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QUEUING ISSUES OF BIG DATA ANALYTICS IN
HEALTHCARE FRAME WORK
S. Maragathasundari
Assistant Professor, Department of Mathematics,
Kalasalingam Academy of Research and Education, Krishnankovi, (India).
E-mail: maragatham01@gmail.com
ORCID: https://orcid.org/0000-0003-1210-6411
C. Prabhu
Associate Professor, , Department of Mathematics,
Kalasalingam Academy of Research and Education, Krishnankovil, (India).
E-mail: cprabhumath@gmail.com
ORCID: https://orcid.org/0000-0003-3879-3299
K. S. Dhanalakshmi
Assistant Professor, Department of Electronics and Communication Engineering,
Kalasalingam Academy of Research and Education
Krishnankovil, (India).
E-mail: k.s.dhanalakshmi@klu.ac.in
ORCID: https://orcid.org/0000-0001-6285-3656
Recepción:
11/11/2019
Aceptación:
03/12/2020
Publicación:
30/11/2021
Citación sugerida:
Maragathasundari, S., Prabhu, C., y Dhanalakshmi, K. S. (2021). Queuing issues of big data analytics
in healthcare frame work. 3C Tecnología. Glosas de innovación aplicadas a la pyme, Edición Especial, (noviembre,
2021), 211-229. https://doi.org/10.17993/3ctecno.2021.specialissue8.211-229
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ABSTRACT
This paper explores an examination on Network trac checking, investigation for
upgrading system asset and improving client involvement in Healthcare Field. Be that as it
may, existing systems accessible in medical clinics, which as a rule, depend on an elite server
with expansive capacity limit, are not versatile for itemized examination of a vast volume
of trac information dependent on the patient examination subtleties, infection subtleties,
blood bunch subtleties and the treatment given to them in intermittent premise and so on.
The advantages of medicinal record trade (MRE), to give some examples, incorporate
oering more data for doctor nding, giving better constant consideration to released
patients, and dispensing with the misuse of copied examinations. In addition, the above
system may be interrupted with all type of arriving patients, emergency cases, diagnosis
period, consultation services etc. All the above issues happening inhuman services is drawn
closer through Queuing hypothesis in this study. Queuing models are helpful for assessing
the framework reaction time and all the execution proportions of the social insurance
framework. Numerical delineation and an expand graphical investigation are completed
toward the conclusion to approve the model. It gives a reasonable considered the calculated
investigation of lining hypothesis in health insurance eld.
KEYWORDS
Setup time, Single stage service, Compulsory Phase I Vacation, Optional Phase II Vacation,
Restricted Admissibility.
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1. INTRODUCTION
Big data in wellbeing and science to handle the diculties in new models is getting to be
huge. In the period of enormous information, the most troublesome issues that stay to
be comprehended are the means by which to prociently manage large quantities and
assortments of information. There are numerous diagnostic speculations and models. In this
segment, late revelations in big data stockpiling and examination models are overviewed.
The procurement of voluminous information relies upon an assortment of clients and
gadgets, just as ground-breaking server farms to store and process the information.
Therefore, building up an unrestricted system foundation is desperately required; this
framework would make it conceivable to accumulate geographically circulated and quickly
produced information and send them to server farms for end clients. In one investigation,
members saw the dierent diculties in Setting up such a system structure.
Among emergency clinics, Electronic medicinal record trade can give more data to doctor
determination and diminish costs from copy examinations. The fast development of data
and correspondence innovation has accelerated advancement of clinical data frameworks.
An ever-increasing number of patient records, research facility reports, drug store drugs, and
budgetary and medical coverage information are currently exchanged through PC systems.
As of now, most emergency clinics have built up their very own electronic medicinal record
frameworks. In any case, these frameworks just help singular medical clinics and don't give
correspondence or oer assets among emergency clinics. Along these lines, it is troublesome
for a patient to visit his specialist in one clinic and have his restorative record from another
medical clinic accessible. The long-haul care units additionally can't get release data from
the medical clinics. Every human services supplier must use much time and exertion to
gather quiet data, along these lines causing information excess, and maybe notwithstanding
imperiling patient wellbeing.
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Graphic 1. Big Data Model in Healthcare System.
Source: own elaboration.
1.1. QUEUING PROBLEM IN HEALTH CARE UNIT PROCESS
Diverse applications have distinctive execution prerequisites. We list here seven such
necessities:
1) Batch landing – Arrival of patients: Assume that the entry time of an outpatient at
a clinic. Specically, expanded asset use does not really suggest longer holding up
neither lines nor longer patient stream times.
