This document summarizes an article from the Annals of Emerging Technologies in Computing (AETiC) journal that models and simulates power dissipation control techniques in internet data centers. It begins with background on internet data centers and the need to reduce power consumption and cooling costs. It then describes three control techniques - CRACs ON-OFF control, multi-step ON/OFF control, and CRACs step-3 ON-OFF control - and finds through simulation that the CRACs step-3 ON/OFF control provides the smoothest power variations and is the best option. The document also includes details on modeling the data center, server racks, and CRAC units to simulate the different control techniques under

1. Annals of Emerging Technologies in Computing (AETiC)
Vol. 5, No. 3, 2021
Firstnames Lastname, Abcd E. Ghij and Klmn Opqr and Stuv Wx Yz, “This is the Title of the Article: without Any Line Break”,
Annals of Emerging Technologies in Computing (AETiC), PrintISSN: 2516-0281, Online ISSN: 2516-029X, pp. 1-7, Vol. 5, No. 3, 1st July
2021, Publishedby International AssociationofEducatorsandResearchers (IAER), DOI: 10.33166/AETiC.2021.03.001, Available:
http://aetic.theiaer.org/archive/v5/v5n3/p1.html.
Review Article
Empirical Analysis Modeling of Power
Dissipation Control in Internet Data
Centers
Rahila Batool1, Mutiullah Jamil2, Ayesha Waheed3, Hafeez ur Rehman4*, Sabi Zahra5
1 The Islamic University Bahawalpur (IUB), Pakistan.
2,3,4,5 Khwaja Fareed University of Engineering & Information Technology (KFUEIT), Pakistan.
rahila_batool@hotmail.com ; mutiullahj@gmail.com ; ayeshawaheeed@gmail.com ; hinagillani16 @yahoo.com
*Correspondence: siddiqov@gmail.com
Received: 8th January 2021; Accepted: 17th March 2021; Published: 1st April 2020
Abstract: Large-scale data centers involve a set of server racks for storage and computations for which they
require a massive amount of power and some cooling arrangement. It is observed in the literature that the size of
the internet data center has increased ten times in the last ten years, and energy cost is going up similarly. So there
is a need for proper power management in the internet data center to reduce power consumption. This paper
focuses on modeling and simulation of internet data centers and comparing three different control techniques to
varying workloads on the servers. The first technique is a CRACs ON-OFF method where the power of computer
room air conditioning (CRACs) is automatically controlled based on the server’s output temperature. In particular,
if the temperature of a server rack in the internet data Centre is more significant than some fixed temperature, the
CRACs are turned on. Otherwise, the CRACs will stay off. The second method is the multi-steps ON/OFF control
in which the CRACs are partially turned on and off based on the outer air temperature of servers. We vary the
intermediate steps to 1 and 3 in the multi-step ON/OFF control. The two different control techniques can ensure
the desired output temperature of server racks. Still, the CRACs ON-OFF control method involves more and sharp
power peaks, which can cause problems in the operation of IDCs (Internet Data Centers). The third technique
CRACs step-3 ON/OFF control, involves smooth power variations and therefore can be considered a better option
than the CRACs ON-OFF method. Various experiments at Matlab Simulink show that the control system's
behavior is almost similar at different workload conditions. So CRACs step-3 ON/OFF proposed control model
minimize the power consumption to a large extent. Future work will consider the state estimation in the modeling
and control strategy under different workloads.
