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Received February 19, 2021, accepted March 26, 2021, date of publication April 7, 2021, date of current version

April 15, 2021.


Digital Object Identifier 10.1109/ACCESS.2021.3071508

Performance Evaluation of an Internet of Healthcare Things


for Medical Monitoring Using M/M/c/K Queuing Models
FRANCISCO AIRTON SILVA 1 , TUAN ANH NGUYEN 2, IURE FÉ3 , CARLOS BRITO1 ,
DUGKI MIN4 , AND JAE-WOO LEE5
1 Federal University of Piauí (UFPI), Teresina 560 054, Brazil
2 Konkuk Aerospace Design-Airworthiness Research Institute (KADA), Konkuk University, Seoul 05029, South Korea
3 Brazilian Army, Picos 64606-000, Brazil
4 Department of Computer Science and Engineering, College of Engineering, Konkuk University, Seoul 05029, South Korea
5 Department of Aerospace Engineering, Konkuk University, Seoul 05029, South Korea

Corresponding author: Dugki Min (dkmin@konkuk.ac.kr)


This work was supported in part by the Brazilian National Council for Scientific and Technological Development—CNPq under
Grant 309335/2017-5, in part by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded
by the Ministry of Education under Grant 2020R1A6A1A03046811, in part by the Ministry of Science, ICT (MSIT), South Korea, through
the Information Technology Research Center (ITRC) Support Program supervised by the Institute for Information & communications
Technology Planning & Evaluation (IITP) under Grant IITP-2020-2016-0-00465, and in part by ‘‘The Competency Development
Program for Industry Specialist’’ of the Korean Ministry of Trade, Industry, and Energy (MOTIE), operated by the Korea Institute for
Advancement of Technology (KIAT) under Grant N0002428.

ABSTRACT Due to the non-stop and rapid spreading of virus pandemics all over the world, traditional
healthcare monitoring capabilities of hospitals and/or medical centers are under a severe over-load. Modern
computing infrastructures with the harmony of various layers of computing paradigms (e.g., cloud/fog/edge
computing) for healthcare monitoring are apparently the essential computing backbone that help access and
process instantly the medical data of every single patient at the very edge of the healthcare system to combat
with global or regional virus contagion. Previous studies proposed different computing system architectures
for healthcare monitoring but few works considered the evaluation of pure performance of medical data
transmission in a comprehensive manner. In this paper, we proposed an M/M/c/K queuing network model
for the performance evaluation of an Internet of Healthcare Things (IoHT) infrastructure in association
with a three layer cloud/fog/edge computing continuum. The model considers a life cycle of medical data
from body-attached IoT sensors in edge layer all the way to local clients (e.g., local medical doctors,
physicians) through fog layer and to remote clients (e.g., medical professionals, patient’s family members)
through cloud layer. Furthermore, we also explore the impact of the alteration in system configuration
and computing capability of computing layers in two scenarios on various performance metrics. Critical
performance metrics related to quality of service are evaluated in a comprehensive manner, such as (i) mean
response time of medical data transmission to fog (local) clients and to cloud (remote) clients, (ii) utilization
of cloud/fog/edge computing layers, (iii) service throughput, (iv) number of medical messages in a period
of time, and (v) drop rate. The simulation results pinpoint bottle-neck parameters and configurations of the
IoHT infrastructure’s system architecture in relation to the frequency of medical data collection for health
check of patients. Thus, the findings of this study can help improve medical administration in hospitals and
healthcare centers and help design computing infrastructures in accordance for medical monitoring in the
severe circumstances of virus pandemics.

INDEX TERMS Healthcare monitoring, internet of healthcare things, queuing model, performance evalua-
tion, quality of service.

I. INTRODUCTION and can extract information about different environments. IoT


The Internet of Things (IoT) is one of the great advances devices are used, for example, to monitor patients in smart
in modern technology. IoT devices are inter-communicable hospitals [1], to monitor smart homes [2], or to detect acci-
dents in vehicular ad-hoc networks [3]. The Statista group 1
The associate editor coordinating the review of this manuscript and
approving it for publication was Alessandro Pozzebon. 1 Statista: https://tinyurl.com/y83kkser