2) Set up time – Nursing Station: It is kept up by the doctor's training to look at the
connection between inspecting room limit and patient stream crosswise over
center-based execution measures. And furthermore distinguishing a few signicant
and generalizable parts of outpatient facility tasks
3) Single Stage Service - Fixed Normal Service: Traditionally, social insurance has been
separated as either inpatient or outpatient. Inpatient care is given when patients
are required to stay at a medical clinic or care oce for the span of their treatment
or disease. With outpatient social insurance, patients are dealt with and discharged
that day. An arriving quiet check in and holds on to be called by a nursing room.
Given both a nursing room and an inspecting room are accessible; the patient is
brought to the nursing room. At the nursing room, the medical caretaker records
the patient's indispensable insights and escorts the patient to an accessible looking
at room.
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4) Feedback Service – "Visit Service": Owing to mechanical advances in diagnostics,
prescriptions, and techniques, a greater part of social insurance needs is currently
taken care of on an outpatient premise. The patient might be sent to the center
research facility or x-beam oce through the attendant helper station for doctor
produced lab or x-beam work. This was regular amid physical examinations and
wandering medical procedure.
5) Compulsory Phase I Vacation – Diagnosis period: The patient might be sent to the
center lab or x-beam oce by means of the attendant helper station for doctor
produced lab or x-beam work. This was regular amid physical examinations
and wandering medical procedure. During this season of Compulsory Phase I
excursion the Server prot get-away (As long as the patient gets the records)
6) Optional Phase II Vacation: Final Consultation after conclusion the nish of a patient's
"underlying" interview with their doctor was motioned by either the patient
leaving the inspecting room (for the nursing station or registration work area) or
the doctor leaving the looking at room. In the event that the underlying meeting
nished with the doctor leaving the analyzing room, administration proceeded for
the patient yet was not really performed in the patient's essence. For the most part,
the expansion of administration as an "arrival" meeting included exercises that
couldn't be nished inside the inspecting room.
7) Restricted Admissibility of Patient to the framework amid Optional get-away:
Emergency/Accident Services - During this Optional Phase II get-away there
will be a limited suitability of the patient to the framework is conceivable.
"Administration" alludes to the period of time a patient went through in meeting
with center work force while "stay" alludes to the all-out time spent at some area
inside the facility. Pausing and administration times were eectively found as the
contrast between the completion and beginning of two continuous administrations.
Since the center lab and x-beam oce are physically outside the family practice
facility, just patient visits at these areas were recorded.
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Graphic 2. Service Mechanism.
Source: own elaboration.
2. METHODOLOGY
2.1. SOLVING OF HEALTH QUEUING PROBLEM BY VARIABLE
SUPPLEMENTRY VARIABLE METHOD OF QUEUING THEORY
The above process carried out in health care unit is a concrete problem which is well
analyzed by queuing theory in this suggested current work. The queuing mechanism is
developed based on the probability distribution in dierent range of communication. The
above Queuing problem is solved through supplementary variable method of Queuing
approach. Hence to start with, we describe the above queuing issue in terms of mathematical
study of queuing theory. The above health care unit process is completely transformed
to a queuing problem. Governing equations of the queuing problem are framed initially.
Then the boundary conditions of the problem are explained. Then by the supplementary
variable technique of usage of variable ‘z’, we derive the probability generating function
of the queue size. Then by the tuberin property, length of the queue is found. Finally, the
other execution measures of the problem are derived using Little’s law. As claried above
in Health care unit process, the procedure comprises of arrival of patients, nurse station,
normal xed service, sojourn service, Diagnosis period, consultation period and emergency,
accidental services.
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2.2. THE HEALTH CARE UNIT QUEUING PROBLEM IS AS FOLLOWS IN
TERMS OF MATHEMATICAL STUDY
Client’s arrival follows Poisson distribution. Administration pursues general circulation.
To begin with, a set up time technique is presented in this procedure. Single phase of
administration is given to all the arriving clients. On the o chance that any of the clients
are in need, they are permitted to get an input administration, which gives a total attractive
to all the arriving clients. After the fruition of the administration, the server needs to attempt
an obligatory excursion, amid which to make the framework run easily to a more prominent
degree, a total upkeep work to be done. Toward the nish of mandatory excursion, the
server has the alternative to take an all-encompassing get-away if the submitted support
work has not been nished amid the past get-away hour.