Keywords: CRAC; Datacenter; Modelling; Power Dissipation
1. Introduction
The number of IoT devices usage is exponentially increasing,and approximately 75.44 billion devices
become part of the IoT network every year [1]. Internet or network of networks has two main parts: the
hardware and the protocols or rules for its functionality. An essential part of the hardware is the data
center, where there are racks of servers that store, retrieve, and transmit data to the clients. Since these
servers involve large computations, they require unique cooling systems for their operation. With the
increase in such computing services, the power consumption in the internet data center is increasing
rapidly. The servers and cooling system both consume immense power and incur a high cost. According
to Computer World, the power requirements of the existing data centers require 34 dedicated power
plants, each capable of generating 500 megawatts of electricity. It is essential to highlight that most data
centers utilize more power than their requirements [2]. Using the topology of IoT devices and placement
of most influence node energy can be saved [3]. In this paper, our focus is on analyzing and controlling
power consumption in the internet data center. We begin with a brief introduction to the data center and
then present the statement of our research problem. Also, we highlighted the importance of the research

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problem and gave our contributions. Nowadays, most organizations keep their data stored online in the
form of archive directives or websites.All online data is stored on powerful computers called web servers.
These web servers require air conditions to keep the servers fully functional and safe around the clock to
provide certain facilities and in cloud computing load balancing is required to efficient performance with
minimum heat generation [4]. This infrastructure is named an internet data center. The virtual backend
environment is provided by internet data centers so that data can be accessed when required. It requires a
reliableinfrastructure with high-security standards and routine IT operations so users can have constant
accessibility to stored data. The internet data center consists of server racks and cooling equipment. Each
server rack has further numbers of servers for computation. Some of them are active having workload
whileothers are inactive.For a better understanding,we consider a simple example from the literature [5].
A network of two front-end Web portals and two internet data centers (IDCs) located in different regions.
Web portal receives the user’s request and distributes their task between IDCs. Then respective IDC
divides the task between servers. The purpose of the task division is to decrease the overall computation
time. There is a presentation of the architecture of a data center with the different numbers of active
servers. In this we have two web portals with IDC (internet data center 1 and 2).
Figure 1. The architecture of Internet Data Centers [Matlab Simulink ]
In Figure 1. There are two front-end Web portals and two internet data centers (IDCs) located in
different regions. Web portal receives the user’s request and distributes their task between IDCs. Then
respectiveIDC divides the taskbetween servers.The purpose of the taskdivision is to decrease the overall
computation time. In figure 1, there are four servers at IDC 1, from which two are active (servers with the
workload) while others are inactive. Similarly, at IDC 2, there are three servers from which only one is
active.
1.1 Research Problem
Due to the inefficient cooling system, the operational cost of IDC, 40% of the total cost, is maximized
[6]. So there is a need to formulate this problem in the form of a mathematical model and reduce the
operational cost of IDC by reducing the power consumption and temperature of internet Datacenters
to save cooling costs.
Due advancement in technology and rapid increase in the demand of internet resource IDC have gone
under pressure in terms of workload. According to published work reviews jin et al. and others, this work
can be classified into two categories: Thermal environment and energy efficiency. Table 1 summarizes the
existing thoughts of thermal environment, energy efficiency, and power models for data centers [7].
Table 1. A summary of Literature review
Reference Year Work and conclusion
Lu et al. [8] 2018 Row and rack-basedsolution withdifferent combinations of air distribution
Alkharabshehet al.
[9]
2015 Present the numerical modeling of experiment measurement and recent cooling techniques and
device-level liquid cooling system.
Chu and Wang [10] 2019 Anexperiment was performed forlong-distance and short-distance cooling and airflow
management of rack-level cooling.