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
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predicts that the installed IoT devices is projected to amount can be useful in this context, making predictions based on
to 21.5 billion units worldwide by 2025. Most of these devices probabilities.
will be located at the edge of the Internet and could provide Queuing networks [19] have become extremely popular
new applications, changing many aspects of both traditional in the applied stochastic modeling field for various appli-
industrial productions and our everyday living. IoT plays an cation areas, such as telecommunications, computers, man-
important role in the healthcare scenario. A great example ufacturing, and transportation. Queuing network models are
is how IoT have been dealing with the pandemic caused by more straightforward and more didactic, in addition to being
the coronavirus (COVID-19) worldwide. The ability of IoT well suited for evaluating performance. The modeling and
services in providing remote data collection and monitoring evaluation of pure performance help focus on the proba-
of patients in quarantine has made it a critical aspect in fight- bilistic nature of user demands (workload) as well as inter-
ing the spread of virus pandemics [4]–[6]. The incorporation nal state behaviors without considering failure and repair
of IoT in health care is broadly termed as IoHT (Internet of occurrences which are often very rare events in physical
Healthcare Things) [7]. systems. Thus, a pure performance model help represent data
IoHT is an ecosystem of medical devices, such as smart transactions within a certain period of time to discover per-
healthcare and monitoring devices (e.g. smart pacemaker, formance bottlenecks due to architecture design. Especially,
smart blood glucose meter etc.) that have the ability to col- in the case of IoHT for medical monitoring with the use
lect, analyze and transmit health data to healthcare systems of high-reliability equipment, a single variation of system
through communication networks. A typical IoHT scenario architecture, operational configuration and/or parameters of
involves smart healthcare devices that monitor the vital signs devices/components apparently cause a sensitive impact on
of focal patients, and transmit that data directly to remote the performance of processing data and service delivery due
servers differentiated basically by location and resources to stream-like end-to-end data transactions from medical sen-
capacity. Cloud platforms are examples of common comput- sors surrounding patients at the edge of the network to display
ing resources in this context [8], [9]. Cloud computing may devices at the medical professionals’ working places. Pure
be used to store and analyze health data, enabling automated performance analysis based on product form queuing network
decision making regarding interventions. However, closer in these cases can consider different aspects in a quick manner
computing resources are needed to provide even lower pro- such as resources capacity variation, sensor grouping by loca-
cessing delays. Fog and edge computing are complementary tion, number of processing cores per machine. Also, various
layers that fills this gap of local processing. Fog [10] brings performance metrics such as throughput, drop rate, mean
part of the cloud capacity closer to the IoT layer. Edge response time, response time distribution, and utilization can
devices [11] connect IoT sensors to the fog and cloud layers. be analyzed in a comprehensive manner.
Such a Cloud-Fog-Edge architecture provides the processing There are some related work that have evaluated health-
support needed by the IoHT constrained devices. This way, care systems using analytical models [9], [20]–[26]. Some of
IoHT technologies can contribute to improve performance, them have focused on security aspects [21], [22], [27], [28].
reduce costs and mitigate risk [12]–[17]. However, although Other studies have focused on infrastructure availability [24],
the IoHT have been adopted to monitor people everywhere, [25]. However, only one paper have observed all the Cloud-
there is a place where technology must be much more effi- Fog-Edge layers [9], but such a work did not evaluate pure
cient due to its inherent criticality: the hospital. performance aspects. In this context, only two related works
A smart hospital is a concept that emerged as a result adopted queue models [21], [24]. Marcu et al. [21] failed to
of rapid digitalization across the healthcare industries with explore the potential of multiple processing layers and they
the use of IoHT, data analytics, availability of personalized have proposed a model too much simplified with only two
services, Artificial Intelligence (AI), and lastly the Cloud- queues. Elter et al. [24] used fog and cloud layer, however,
Fog-Edge processing capacities [1], [18]. Smart hospitals with the limitation of measuring only the mean response
offer new opportunities to provide fast and accurate responses time (MRT) of the system. Furthermore, all related work have
by obtaining relevant information. This intelligent smart failed in representing essential smart hospitals characteristics,
hospital’s network can receive data from several sources such as: sensors grouped by location and mean response time
(hospital rooms), process data in a decentralized manner calculated per layer.
with higher digital computing resources to make smarter In that sense, this paper proposes to evaluate IoHT sys-
decisions. From this, intelligent recommendations, predic- tems supported by Cloud-Fog-Edge using a comprehensive
tive analysis, or pattern detection can be made. However, queuing model of type M/M/c/K. Queuing networks are suit-
the system requirements of smart hospitals are highly crit- able for detecting performance bottlenecks due to shared
ical, including performance. The performance evaluation resources in distributed systems [29]. An advantage of the
of smart hospital systems is essential to ensure their opti- queue models is the low complexity of the steady-state solu-
mal operation. Evaluating the performance of IoHT sup- tions (polynomial in the number of queues and customers),
ported by Cloud-Fog-Edge resources with real experiments as they can be obtained as a product of the steady-state
can be highly expensive and impractical with real patients. solution for each of the individual queues in the network [30].
There are many involved parameters and analytical models Therefore, the contributions of this paper are the following:

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TABLE 1. Related Works.

• A queuing model is presented for performance evalu- results. Finally, Section VI draws the main conclusions and
ation, as a useful tool for designers of IoHT scenarios suggestions for further works on the topic.
based on Cloud-Fog-Edge resources to verify the per-
formance of changes in the system even before they are II. RELATED WORKS
implemented. The model permits to configure dozens This section presents works that have approaches more sim-
of parameters depending on how many components ilar to the present work. Table 1 presents a comparison of
the designer needs, including service time, transmission the collected works, highlighting our proposal’s main dif-
time, resource capacities, and queue sizes; ferences. Eight studies were surveyed, ordered by year. The
• Resource capacity analysis that serves as a practical oldest one was from 2014. All the papers have in common the
guide for performance analysis in a IoHT monitoring use of some analytical model (e.g., queuing, Markov chain,
scenario with the proposed model. The tested scenarios Petri net models) to evaluate an architecture for monitoring
have included the variation of Cloud-Fog resources. A people with sensors. All works focus on health context, with
significant number of performance metrics were con- the exception of the article [26], which does not specify such
sidered in this work, such as resource utilization, mean a context. Next, the works are discussed in a grouped manner
response time, drop rate, and throughput. according to each comparison criterion.
The remaining of this paper is organized as follows.
Section II presents related work with an extensive table com- A. MAIN ARCHITECTURE COMPONENTS
paring the literature with our proposal. Section III describes Most works have highlighted the use of IoT supported by
the architecture considered for designing the model including some remote processing. However, as IoT is a relatively
all necessary assumptions. Section IV details the proposed recent paradigm, the oldest collected articles [20], [21] did
analytical queuing model and its workflow explanation. not use the term IoT explicitly. Kartsakli et al. [20], for
Section V presents and analyzes the obtained simulation example, focuses on the use of communication protocols,