Restricted admissibility in the arriving customers is considered during the time of optional
extended vacation to reduce the length of the queue. The lining issue (Health care unit
enormous information issue) is all around explored by strengthening variable technique. For
every one of the set-up time, administration process, mandatory get-away and discretionary
broadened excursion, benecial components are distinguished. A determined state line
measure assignment and the distinctive execution checks like length of the line, number
of clients in the framework, usage factor, latent time of the server, holding up time of the
clients in the line likewise as in the structure are inferred. Numerical depiction legitimizes
the model and the graphical outline gives a sensible picture about the decisions to be taken
before the beginning of the aliation. To break down the issue in social insurance unit, a
veriable endorsing is rendered close to the end, by strategies for looking numerical results
and graphical examination of the model.
Huge information examination has been considered by various creators. In any case,
the issue of huge information investigation in medicinal services unit is drawn closer
through lining hypothesis is another thought of execution in this examination. McAfee
and Brynjolfsson (2012) examined the work on big information the board insurgency.
Development of information investigation is totally very much concentrated by Lynch
(2008). Big information pathologies are all around assessed by Jacobs (2009).
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Zikopoulos et al. (2011) made an analysis on examination for big business class Hadoop
and Streaming Data. Manyika, Chui, and Brown (2011) learned about the developments
and preparations on Big Data. Celi et al. (2013) examined the work on big information in
the emergency unit. Sobhy et al. (2012) considered the enormous information on human
services distributed computing system. Queuing frameworks with expansive scope of
excursion arrangements have been planned by various authors. Single get-away strategy is
all around examined by Choudhury (2002).
Dhanalakshmi and Maragathasundari (2018) contemplated Mobile ad hoc systems issue
through queuing approach. Maragathasundari (2015) inferred the execution measures
for a mass entry queuing model of three phases of administration with various excursion
policies. Maragathasundari and Srinivasan (2012) made an Analysis on M/G/1 input line.
Maragathasundari and Karthikeyan (2016) explored a mass queuing model with short and
long get-away.
In this study, we have introduced the big data analytic issue as a batch arrival non-
Markovian queuing model with setup time, single service and feedback service. As this is
a non markovian queuing model, service time follows a general distribution. A concept
of Phase I compulsory vacation and phase II optional vacation are launched in this work
which plays a very important role in our study. Here vacation in the sense we mean the
maintenance work to be carried out in due course of time which helps the system to run
smoothly to a maximum extent. It is expected that during the time of vacation, length of
the queue will be maximized. So, to avoid the congestion in the system a phenomenon
known to be restricted admissibility is brought in during the time of vacation.
2.3. MATHEMATICAL DEPICTION OF THE MODEL
The arithmetical interpretation of the Queuing framework has the capacity to be described
by the resulting hypothesis:
Customers cluster arrival follows Poisson procedure Let λd
i
dt (i=1,2,3….) be the rst
order probability where 0 ≤ d
i
≤1 and =1 and λ>0 is the mean landing rate of
the batches. There is one server giving single sort of administrations of general course. The
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organization time seeks after general (arbitrary) course with rst basic distribution function
E(x) and density function e(x). Let μ(x)dx be the prohibitive probability of organization
nish of the principle period of organization in the midst of the interval (x,x+dx), given
that the snuck past time is x, so that
(a)
For the purpose of maintenance work to be carried out, the server takes a compulsory
vacation with probability r.
For compulsory vacation,
(b)
After the completion of compulsory vacation, if in need the server may take an extended
vacation with probability k.
For the optional vacation, we have:
(c)
After completion of the service, if the client is disappointed with the essential administration,
he can quickly join the tail of the rst line as a feedback client with likelihood e to rehash the
administration until the point when it is fruitful or may leave the framework with likelihood
1- e.
2.4 GOVERNING EQUATIONS OF THE MODEL
S
n
(t) - This is the probability that at time ‘t’, the server is in setup while there are ‘n’
customers in the queue. (n ≥1 )
(1)
(2)
(3)
(4)
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(5)
(6)
(7)
(8)
The accompanying limit conditions are utilized to settle the above conditions.
(9)
(10)
(11)
3. DISTRIBUTION OF THE QUEUE LENGTH
To settle conditions (1) to (7) for a shut structure arrangement we pursue the system set out
beneath:
We multiply (1) by z
n
and sum over n from 1 to ∞ add it to (2), we get
(12)
(13)
(14)
(15)
Multiplying (9) by z
n+1
and summing over n from 0 to ∞ results in:
(16)
Using (8) in (16), we get:
(17)
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(18)
(19)
Now integrating (13) from 0 to x yields,
(20)
Integrating (20) by parts with respect to x yields,
(21)
Where,
is the Laplace stieltjes transform of the service times
E(x).