Rambo and Joshi
[11]
2007 (1) Datacenter modeling objectives
(2) Numerical modeling
(3) Model validation

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(4) Rack-level compact modeling
(5) Datacenter dynamics
Ge et al. [12] 2013 Provide the various power-saving strategies
Mittal [13] 2014 Give the techniques for managing power consumption of the embeddedsystemsand discussthe
need forpower management
Orgerie et al. [14] 2014 Studies and models forestimating the energy consumptionof
these resources
Shuja et al. [15] 2016 Computing systems including server architectures, power
distribution, and cooling
Mobius et al. [16] 2013 (1) Estimationmodels’ essential steps: model inputsand training
model withbenchmarks
(2) CPU models
(3) Virtual machine models
(4) Server models
2. Materials and Methods environment and energy efficiency
2.1. Modelling of Data Center
In Figure 2. There are a network simulation of C front end, Web portals, and N internet data centers
(IDCs) located in different regions [5]. Each of the front end Web portals has a workload Li, i = 1, . . . , C
assigned by the client request, which is further subdivided into λj ≥ 0 workloads and forwarded by Web
portal i to IDC j. Thus, we have
Li =∑ 𝜆𝑖𝑗
𝑁
𝑗 =1 , ∀ i = 1...C. (1)
There is the total number of Mj servers in each IDC, with mj active servers (blue) having a capacity of
λj workload. It means that
𝜆𝑗 =∑ 𝜆𝑖𝑗
𝑁
𝑗=1 , ∀ j=1... N (2)
The power consumption Pjk of the individual active server k (k = 1,...,mj) in the IDC j is dependent on
the CPU utilization Ujk and frequency ƒ of the server. To map the above two parameters into power
consumption , the curve fitting method is often utilized [17] through a set of experiments. The derived
power consumption model for an active server k having workload λjk becomes
𝑝𝑗𝑘
= 𝑏1𝜆𝑗𝑘 + 𝑏0 ,∀ k = 1... j (3)
Figure 2. The architecture and simulation of C front end and N Internet Data Centers [18]
Where b1 and b0 are fitting parameters, and the CPU utilization Ujk is approximated by λjk.
Assuming that each IDCj have fixed and equal frequency servers, the total power consumption Pj for IDCj
is

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𝑝𝑗 = 𝑏1𝜆𝑗 + 𝑏0𝑀𝑗 (4)
To process the incoming workload from front end Web portal, each IDC can utilize the M/M/n
queuing model. In which the average service latency D can be written as D = PQ/(nµ-λ ). Where n is the
number of active servers, λ is the workload arrival rate, µ is the service rate, and PQ is the probability of
clients waiting in the queue. The actual average latency for IDCj becomes
𝐷𝑗
𝑎
=
1
𝑚𝑗𝜇𝑗−𝜆𝑗
(5)
It is assumed that therearealways client requests waitingin thequeue, i.e., PQ = 1.
In general, each IDC has thousands of servers mounted onto racks that can be treated as discrete
thermal nodes. If we assume that there are N racks of servers in a single IDC connected to C front-end
Web portals, the framework will be similar to Figure 2. The dynamic thermal model for rack j can be
written as [19].
𝑑𝑇𝑜𝑢𝑡
𝑗
𝑑𝑡
= −𝑐𝑗𝑇𝑜𝑢𝑡
𝑗
+ 𝑘𝑗𝑇𝑖𝑛
𝑗
+ ℓ𝑗𝓅𝑗 (6)
Where𝑇𝑖𝑛
𝑗
and 𝑇𝑜𝑢𝑡
𝑗
are the ambient air temperatureand outer air temperatureof theserver
Rack respectively.Also, Pj is the total power consumption of rack j and𝑐𝑗, 𝑘𝑗 is a constant coefficient.
𝑇𝑖𝑛
𝑗
The ambient air temperature is represented as ℓ and 𝓅 is mapping ambient air temperaturefrom
output air temperatures,thenonnegativecoefficient for rack j, whosesum equals 1.
𝑇𝑖𝑛
𝑗
=∑ 𝒢𝑗,ℓ
ℓℰ𝑀 𝑇𝑜𝑢𝑡
ℎ
+∑ ℋ𝑗,𝒽
ℎℰ𝐹 𝑇𝑜𝑢𝑡
ℎ
(7)
We define F = 1,2, F as a set of CRACs in an internet data center.Analogous to the thermal model of racks,
the dynamics of CRACs can be written as
𝑑𝑇𝑜𝑢𝑡
ℎ
𝑑𝑡
= −𝐴ℎ 𝑇𝑜𝑢𝑡
𝑗
+ 𝐴ℎ 𝑇𝑖𝑛
ℎ
+ ℬℎ 𝒫ℎ (8)
Where 𝑇𝑖𝑛
ℎ
and 𝑇𝑜𝑢𝑡
ℎ
are the ambient air temperature and extreme air temperature of CRAC h, respectively.