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proposing the cloud-assisted RLNC-based MAC protocol Kartsakli et al. [20] did not observe the issue of capacity as
(CLNC-MAC) and develop a mathematical model for the it focused on communication protocols. Strielkina et al. [22],
calculation of the key performance metrics. The term cloud and Lomotey et al. [23] did not study capacity issues as they
in Kartsakli’s work refers to the cluster of sensors that com- focused on information security.
municate through a mesh network. They show the importance The last three comparing criteria have added a significant
of central coordination in fully exploiting the gain of RLNC contribution to the theme because they are unique character-
under error-prone channels. Marcu et al. [21] present an istics of the model proposed in this study. Sensors Grouped
e-health solution based on healthcare information systems by Location refers to how the proposed model represents
supported by hybrid (public-private) cloud computing with a different groups of sensors. The related work uses only a
focus on the medical imaging department. The other works single group of sensors and thus assigns a single arrival rate.
used IoT devices as a component of the architecture and, Our model allows to assign different arrival rates depending
in most cases, also used the fog layer. Our proposal explores on their location. Such a location in our model is charac-
not only IoT but also the edge, fog, and cloud layers as terized as being a hospital room. This unique functionality
complementary resources. Only Santos et al. [9] explored aims to imitate reality, because depending on the location,
such components. Thus, Santos et al. [9] propose surrogate the sensors may have different criticisms, requiring more or
models to estimate the availability of e-health monitoring less frequent data sending. Our model also has the unique
systems, applying a multi-objective optimization algorithm feature of representing Number of Processing Cores per
to improve system availability considering component costs Machine. Both the fog (physical) and the cloud (VM) have
as a constraint. We believe that it is essential to explore all machines with multiple cores. The model allows varying
four layers to decrease the coupling between components and the capacity of the number of machines and each machine’s
improve system performance. Santos et al. [9] did not explore capacity in terms of cores. It is observed that in the related
performance issues and did not offer the same architectural works, the number of cores is somewhat abstracted, and only
contributions that we highlight in the comparative table. the number of machines is observed. We believe that this
feature is essential to represent the reality of multi-layer
B. METRICS architecture more accurately. Finally, our model also has
The more evaluation metrics, the better the understanding of the differential of calculating two different response times
the system behavior. Our study covers the largest number (Mean Response Time per Layer), one for the fog and
of performance metrics: MRT, utilization, system number of one for the cloud. We believe it is an essential requirement
messages, throughput, and drop rate. Besides, we observed because our model expresses two types of clients, the client
usage and MRT at different points in the model, not just (doctors) who stays inside the hospital and requires a speedy
in general. In contrast, two studies [22], [23] investigated response time, and another one that does not have the same
metrics related to information security. Strielkina et al. [22] need (family members, for example). Thus, the calculated
simulated attacks on IoT vulnerabilities and how to recover MRTs allow to have a deep understanding of each part
from them. Lomotey et al. [23] have proved that distributed of the system. These three features further reinforce the
health information system threats such as the denial of model’s contribution to the IoT area supported by remote
service, man-in-the-middle, spoofing, and masking can be processing.
effectively detected through simulations with Petri nets. Two
other works studied the metric of availability [9], [26]. III. SYSTEM ARCHITECTURE
Andrade et al. [26], for example, revealed that adopting a Fog A. OVERALL SYSTEM ARCHITECTURE
device can improve availability. However, the performance is A typical system architecture of an IoHT infrastructure for
only improved in certain conditions, like when the environ- medical monitoring in hospitals or medical centers is pre-
ment is not full capacity. Both security and availability issues sented in Figure 1. The IoHT infrastructure in consideration
are critical. However, the area explored by our work needed is constituted of three main computing layers including (i) a
a more comprehensive and detailed performance study. cloud computing layer at cloud data centers for the remote
access of distant clients (e.g., family members, overseas med-
C. RESOURCES CAPACITY ANALYSIS ical professionals), (ii) a fog computing layer at fog data
Normally, the main objective of the performance evaluation centers for the local access of internal clients (e.g., medi-
of systems – whether by measurement, simulation, or mod- cal doctors, medical physicians) and, (iii) edge computing
eling – is to predict the system’s future behavior and be layer at local medical treatment rooms for health sensor
prepared to meet requests demand. Another critical point data aggregation and integration. At the very edge of the
is to avoid wasting computational resources [31]. There- computing network, edge computing layer offers real-time
fore, analyzing the resources capacity to support the gen- health data monitoring and aggregation by using edge devices
eration of IoT data is essential, especially in time-critical to periodically collect and process raw data of patients’
systems, such as healthcare. Almost all related works varied health in each room. To provide health monitoring services
the resource capacity and observed different scenarios. Only in a hospital or a medical center, edge computing layer is
three studies did not observe this aspect [20], [22], [23]. designed with multiple edge nodes to perform health data