Multiply (20) by η(x) on both the sides, we get
(22)
Using (20) in (18), we get
(23)
Similarly,
(24)
(25)
(26)
Hence,
(27)
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Now using (22), (25) and (27) in (17), we get
(28)
(29)
(30)
(31)
Also,
(32)
4. EXECUTION MEASURES
(i) LIKELIHOOD GENERATING CAPACITY OF THE QUEUE SIZE
Let
be the probability generating function of the queue size
Adding (29) – (31), we get
The idle time Q is determined using the normalization condition + Q=1 .
From, the utilization factor ρ can be determined.
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(ii) STEADY STATE ARRANGEMENT OF THE QUEUE SIZE
Let L
q
a chance to demonstrate the reliable state typical number of customers in the line.
By then
Where N(Z) and D(Z) are the numerator and denominator of (27).
Since
= =1 , we utilize two-fold separation and get
(33)
Substituting (34) – (37) in (23), we obtain L
q
and all the other measures are obtained using
Little’s formula
(34)
(35)
(36)
(37)
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5. NUMERICAL RESULTS
We depict a numerical perspective with a denitive goal to see the impact and credibility
of our consequences of the specic parameters utilized in our model. The estimations
of the parameters are collected with a denitive target that the enduring condition is not
disturbed.
Assume service time follows an exponential distribution:
Table 1. Effect of change ofe (e=6,5.5,5,4.5,4).
Q
ρ
Lq L W
�
W
0.7239 0.2761 15.551 15.827 5.184 5.184
0.7512 0.2488 15.167 15.415 5.056 5.139
0.7728 0.2272 14.889 15.116 4.963 5.039
0.7903 0.2097 14.679 14.889 4.893 4.963
0.8049 0.1951 14.518 14.713 4.839 4.904
Source: own elaboration.
Graphic 3. Effect of Variation of e.
Source: own elaboration.
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Table 2. Effect of Variation Of γ (γ=2.1,2.2,2.3,2.4,2.5)
Q
ρ
Lq L W
�
W
0.8751 0.1249 4.9967 5.1216 1.2492 1.2804
0.8806 0.1194 4.3960 4.5154 1.0990 1.1289
0.8856 0.1144 3.9666 4.0810 0.9916 1.0202
0.8902 0.1098 3.5038 3.6136 0.8759 0.9034
0.8945 0.1055 3.0698 3.1753 0.7674 0.7938
Source: own elaboration.
Graphic 4. Effect of Variation of γ.
Source: own elaboration.
Table 3. Effect of Variation Of β (β=1.6,1.8,2,2.2,2.4)
Q
ρ
Lq L W
�
W
0.6952 0.3048 20.334 20.639 5.083 5.1596
0.7077 0.2923 19.597 19.889 4.899 4.9723
0.7190 0.2810 19.047 19.328 4.762 4.8319
0.7295 0.2705 18.632 18.902 4.657 4.7255
0.7391 0.2609 18.319 18.579 4.579 4.6450
Source: own elaboration.
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Graphic 5. Effect of Variation of β.
Source: own elaboration.
6. DISCUSSION
It is evident from Table 1 that lessening the estimation of e, decreases the trac power,
normal length of the line and the normal reaction time while the server inert time increases.
From Table 2, the information we collect here is, as the probability of set up time constructs,
it prompts a smart presentation of the structure. From now on, the length of the line gets
lessens. Also, the other execution measures in like manner get decreased. Furthermore,
restricted admissibility yin table3 expect a noteworthy activity in this model. To avoid stop
up this thought is exhibited. It means a nice impact in the model. On account of the
extension in the conned suitability, the blockage in the structure is avoided. Length of the
line gets reduced and moreover the holding up time of the customers in like manner gets
diminished. All of the examples showed up by this are true to form. In extension, Graphical
examination gives an undeniable picture about the model described in this paper.
7. CONCLUSIONS
In this model, we analyzed a Queuing framework with general administration conveyance
with various vacation arrangements. Here two kinds of vacations are presented viz.
mandatory excursion and discretionary broadened get-away. Also, the idea of feedback
administration encourages the clients to get a total fulllment regarding the administration.
Amid the season of both the excursions, a legitimate support work is done which encourages
the framework to run easily without intrusion to a greatest dimension. By including another
presumption, restricted admissibility in this model, an assorted and a much-created lining
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framework is developed. The relentless state arrangement and the execution proportions
of the lining framework are determined. As a future work, building up the above lining
model with administration intrusion, postpone time, shut down time, Balking and reneging
is proposed
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