Also, 𝒫ℎ is the total power consumption of CRAC h and 𝐴ℎ , ℬℎ are constant coefficients [20]. 𝑇𝑖𝑛
ℎ
is the
ambient air temperature represented as
𝑇𝑖𝑛
ℎ
= ∑ 𝐺ℎ ,𝑔𝑇𝑜𝑢𝑡
𝑔
+
𝑔ℰ𝐹
∑ 𝐻ℎ,𝑗𝑇𝑜𝑢𝑡
𝑗
𝑗ℰ𝑀 (9)
G and H are mappingambient air temperaturefrom output air temperatures,nonnegativecoefficients for
CRACs h, whosesum equals 1.
2.2. Internet Data Center Configuration and Limitation
This section presents the details of a specific internet data center taken from the literature [20].Thedata
center comprises three server racks and three CRAC units, as given in figure 2. The total number of
servers in rack j = 1,2,3 are given as M1 = 300, M2 = 400 and M3 = 200. The tolerance level for each rack's
latency delay or queuing delay is fixed to Dj = 10ms. Also, it is observed that a single server with
maximum utilization consumes a power of 285 Watts while the completely idle server consumes 150
Watts. This is the case for all servers in each rack, and therefore, the high power is represented by PjH =
285 W and the low power by PjL = 150 W. Also, the service rate for each rack is constant, which is µj = 2
jobs/sec. The configuration of racks is summarized in table 1. Regarding the CRAC units, it is assumed
that the power consumption by each CRAC is constant, that is, P1 = P2 = P3, and its value is either 0 or 100
kW. The dynamics of the ambient temperature and the output temperature of both server racks and
CRAC units are related by some parameters, as discussed in table 2.
Table 2. Configuration of Racks in IDCs
i 𝝁𝒋 𝑷𝒊
𝑯
𝑷 𝒊
𝑳 𝑴𝒋 𝑫𝒋
1 2 285 150 300 0
2 2 285 150 200 0
3 2 285 150 400 0

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Table 3. Parameters of Racks in IDCs
Node Rack 1 Rack 2 Rack 3
Rack 1 G11 = 0.01 G 12 = 0.02 G 13 = 0.06
Rack 2 G 21 = 0.03 G 22 = 0.01 G 23 = 0.05
Rack 3 G 31 = 0.04 G 32 = 0.04 G 33 = 0.84
CRAC 1 H11 = 0.85 H12 = 0.07 H13 = 0.03
CRAC 2 H21 = 0.04 H22 = 0.88 H23 = 0.02
CRAC 3 H31 = 0.07 H32 = 0.0 H33 = 0.81
Table 4. Parameters of CRACs in IDCs
Node CRACs 1 CRACs 2 CRACs3
Rack 1 H11 = 0.80 H 12 = 0.07 H 13 = 0.04
Rack 2 H 21 = 0.04 H 22 = 0.85 H 23 = 0.02
Rack 3 H 31 = 0.04 H 32 = 0.03 H 33 = 0.84
CRAC 1 G11 = 0.01 G12 = 0.01 G13 = 0.04
CRAC 2 G21 = 0.01 G22 = 0.01 G23 = 0.04
CRAC 3 G31 = 0.05 G32 = 0.04 G33 = 0.01
Before going into the details of the control techniques for this internet data Centre, we discuss some
elements of the control input (power dissipation of racks and CRACs) and its relationship with the job
arrival rate or workload on the server racks parameters. Details of RACs and CRACs are given in Table 3
and Table 4, respectively [21].
2.3 Assumptions of Environment
The problem is studied dynamically (transient)and undergoes thefollowing assumptions:
 It assumed that theroom transfers noheat to the outside the room.