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FIGURE 1. Conceptual Architecture of an IoHT Infrastructure for medical monitoring.

collection and processing at every room on every floor of and also transmitted to remote cloud data centers for further
a building. In the middle layer, the fog computing layer is data processing and storage through a fog-cloud gateway.
composed of (i) a number of fog nodes for parallel processing The cloud layer offers a high level of processing and storage
of data regardless its source, with (ii) an edge-fog gateway with multiple virtual machines (VMs) to deliver the processed
for data aggregation and load balancing between edge and data to distant clients. It is then a matter of curiosity that,
fog computing layers, and with (iii) a fog-cloud gateway for (i) how the variation of periodic interval for medical data
data transactions between fog and cloud computing layers. generated by health sensors attached on patients’ body and
At the very center of the whole IoHT infrastructure, cloud collected by edge devices in edge computing layer impacts
computing layer offers powerful computing and storage capa- the performance metrics of provided services (e.g., mean
bilities for advanced data processing. It also plays a role of a response time, throughput) and, (ii) how a specific configura-
center hub for accesses of distant clients to common medical tion of each layer in the IoHT infrastructure and its variation
data. impact the performance metrics of data transactions from
patients’ attached health sensors all the way to internal clients
B. LIFE-CYCLE OF MESSAGES at local medical centers through fog computing centers and
to external clients at distant areas through cloud computing
The architecture also indicates the life cycle of data packages
centers.
and operational behaviors of the system for healthcare mon-
itoring purposes. Particularly, patients’ medical data is peri-
C. ASSUMPTIONS AND DISCUSSIONS
odically collected by IoT health sensors, then automatically
aggregated and encapsulated by edge devices (e.g., embedded For the simplification of modeling, several assumptions on
system boards, IoT edge gateways) into medical messages. the architecture and operations of the IoHT infrastructure in
These medical messages are then transmitted to an internal consideration are given as follows.
fog center through an edge-fog gateway. The edge-fog gate- • Edge layer
way plays a role as an entrance door for data distribution and – [e1]: Heterogeneous types of medical sensors are
load-balancing to computing fog nodes. For the sake of high not considered in modeling. We model the gen-
processing performance at local medical centers, we assume eration of medical data by all sensors attached to
to use bare physical machines as fog nodes in the fog layer. patient in a room as a data burst to an edge device
Medical messages are processed on fog nodes by specialized of the room.
medical services and applications, which are customized for – [e2]: Various types and latency of communica-
the types of medical data as well as for the local medical tion between medical sensors and edge devices
departments. The processed medical data in the fog layer are not taken into account in the modeling.
is delivered to internal clients’ front-end interface directly In practice, the connection is formed by wireless

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communication. But, we neglect the negative failure and recovery behaviors of components are
impact of near-distance communication in edge not considered in the modeling for performance
layer on the overall performance metrics. evaluation [33].
– [e3]: Communication latency of the connection – [i2]: Our main focus is (i) to explore the bottle-neck
between edge and fog layers is simply assumed to in the considered IoHT architecture in real-time
be an edge-fog delay of the data transmission from medical data transmission, (ii) to explore the impact
each edge node to the fog layer, which will be taken of configuration alteration in fog and cloud lay-
into account in the modeling. ers on the performance metrics and (iii) to realize
– [e4]: Periodic health check and medical data col- the performance-related trade-offs between internal
lection are independent to each other and thus the clients at local places and distant clients. There-
arrival of requests is exponentially distributed with fore, the complexity of system architecture of the
an arrival rate λ. overall IoHT infrastructure is diminished to sim-
• Fog layer plify performance models using queuing network
– [f1]: Advanced load balancing in fog layer is not theory. In this way, we can put more efforts for
taken into consideration. Jobs received from edge performance evaluation of the system for real-time
layer through edge-fog gateway are equally dis- medical applications.
tributed to each of the fog nodes in the fog layer.
For the simplification in modeling, load balancing IV. QUEUING MODEL
problem of fog nodes is not our main focus. A com- Figure 2 illustrates a model based on queuing theory for
prehensive extension in future work could consider the presented architecture. All the model components follow
this problem for fog computing layer based on the same name patterns used in the architecture description.
round-robin mechanism [32]. All the aforementioned assumptions were attended in the
– [f2]: Heterogeneous configuration of each fog node model. Java Modeling Tools (JMT) [34] tool was used to
is not of our main focus. We assume that fog nodes model and evaluate the proposed scenario. JMT is a kit of
and their processing capabilities and resources are open source tools to simulate and evaluate communication
identical while data processing on each fog node is systems’ performance based on queue theory [35].
independent to one another. Each fog node can have Data flow occurs from left to right. Sensors generate
multi-core CPU for parallel processing. We neglect requests within a predefined time interval following a par-
the role of data storage in fog layer. ticular probabilistic distribution. The model has multiple
– [f3]: Communication latency of the connection entry points, corresponding to the hospital rooms. Each room
between fog and cloud layers is supposedly consid- generates constant data collected from patients in possibly
ered as a simple fog-cloud delay of data transmis- distinct arrival rates. Each room has an edge device which
sion from fog layer to cloud layer. works as a gateway between the edge and the fog layer.
Such a edge device is represented by a queue and a unique
• Cloud layer
internal server (M/M/1 service station). The rooms can have
– [c1]: Data processing in cloud layer is supposedly n patients, depending on the hospital organization. The arrival
performed on its virtual machines (VMs) instead of rate will depend on the number of patients and the distribution
its bare physical machines. Therefore, we assume of data generation performed by the patients’ sensors. We
to not take into account bare physical machines and consider that the rooms are organized in floors. Each floor
associated storage devices in the modeling to reduce has some distance to the fog layer. This way, there is a delay
the modeling complexity since we mainly consider (‘‘delay edge-fog") from each floor to the fog layer. Delay
the components (i.e., virtual machines) in charge of components do not have a specific service; that is, it is only
processing medical data in real time scenarios. a component that causes a delay in the transmission of a
– [c2]: As of modern cloud computing systems, vir- request, simulating a delay of the network.
tual machines in cloud layer can have multiple In the fog layer there are two gateways, one as entry point
cores for parallel processing. And at a certain time, and other as exit point. When arriving at each gateway, these
the cloud layer can elastically scale and balance messages can be distributed following a specific load balanc-
access load of a certain number of distant clients ing strategy. We consider in this work the equally distribution
on a multi-core virtual machine. strategy. Since the random distribution is not time consuming,
• IoHT Infrastructure the time to perform such distribution is unconsidered in this
– [i1]: Pure performance of data transactions between paper. Cloud and fog have a service time referring to the time
IoT sensors and internal/external clients (e.g., medi- to save the data and forward it to other analysis services for
cal professionals, medical physicians, family mem- alert notices that can be applied. It is worth mentioning that
bers) is the main focus of the modeling, therefore the cloud is usually more potent than the fog, but the fog is
the involvement of physical components and their closer to the sensors. It is assumed that health data received
operational availability are minimized. And that, in each element of the general system will be processed

