Sig.
.000

Total Variance Explained
Component
Initial Eigenvalues Extraction Sums of Squared Loadings Rotation Sums of Squared Loadings
Total % of Variance Cumulative % Total % of Variance Cumulative % Total % of Variance Cumulative %
1
2.164 36.066 36.066 2.164 36.066 36.066 1.757 29.279 29.279
2
1.208 20.132 56.197 1.208 20.132 56.197 1.407 23.457 52.736
3
.853 14.225 70.422 .853 14.225 70.422 1.061 17.686 70.422
4
.764 12.734 83.156
5
.600 9.997 93.152
6
.411 6.848 100.000

Component Plot In Rotated Space

Results ( Factor Analysis )
The results from the component analysis in rotated
space has shown that the most time consuming
factors, which the patient perceived, were the nurse
availability and ED Physician availability for the
treatment , following which the ease of documentation
factor was being reported .The most satisfying factor
among the patients , the location , medicine availability
and the patient assistance at gate were, in the perception
of the patients, on within acceptable time and they do
not think that these processes have delayed the
emergency healthcare delivery at AIIMS .

Results :
 Process time break up ( min . )
21.43
4.47
1.01
7.48
2.13
8.68 10.95
1.65
28.40

Break Up ( percentage )
dr delay
25%
triage
5%
going for registration
1%registration
timing
9%
post registered travel time
2%
clinical
examination
initiation timing
10%
clinical examination
13%
sample withdrawl
2%
nursing treatment delay
33%
Percentage Break Up Of Delay

Total delay
 Thus a total average delay was found to be 85.69
minutes from entry till the start of treatment by a
nurse .

Waiting time
0
10
20
30
40
50
60
70
7 am to 1 pm
1 pm to 7 pm
7 pm to 1 am
1 am to 7 am

Recommendations
On the basis of above results , the recommendations to reduce the
waiting line strength in front of the emergency department were as
follows ;
 Assignment of a unique number of patients to the doctors as their
target number on daily basis , falling which they will be liable to get
terminated .
 Making the 2 phase model for the emergency healthcare delivery
that is
In first phase doctor starts treatment and writes prescription
for the emergency patient
And in the second phase , the patient goes to the nursing
station for the start of nursing treatment

Recommendations (contd.)
 Making this model as a single phase model by assigning 1
nurse to each doctor , the feasibility of working of this
model is 100 % as there are a total of 19 nurses in the peak
time and already 4 nurses are assigned specially for the
emergency patient but the lack of communication between
the doctor , patient and nurse is the major drawback in
retardation of emergency healthcare delivery , also , the
nurse only takes a total of 5 minutes (on an average of 500
patients) to start the treatment and as observed it is half
the time of a doctor’s service time , so assigning one nurse
to one doctor and making the 2 phase model as single
phase will eventually rid off the drawback of
communication failure between the trio and eventually
reduce the delay in the service delivery.

Recommendation(s)
 The morning shift from 8:30 am till 1:30 am faces a lot of problem while the
closing timings of OPD i.e. 1:00 PM , this may be tackled by increasing the
morning shift by 30 minutes , i.e till 2:00 PM and starting the evening hours
earlier by 30 minutes that is at 1:00 pm , this will eventually result in an overlap
of two shifts for 1 hour , and that too in the peak timing of traffic intensity , this
will result into availability of 8 servers ( double the number of normal servers )
during the highest traffic intensity hour i.e 1 pm to 2 pm.
 Availability of handy and portable saturation meters , which may reduce the
ABG analysis timing of certain patients , for which the ABG is done only to
check their saturation pressures ( for eg . the chest patients ) , this will reduce a
significant time of physician in analyzing the spo2 of the patient . also , the
emergency department is starving for simple instruments such as a blood
pressure moniter , the whole emergency department with average arrival of 300
patients each day has only a single blood pressure monitor to serve the
diagnose the patients for their bood pressure . suggestion is given to immediate
introduction of 3 more blood pressure monitors i.e 1 each for Emergency
Physicians who work on the counter.

Conclusion
The queue assessment of the New Emergency
Department has came up with many unforeseen factors
that were identified as the most retarding factors and
now as these factors have been drained out , these
factors must be checked to enhance the medical
emergency department services in delivering a faster
delivery to the patients thus minimizing the waiting line
build up in front of the emergency department.

operation research at medical emergency at AIIMS

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