 The air flows only through servers and heat exchangers.
 Heat conduction allowed through the aisle containment walls.
 It assumed that thepower consumption by each CRAC is constant,that is P1 = P2 = P3, and
its value is either 0 or 100 kW
 All the environment and simulation is done by using MATLAB
3. Power Dissipation and Workload
Each server rack and CRAC unit's power consumption is used as control input in the state space
model. Since the power consumption of the server racks is related to the workload of the servers, we have
expressed the total power consumed by mj active servers in a rack as [7] [22].
𝑃
𝑗 (λ) = 𝑏1λ𝑗 +𝑏0𝑚𝑗 (10)
The total power consumed by all servers (including active and idle servers) in a rack [23] are therefore
𝑃𝑎𝑗 (λ) = 𝑏1λj +𝑏0𝑀𝑗 (11)
To identify the parameters b1 and b0 for the internet data center, it is clear that for a single server, the
power consumption is related to the CPU utilization of the server as
P = (𝑃𝑖
𝐻
- 𝑃 𝑖
𝐿
)Ucpu +𝑃
𝑖
𝐿
(12)
This means that if a server is 100% utilized, Ucpu = 1 and therefore P =𝑃𝑖
𝐻
. Similarly if Ucpu = 0, we get
P = 𝑃𝑖
𝐿
.
The relationship between CPU utilization and power consumption is shown in the figure. The CPU
utilization is related to the arrival rate λ and service rate µ of a server, that is Ucpu =
𝜆
𝑢
. Let the arrival
rate or workload of the ith server in rack j is represented by λij, then the power consumed by the ith
server in rack j is [24]
Pij = (𝑃𝑖
𝐻
- 𝑃𝑖
𝐿
)
𝜆𝑖𝑗
µ𝑗
+𝑃
𝑖
𝐿
(13)

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Power Dissipation and WorkloadWhere it is assumed that the frequency/rate of service µ is constant
for each server in rack j, and therefore, it is represented by µj.
The total power consumption for mj active servers in rack j can be written as [25]
Figure 3 Relationship between CPU Utilization and Power Consumption
𝑝𝑗 = ∑ 𝑝𝑖𝑗 = (𝑝𝑗
ℎ
− 𝑝𝑗
𝑙
)
∑ λij
𝑚𝑗
𝑖=1
µj
𝑚𝑗
𝑖=1 + 𝑝𝑗
𝐿
𝑀𝑗 (14)
Since the workload assigned to rack j is ∑ 𝜆𝑖𝑗
𝑚𝑗
𝑖=1 = λj, we have
𝑝𝑗 =
(𝑝𝑗
𝐻−𝑝𝑗
𝐿)
µj
λ𝑗 + 𝑝𝑗
𝐿
𝑀𝑗 (15)
Comparing the above Equation with (11), weobtain
𝑏1 =
(𝑝𝑗
𝐻
−𝑝𝑗
𝐿
)
µj
, 𝑏0 = 𝑝𝑗
𝐿
(16)
This means that for the internet data center discussed in the previous section, the parameters are
b1 = ((285-150))/2 =67.5 and b0 = 150.So the power consumption of mj activeservers becomes
𝑝𝑗 = 67.5 λj + 150𝑚𝑗 (17)
Notice that the total power consumption of rack j, including active and idle servers, becomes
P_ja = 67.5λj +150Mj and Pj ≤ P_ja [26].
We are considering the small internet data center w ith three racks whose configuration is
summarized in table 2. We are observing the effect of different workload levels on power consumption by
IDCs. In the first case, we are considering the linear workload percentage. Every rack is utilizing CPU
100% [27] it means each rack has its complete workload without any distribution
Figure 4. Case 1: Relationship of Power Consumption and Full Workload of each rack without any Distribution

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When workload percentage is zero, it means all servers are idle but still they are consuming P_1a
= 150∗300 = 45 KW, P_2a = 150 ∗ 400 = 60 KW and P_3a = 150 ∗ 200 = 30 KW respectively. During this
experimental study, it is observed that when the workload increases from 0 to 100%, then power
consumption also increases. When workload percentage is one, it means that all servers in a rack are active
and consuming P_1a = 285 ∗ 300 = 85.5 KW, P_2a = 285 ∗ 400 = 114 KW and P_3a = 285 ∗ 200 = 57 KW
respectively. We assumed the workload distribution has a linear range. Rack 1 has a 33% to 66% workload.