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FIGURE 2. A queuing network model for performance quantification of an Internet of Healthcare Things (IoHT) infrastructure for medical
monitoring.

considering a Fist-In-First-Out (FIFO) queuing discipline. TABLE 2. Simulation parameters.


The queues from the fog and the cloud are modeled con-
sidering the M/M/c/K queue model. The main parameters of
such stations are: the queue size, service time and number
of internal servers (which we consider as processing cores in
this work). The M/M/c/K model refers to c service stations.
Each service station has a capacity limitation of K nodes. The
fog has a sink station corresponding to the place where the TABLE 3. Scenario A component parameters.
doctors can access sensitive and real-time data. Between
the fog and the cloud there is the delay fog-cloud. Particularly,
such a delay takes the longest time to finish due to the
significant geographic distance of the cloud service. In the
cloud, multiple Virtual Machines can be used, however, in this
paper we simulated the use of only one powerful VM, since A. SCENARIO A - FOG CAPACITY VARIATION
public clouds today offers VMs with incredible high number This section presents a simulation of the health monitor-
of cores (72 vCPU cores for example in the Amazon AWS ing system by varying the fog layer’s number of resources.
2 ). Finally, in the cloud layer there is a sink where the cloud Table 3 presents the configuration used in scenario A experi-
processed data can be accessed. ments. The number of fog nodes was varied in 1, 2, 3, and
4 nodes, maintaining the fixed values for the other com-
V. SIMULATION RESULTS ponents. Figure 3 presents the results considering different
This section presents Simulation analyzes using the proposed number of fog nodes.
model. Table 2 shows the input parameters used for each Figure 3(a) shows the MRT referring to the system’s first
model component. The X tag indicates that the component exit point (Fog Client MRT). In general, maintaining the
does not have a capacity definition for the queue. The time processing capacity, the greater the number of resources,
column represents the service time for the queue components. the lower the response time. The MRT is much lower with
The time between for the delay components represents com- 3 and 4 fog nodes than with 1 and 2 fog nodes. The configura-
munication time. tions with 3 and 4 fog nodes obtained an MRT between 46 and
Next subsections present three use case scenarios 174ms. Configurations with 1 and 2 fog nodes peaked at over
(A and B). The scenario A investigates the variation of 3500ms. The stabilization of MRT growth for 1 and 2 fog
fog nodes. The scenario B explores the variation of cloud nodes is due to the system having saturated all its resource
VM cores. capacity up to the Fog Client component. This saturation
occurs from the arrival rate (AR) equal to 0.011msg/ms for
2 Amazon AWS VMs: https://aws.amazon.com/pt/ec2/instance-types/ 1 fog node and 0.015msg/ms for 2 fog nodes. The fog node’s

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FIGURE 3. Results of model simulations considering different number of fog nodes.

saturation can be justified in the fog utilization 3(c). For messages begins (see drop rate in Figure 3(h)). The drop rate
1 and 2 fog nodes at the arrival rate points mentioned above, for 1 and 2 fog nodes start to grow exactly at the two inflection
the fog utilization reaches 100% of the capacity. When such points: AR = 0.011msg/ms and AR = 0.015msg/ms. Such
saturation and stabilization of MRT growth occurs, loss of growth is expected due to the depletion of resources. In this

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section, we will give a hypothetical example of practical use TABLE 4. Scenario B component parameters.
of the results for each metric. Let us say that the system
designer is not sure what the system’s arrival rate will be,
but that it will vary between 0.01msg/ms and 0.024msg/ms.
The system designer wants a Fog Client MRT below 200ms.
In this case, the model suggests that the system designer can
deploy 3 fog nodes sufficient to meet the demand. just 16% at the highest arrival rate. The low utilization is
Figure 3(b) shows the MRT considering the system’s sec- due to two factors. First, the edge devices’ service time was
ond exit point (Cloud Client MRT). In this case, it is expected configured with a shallow value (5ms) as it represents only
that the response time will be longer than the Fog Client the time for forwarding messages. Another factor is that each
because there are significant communication time and certain edge device receives data from a single data source, that is,
processing in the cloud as well. Thus, as expected, comparing from a single hospital room.
the graph 3(a) and 3(b), there is a significant increase in the Figure 3(f) shows the number of messages within the
MRT in the cloud in all fog resources configurations. system. Until AR = 0.019msg/ms, the system number of
The MRT for 2, 3 and 4 nodes are equivalent until messages are similar to the four configurations. After that,
AR = 0.016msg/ms in about 2200ms. The MRT for 1 node is the arrival rate becomes so high that for 3 and 4 fog nodes, the
in average 5800ms to all arrival rates. The highest variation cloud queue reaches its maximum capacity (5,000msg).
occurs from the AR = 0.021 with 3 and 4 nodes, because The lower configurations (1 and 2) do not reach the same
much more messages reach the cloud and are not dropped. maximum cloud queue capacity because in this case there are
Now, let us say that the system designer is sure that the system dropped messages.
arrival rate will be 0.012msg/ms and that the MRT in the Figure 3(g) shows the general throughput of the system.
Cloud Client should be below 10,000ms. In this case, the use The higher the system’s processing capacity, the lower the
of one fog node would meet the demand. drop rate and the higher the throughput. When there is no
Figure 3(c) shows the fog layer utilization. There is a data loss, a system throughput will equal the total system
significant difference between the lines, considering the four arrival rate. The evaluated model has 6 hospital rooms,
fog capacities. However, there is only a full saturation of so for AR = 0.01msg/ms there is a result of 0.01 × 6 =
resources (100%) with 1 and 2 fog nodes. Such saturation 0.06msg/ms. The throughput is very low and constant for
happens at different times for 1 and 2 fog nodes. For 1 and 1 fog node because, in the second arrival rate, the throughput
2 fog nodes, saturation occurs at AR = 0.011msg/ms and stagnates at 0.066msg/ms. Therefore, with only 1 fog node,
AR = 0.015msg/ms, respectively. The difference in usage it would be possible to serve the 6 hospital rooms with
depends on the workload. There is a small difference of 10% a low arrival rate of around 0.01msg/ms. After this point,
between 3 and 4 fog nodes observing the extremes with there would be data loss. For 2 fog nodes, the through-
minimum AR (0.01msg/ms). There is a more significant put stagnated at 0.14msg/ms because the resources were
difference of about 20%, considering the maximum arrival exhausted.
rate (0.024msg/ms). Let us say that the system designer only Figure 3(h) shows the system’s drop rate. As expected,
requires that the fog utilization being between 70% and 90% there are no discarding requests for 3 and 4 fog nodes in the
with an arrival rate of 0.019msg/ms. In this case, 3 fog nodes system. For 1 and 2 fog nodes, there is an increasing number
would be ideal to meet the imposed requirements. of discards, starting at the arrival rate of 0.011msg/ms and
Figure 3(d) shows the cloud utilization. The usage 0.018msg/ms, respectively. The drop rate increase is caused
increases proportionally to the arrival rate for 3 and 4 fog by the depletion of resources in 1 and 2 fog nodes and is
nodes and mostly for 2. However, with 1 and 2 fog nodes, reflected in several system metrics. Let us say that the system
there is stagnation at 40% and 80%, respectively. With 3 and designer allows data to be lost but that such loss does not
4 fog nodes the utilization is very similar, reaching 100% with exceed a rate of 0.05msg/ms. In this case, 2 fog nodes would
AR = 0.021msg/ms. Such stagnation is also caused by the be sufficient to meet the requirement.
bottleneck of resources in the fog node layer. This bottleneck
makes it possible to discard requests beyond capacity, making B. SCENARIO B - CLOUD CAPACITY VARIATION
fewer requests arrive at later architecture components. The This section shows the model simulation results by varying
available capacity of the cloud is wasted by a low perfor- the cloud’s processing capacity in terms of the number of
mance at the Fog layer. Let us say that the system designer virtual machines. Table 4 presents the configuration used in
looks for an arrival rate between 0.012 and 0.016msg/ms scenario A experiments. The variation was performed with 1,
and only requires that the cloud utilization being above 50% 2, 3, and 4 virtual machine cores. Figure 4 presents the
without data loss. In this case, at least 3 fog nodes would meet corresponding results.
the requirement. Figure 4(a) shows the MRT considering the Fog Client
Figure 3(e) shows the edge utilization. There is a relatively output. As the capacity variation was performed in the cloud,
linear increase proportional to the increase in arrival rate. there was no distinction between MRT’s behavior for these
The utilization level is shallow at all arrival rates, reaching different cloud capacities. In other words, the Fog Client

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FIGURE 4. Results of model simulations considering distinct number of cloud VM cores.

MRT does not change as the measurement of this MRT occurs observed, reaching a time of 180ms. Still, the Fog Client MRT
in a component before the cloud component. However, for is much lower than most Cloud Client MRT, as can be seen
the four capacities together, significant growth in MRT is in Figure 4(b).