Rack 2 has 0% to 33% workload while rack 3 has 67% to 0% of workload as in figure.
Figure 5 (a) Workload distribution in 3 racks (b) Power Consumption in 3 racks
Put these values in equation 14 when the workload is 33% on rack1,0% on rack 2, and 67% on
rack 3 then we get thetotal power consumed by rack 1, 2, and 3 is P_1a =[
((285−150)∗0.33+150)∗300 )
1000
] = 58.36
KW, P_2a=[(
(𝟐𝟖𝟓−𝟏𝟓𝟎)∗𝟎+𝟏𝟓𝟎)∗𝟒𝟎𝟎)
𝟏𝟎𝟎𝟎
]=60 KW and, P_3a
=[((𝟐𝟖𝟓−𝟏𝟓𝟎)∗𝟎.𝟔𝟕+𝟏𝟓𝟎)∗𝟐𝟎𝟎)
𝟏𝟎𝟎𝟎
] =47.82 KW respectively
3.1. Methodology
The above mathematical model provides the maximum power consumption, which is evaluated
by performing empirical analysis with three techniques Computer Room Air-condition CRACs ON/OFF,
CRACs 1-Step ON/OFF, and Multi-Step-3 CRACs ON/OFF at various parameters and configuration are
given in Table 2 to Table 3 called case 1 and case 2. Detailed descriptions of three techniques are given
below.
Case 1: Workload distribution percentage is 33%, 33%, and 34% on servers one, two, and server
three, respectively.
Case 2: Workload distribution percentage is 0%, 33%, and 67% on servers One, two, and three,
respectively.
3.2. CRACs ON/OFF Control Method
CRACs ON/OFF control in which there are only two possibilities and that if it is turned off, it will
consume no power means 0 KW. The second is if it is turned on, then it will consume 100 KW. So, it has
more total power peaks between 175.36 KW to 475.36 KW. The maximum outer air temperature of server
1 is 25.19◦ . Server 2 has 25.21◦ , and Server 2 has 25.21◦ Server 2 has 25.11◦. In this case, ambient
temperature shows sharp peaks fluctuation. Figures 6 and 7. CRACs 1-Step ON/OFF Control method
3.3. CRACs 1-Step ON/OFF Control method
In 1-step CRACs, CRACs can be partially turned ON/OFF. There are three values of 0,50,100.
When the ambient temperature of servers increases from 25◦ , it checks the value of control input of
CRACs if CRACs were completely off means consumes 0 KW, then CRACs will 50% turned on means will
consume 50KW else 100 KW. Similarly,if theambient temperature of servers decreases from 25◦ , it checks
the value of control input of CRACs if CRACs were completely on means consumes 100 KW, then CRACs

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will 50% turned off means will consume 50 KW otherwise 0 KW. The benefit of using multi-1-step CRACs
ON/OFF control is that the maximum power consumes 325.36 KW less than CRACs ON/OFF control,
which was 475.36 KW. If we compare the ambient air temperature, then, in this case, it is closer to 2525◦ ,
so it shows small peaks as compare to CRACs ON/OFF control.
3.3. CRACs 3-Steps ON/OFF Control method
The third technique in which we are turning OFF/ON is three steps. This controller checks the
ambient temperature of racks if it is greater than 25◦. then it will check the value of controlled input. If
CRACs were turned off means 0 KW, it would be partially turned on at 25 KW. If 25 KW, it will be turned
on 50 KW; if it is 50 KW, then it will be turned on 75 KW or 100 KW if the ambient air temperature is less
than 25◦ , then vice versa.