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Figure 4(b) shows the Cloud Client MRT. Unlike the Fog cores = 0.1691msg/ms. This difference of 0.01msg/ms is
Client MRT, here, there is a significant distinction between equivalent to 360,000 messages per hour. Therefore, the sys-
the four cloud capacities. The greater the capacity of the tem designer must carefully observe the throughput metric
cloud, the lower the MRT obtained. The lowest results for 2, before deciding how many VM cores to configure to meet
3, and 4 cloud VM cores ranged between 2000 and 2300ms. A the demand.
higher capacity and a lower arrival rate result in an MRT very Figure 4(h) shows the system’s drop rate. As mentioned
dependent on the communication time between the fog and earlier, the smaller the number of resources, the greater the
the cloud, configured with the time of 2000ms. Despite this likelihood of data loss. With 4 VM cores, there was no data
initial stability, for capacities 2, 3 and 4 there is a sudden rise loss in any of the simulated arrival rates. For 1 VM core,
in MRT at points AR = 0.012msg/ms, AR = 0.016msg/ms, there is loss in all simulated scenarios. For 2 and 3 VM
and AR = 0.021msg/ms. This increase is again due to the cores, data losses started from points AR = 0.013msg/ms
high use of resources that reached 100% precisely at these and AR = 0.018msg/ms, moments in which resources were
points (see Figure 4(d). Considering 1 cloud VM core, with exhausted.
constant 100% utilization, the MRT has reached an exorbitant
250 seconds. Let us say the system designer is looking for VI. CONCLUSION AND FUTURE WORKS
an arrival rate of about 0.016msg/ms. The simulation would This work proposed a queuing model of type M/M/c/K to
allow the system designer to identify that 3 VM cores would represent and evaluate the performance of a health monitor-
obtain an MRT of 84800ms and 4 VM cores would obtain ing scenario corresponding to a hospital or medical center
an MRT of approximately 2154ms. Therefore, in this case, in the context of IoHT. The evaluated architecture includes
the designer would undoubtedly prefer to rent 4 VM cores IoT sensors, edge, fog and cloud components. The model
instead of 3. allows estimating a significant number of metrics, such as:
Figures 4(c) and 4(d) show the fog and cloud utilization, mean response time, the utilization level, and drop rate.
respectively. Similar to the behavior of the Fog Client MRT, The model offers unique contributions compared to related
the fog utilization does not suffer any change due to the work. The model is composed of four layers, more signif-
cloud capacity variation. However, there is a strong relation- icant number than the literature. The sensors are grouped
ship between the use of fog and the increasing workload. In by location, which permits configure distinct arrival rates
the cloud, as previously mentioned, the utilization reaches based on sensors group. The model represents not only num-
100% in all scenarios, and the lower the capacity, the earlier ber of machines as capacity but also its internal number
this top is reached. For 1 cloud VM core, the maximum of processing cores. Finally, the model also enable us to
capacity is obtained from the first arrival rate. For 2, 3 and calculated more than one mean response time, on the fog
4 cloud VM cores, depletion occurs at AR = 0.012msg/ms, and on the cloud. Two scenarios were explored in simulation
AR = 0.016msg/ms and AR = 0.021msg/ms. Figure 4(e) to exemplify the model utility. The first scenario observed
shows the edge utilization. The result is identical to the the impact of varying fog resources under the system per-
variation in the fog capacity (scenario A), as both varied formance. The second scenario did the same but focusing on
components occur after the edge layer. There is a relatively the cloud capacity. The simulations allowed to observe the
linear increase proportional to the arrival rate. However, it is relationship between the arrival rate and cloud/fog capacity
essential to note that the level of utilization is low at all points, variation under distinct perspectives. Moreover, the analysis
reaching 16% with no higher arrival rate. indicated that even the fog being closer to sensors, cloud
Figure 4(f) shows the number of messages within the still plays an important role in the process. The results also
system. The behavior of capacities 2, 3, and 4 are similar, show that queue size parameter has a significant impact on
distinguished by the moment of the rise in the number of performance, and dropped messages can be avoided making
messages. The depletion of cloud resources causes such a small calibrations in fog/cloud resource capacities. As future
rise. At the bottom of the graph, the system’s number of work, it is intended to extend the model to explore different
messages without data loss varies between 66 and 180 mes- communication types between the components. More ele-
sages. However, with the depletion of resources, the number ments can also be included, such multi-clouds (e.g., pub-
of messages is approximately 5,000, which is equivalent to lic, private and hybrid). The type of the queues can be
the queue’s size in the cloud. changed by including or excluding restrictions and buffer
Figure 4(g) shows the overall system throughput. The policies. Besides, further simulations can also be done,
greater the number of resources, the greater the throughput for example, exploring the load balancing strategies in the
will be. The throughput for 2, 3, and 4 cloud VM cores are gateways.
the same in the first three arrival rates. This equality occurs
because there is no data loss in these three points, as can
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FRANCISCO AIRTON SILVA received the B.S.
[19] I.-M. Haragos and C. Cernazanu-Glavan, ‘‘Modeling road traffic using
degree in information systems from the Insti-
service center,’’ Adv. Elect. Comput. Eng., vol. 12, no. 2, pp. 75–80, 2012,
tuto Federal do Piauí (IFPI), in 2008, and the
doi: 10.4316/aece.2012.02013.
M.S. and Ph.D. degrees in computer science from
[20] E. Kartsakli, A. Antonopoulos, L. Alonso, and C. Verikoukis, ‘‘A cloud-
assisted random linear network coding medium access control proto- the Universidade Federal de Pernambuco (UFPE),
col for healthcare applications,’’ Sensors, vol. 14, no. 3, pp. 4806–4830, in 2013 and 2017, respectively. He is currently a
Mar. 2014. Professor of Information Systems with the Univer-
[21] R. Marcu, D. Popescu, and I. Danila, ‘‘Healthcare integration based on sidade Federal do Piauí (UFPI). In 2015, he studied
cloud computing,’’ UPB Sci. Bull, vol. 77, no. 2, pp. 31–42, 2015. at the Sapienza Università di Roma. He was a col-
[22] A. Strielkina, D. Uzun, and V. Kharchenko, ‘‘Modelling of healthcare IoT laborative researcher in multinational technology
using the queueing theory,’’ in Proc. 9th IEEE Int. Conf. Intell. Data Acqui- companies, such as EMC and OKI. His research interests include distributed
sition Adv. Comput. Syst., Technol. Appl. (IDAACS), vol. 2, Sep. 2017, systems with emphasis on cloud-fog-edge integration, mobile computing,
pp. 849–852. and systems performance evaluation techniques.

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TUAN ANH NGUYEN received the B.Eng. and DUGKI MIN received the B.S. degree in indus-
M.Sc. degrees in mechatronics from the Hanoi trial engineering from Korea University, in 1986,
University of Science and Technology (HUST), and the M.S. and Ph.D. degrees in computer sci-
Hanoi, Vietnam, in 2008 and 2010, respectively, ence from Michigan State University, in 1991 and
and the Ph.D. degree in computer science and sys- 1995, respectively. He is currently a Professor with
tem engineering from the Department of Computer the Department of Computer Science and Engi-
Engineering, Korea Aerospace University, Seoul, neering, Konkuk University. His research interests
South Korea, in 2015. He was a Research Engineer include cloud computing, distributed and parallel
with the TRON Laboratory, FPT Software, FPT processing, big data processing, intelligent pro-
Cooperation, Hanoi, and the F-Space Laboratory, cessing, software architecture, and modeling and
FPT Technology Research Institute (FTRI), FPT University, FPT Coop- simulation.
eration, in 2008 and from 2009 to 2010, respectively. He was a Ph.D.
Research Associate with the Network Security and Systems Laboratory
(NS Laboratory), Korea Aerospace University (KAU), from 2011 to 2015.
He was a Postdoctoral Research Associate with the Distributed Multimedia
Systems Laboratory (DMS Laboratory), Konkuk University, Seoul, South
Korea, from August 2015 to February 2016. He worked for Office of
Research, University-Industry Cooperation Foundation, Konkuk University,
from March 2016 to February 2020 as a (Research) Assistant Professor.
He is currently a (Research) Assistant Professor with the Konkuk Aerospace
Design-Airworthiness Research Institute (KADA), Konkuk University. His
research interests include intelligent, dependable and secure digital twins,
digital twin for urban aerial mobility, reinforcement learning based intelli-
gent control for unmanned vehicles and robotic systems, generative adversar-
ial networks (GANs) for digital twins, dependability and security of systems
and networks, fault tolerance of embedded systems in aerospace and mecha-
tronics, disaster tolerance and recovery of computing systems, integration of
cloud/fog/edge computing paradigms, dependability and security analytical
quantification for Internet of Things, cloud data centers, unmanned vehicles, JAE-WOO LEE received the B.S. and M.S. degrees
mechatronic production chains, and e-logistics. in aerospace engineering from Seoul National Uni-
versity, Seoul, South Korea, and the Ph.D. degree
IURE FÉ received the degree in computer science from the Department of Aerospace Engineering,
from the Federal University of Piauí, and the mas- Virginia Tech, USA, in 1991. He is currently
ter’s degree in computer science from the Federal a Professor and the Director with the Konkuk
University of Pernambuco. He is currently work- Aerospace Design-Airworthiness Research Insti-
ing as a Systems Analyst with the Brazilian Army. tute (KADA), Konkuk University. He is also
His current research interests include distributed the President of the Korean Society of Design
systems and performance evaluation of systems. Optimization (KSDO) and also serves as the vice
president for several academic societies, including the Korean Society of
Aeronautics and Space Science (KSAA), and KOSSE. He is the correspond-
ing author or the coauthor of over 570 publications, including 13 patents
and 74 international journal articles. His research interests include mul-
CARLOS BRITO is currently a Senior College tidisciplinary design and optimization, MDO, aerodynamic design and
Student with the Information Systems course, Fed- optimization, aerospace vehicle design for aircraft, space launcher, and
eral University of Piauí. He has experience in UAV/Drones. He received several honors and awards in his academic career.
computer science and information systems, with He has been serving as the conference chair, the technical program chair,
emphasis on systems and distributed systems eval- and the symposium chair for various international conferences, including
uation. He is interested in researching themes APISAT, KSAS, and KSAA. He has served as a Specialized Member for
related to distributed systems, including the Inter- Defense Acquisition Committee, Ministry of National Defense, South Korea,
net of Things and cloud computing. and for Policy Planning Committee/Business Committee, DAPA, MND,
South Korea.

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