4. Results and Discussion
4.1. CRACs simple ON/OFF method
Figure 6 Power consumption and ambient temperature in centigrade of case 1
Figure 6 shows the result of a CRACs ON/OFF control method of case 1 in which there are only two
possibilities and that if it is turned off, it will consume no power means 0 KW. The second is if it is turned
on, then it will consume 100 KW. So, it has more total power peaks between 175.36 KW to 475.36 KW. The
maximum outer air temperature of server 1 is 25.19◦ , Server 2 has 25.21◦ , and Server 2 has 25.21◦ Server 2
has 25.11◦. In this case, ambient temperature shows sharp peaks fluctuation.
Figure 7 Power consumption and ambient temperature in centigrade of case 2
We will now compare different workload effects as compare to case 1 while techniques are the
same. Similarly, in this, CRACs are completely turned ON at 100 KW and completely turned OFF at 0KW.
There is no concept of the partially turned ON/OFF concept of CRACs. From figure 7, rack 1 has 0%

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workload, but it still has 25.1463◦ maximum output air temperature. In this case, two racks 2 has the
highest air temperature as compared to other racks. It has more workload and the highest number of the
activated server.Rack 2 is 25.2179◦,and rack 3 has 25.1425◦.In this case, the maximum power consumption
is 470.91 KW while the minimum is 170.91 KW which is different from case 1. It means that workload
affects power consumption. Ambient temperature, in this case, shows fluctuations.
4.2. CRACs 1-Step ON/OFF Control method
In case 1, we are also considering CRACs 1-Step ON/OFF control figure 8. In 1-step CRACs,
CRACs can be partially turned ON/OFF. There are three values of 0, 50,100. When the ambient
temperature of servers increases from 25◦ , it checks the value of control input of CRACs if CRACs were
completely off means consumes 0 KW, then CRACs will 50% turned on means will consume 50 KW
otherwise 100 KW.
Similarly, if the ambient temperature of servers decreases from 25◦ , it checks the value of control input of
CRACs if CRACs were completely on means consumes 100 KW, then CRACs will 0% turned off means
will consume 50 KW else 0 KW. The benefit of using multi-1-step CRACs ON/OFF control is that the
maximum power consumes 325.36 KW less than CRACs ON/OFF control, which was 475.36 KW. If we
compare the ambient air temperature, then, in this case, it is closer to 2525◦ , so it shows small peaks as
compared to CRACs ON/OFF control.
Figure 8 Case 1: CRACs 1-Step ON/OFF Method power consumption and ambient temperature in centigrade
Similarly, Figure 9 shows the result of case 2 CRACs 1- step method result that is 50 KW turned
OFF/ON instead of directly turned ON/OFF. It minimizes the ambient air temperature peaks than CRACs
ON/OFF Control. The power consumption peaks vary between 320.91 KW to 170.91 KW, far lesser than
CRACs ON/OFF Control.
Figure 9 Case 2: CRACs 1-Step ON/OFF Method power consumption and ambient temperature in centigrade
4.3. CRACs 3-Steps ON/OFF Control method

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Figure 10 shows the result of our third technique with case 1 configuration in which we are
turning OFF/ON in three steps. This controller checks the ambient temperature of racks. If it is greater
than 25,◦ then it will check the value of controlled input. If CRACs were turned off means 0 KW, then it
will be partially turned on at 25 KW. If 25 KW, then it will be turned on 50 KW. If it is 50 KW, then it will
be turned on 75 KW else 100 KW if the ambient air temperature is less than 25◦ , then vice versa. The
maximum power consumed by CRACs and servers is 250.36 KW which is even less than both techniques.
If we compare the ambient temperature of this technique, it is closest to 25◦ compared to the other two
techniques.
e
Figure 10 Case 1:CRACs 3-Step ON/OFF Method power consumption and ambient temperature in centigrade
The result of CRACs 3-Steps with case 2 configuration shown in Figure 11, which is the last case.
Our goal was to reduce power consumption, and in CRACs 3-step control, the power consumption varies
between 245.91 KW and 170.91 KW. It is the minimum power consumed than all other cases
Figure 11 Case 2: CRACs 3-Step ON/OFF Method power consumption and ambient temperature
Ambient air temperature is also closer to 25◦. CRACs all three approaches are following few
constraints given below: -
• The temperature of IDCs is nearly equal to 25◦.
• Power consumed by racks and CRACs must be positive integers greater than zero.
• The total consumed power is equal to the summation of power consumed by racks and CRACs.
5. Conclusions

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Mathematical representation of the internet data center in the State Space model and its
simulation in MATLAB. Both algorithms are given in Appendix 1 and Appendix 2.
Two different control techniques have been used to minimize the power consumption of IDCs.
The response of control techniques has been observed under different workload conditions. Based on
observation, we conclude that CRACs multi-step (1-Step and 3-Step) ON/OFF control, especially CRACs
step-3 ON/OFF control, presented a good sign for our problem statement and has some useful benefits as
shown below
• CRACs step-3 ON/OFF control minimizes power consumption more than the other two
techniques.
• It is observed that CRACs step-3 ON/OFF control has smooth power variations while CRACs
step-1 ON/OFF and CRACs ON/OFF control shows sharp power peaks.
6. Future Work
The power reduction modeling proposed CRACs step-3 ON/OFF control has significantly
reduced the heat emission. It is required to model the experimental phenomena in mathematical
interpretation.Subsequently, this will help the mathematician implement the above model at a large scale
to control the limitations given in the manuscript.
.
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Appendix 1
Algorithm CRACs ON/OFF Control
Input: Ad, Bd, and Cd matrices are given.
Calculate P1, P2, P3 by using Equation (14).
Initialindon:
u(:, 1) = [P1;P2;P3;0;0;0]
x(:, 1) = [25;25;25;25;25;25]
Loop:
For k = 1,...,100
x(:,k +I) = Adx(:,k) + Bdu(:,k)
Y(:,k + I) =Cdx(:, k + I)
If (y(1,k+ I) > 25) || (y(2,k + I) > 25) II (y(3,k+ I) > 25)
u(4 :6,k + I) = [100;100;100]
else

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If (y(1,k+1)<25) || (y(2,k+1) < 25) || (y(3,k+1) < 25)
u(4 :6,k + I) = [0;0;0]
else
u(4 :6,k + I) = u(4 :6,k);
Endif
Endif
u(:,k+ I) = [P1;P2;P3;u(4.k + I);u(5,k + I);u(6,k+1)
EndFor
Appendix 2
Algorithm CRACs Multi-Steps ON/OFF Control
Input: Ad, Bd, and Cd matrices are given.
Calculate P1, P2, P3 by using Equation (14).
Initialindon:
u(:, 1) = [P1;P2;P3;0;0;0]
x(:, 1) = [25;25;25;25;25;25]
Loop:
For k = 1,...,100
x(:,k +I) = Adx(:,k) + Bdu(:,k)
Y(:,k + I) =Cdx(:, k + I)
If (y(1,k+ I) > 25) || (y(2,k + I) > 25) II (y(3,k+ I) > 25)
If u(4 :6,k + I) = [0;0;0]
Intermediate level:
.
.
.
else
Intermediate level:
EndIf
If (y(1,k+1)<25) || (y(2,k+1) < 25) || (y(3,k+1) < 25)
If u(4 :6,k + I) = [100;100;100]
Intermediate level:
.
.
.
else
Intermediate level:
EndIf
EndIf
u(:,k+ I) = [P1;P2;P3;u(4.k + I);u(5,k + I);u(6,k+1)
EndFor
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which can be accessed at http://creativecommons.org/licenses/by/4.0.