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Stochastic Model for Evaluating Smart Hospitals Performance
La´
ecio Rodrigues∓, Patricia Takako Endo?and Francisco Airton Silva∓
∓Universidade Federal do Piau´
ı (UFPI), Brazil
?Universidade de Pernambuco (UPE), Brazil
E-mail:faps@ufpi.edu.br, patricia.endo@upe.br
Abstract—Hospital systems must be efficient to prevent loss
of human lives. Low latency and high availability of resources
are essential features to guarantee quality of service (QoS)
in such environments. Taking advantage of Internet of Things
(IoT) emergence, smart hospitals apper as a health revolution
by capturing and transmitting patient data to physicians in
real time through a wireless sensor network. For that, smart
hospitals need local and remote servers for processing and storing
data efficiently. Commonly, the patient information is shared
among different devices, ensuring continuous operation and high
availability. However, there is a significant difficulty in evaluating
the performance of such systems in real contexts, because the
failures are not tolerated (one can not unpluged the system to
perform experiments) and the cost of a prototype implementation
is high. To cover this issue, this paper adopts the analytical
modeling approach to evaluate the performance of a smart
hospital system, avoiding the investment in real equipment. Using
Stochastic Petri Nets (SPNs) and Reliable Block , we propose a
model to represent the architecture of a smart hospital, and
estimate metrics related to the mean response time and resource
utilization probability. The model are quite parametric, being
possible to calibrate server resource capacity and service time.
One can define 13 parameters, allowing to evaluate a large
number of different scenarios. Results show that this work has
the potential to assist hospital system administrators to plan more
optimized architectures according to their needs.
Index Terms—Smart hospital, Stochastic Petri Net, Perfor-
mance, Internet of Things
I. INTRODUCTION
The Internet of Things (IoT) is bringing innovation to all ar-
eas of our society, connecting millions of devices and making
everyday life easier for people. The health sector is also taking
advantage from IoT. The usage of smart devices and sensors is
revolutionizing people’s health in several environments, such
as home or at the streets. At hospitals, it would not be different;
vital signs of patients in Intensive Care Units (ICU) can be
captured by sensors and different metrics can be calculated,
such as bed occupancy rate, employee productivity index,
among others. Therefore, there are many possibilities of IoT
in health field [1].
The usage of IoT in smart hospitals has been highlighted
as a trend that allows the creation of new and alternative
treatments, with more wealth of information and more precise
[2], [3], [4]. With these new set of vital information, it is
possible to track the patients continuously, and provide a
complete and more accurate picture of their illness. Moreover,
given the real-time nature of these smart systems, doctors can
have more (and dynamic) information about the patients, and
then take decisions timely.
The patients’ information are captured through not only one,
but a set of sensors that compose a wireless sensor network
(WSN). WSN integrates a series of spatially distributed au-
tonomous sensors into a network and cooperatively transmits
the data through some wireless communication channel [2].
Commonly, such sensors are resposible for capturing patients’
data and route them through the wireless communication
channel to a gateway that is responsible for processing that
data. Subsequently, the gateway can possibly route the data to
several distributed servers, local servers (edge computing) or
cloud computing [3]. Edge computing is a distributed archi-
tecture that presents decentralized processing power, enabling
mobile computing and IoT technologies. In edge computing,
the data is processed by devices near the end user (in comput-
ers or local servers) instead of being transmitted to the cloud
[5], [6]. This approach is quite attractive considering smart
hospitals since we are dealing with sensitive information and
delays may result, in the worst case, in deaths.
The WSN is responsible for monitoring patients’ vital data
and notifying physicians in cases of emergency. Therefore,
these networks should be designed to minimize downtimes
(failures) and high latency since, if it happens, it can compro-
mise the health treatment of a patient.
However, it is important to evaluate the performance of
computing architectures applied into smart hospitals even
before implementing it in a real infrastructure. In this work, we
decided to apply an analytical modelling approach to represent
and evaluate the performance of smart hospitals; and for that
we use Stochastic Petri Nets (SPNs) [7], [8], [9], [10]. SPNs
are analytical models that can represent complex systems with
diverse characteristics, including parallelism and concurrency.
SPNs have probabilistic fundamentals and allow us to estimate
systems’ performance .
This paper proposes to evaluate, through a SPN model, the
usage of resources and the mean response time (MRT) of a
given architecture for smart hospitals. In summary, the main
contributions of this paper are:
1) A SPN model to represent a smart hospital, including a
local terminal for monitoring the patients, data storage
in two different places: local data center and cloud.
2) A flexible model having multiple parameters, allowing
the evaluation of a large number of different scenarios.
3) Case studies using the proposed SPN model that serve
as guides for system administrators to plan their specific
hospital infrastructures.
978-1-7281-3955-5/19/$31.00 c
2019 IEEE
The rest of the paper is structured as follows: in Section II
are detailed some related works; in Section III, the SPN model
and its respective case studies are presented; Finally, Section
IV presents the conclusion and future work.
II. RE LATE D WOR K
IoT in healhcare context is a common topic in research
field nowadays. Sigwele et al. [15] proposes a conceptual
semantic based healthcare collaboration framework based on
IoT infrastructure that is able to offer a secure cross system
information and knowledge exchange between different health-
care systems seamlessly that is readable by both machines and
humans. In the proposed framework, an intelligent semantic
gateway is introduced where a web application with restful
Application Programming Interface (API) is used to expose the
healthcare information of each system for collaboration. Tata
et al. [11] identify how the IoT application development lifecy-
cle is different compared to the one of traditional applications.
They show how IoT application architectures are evolving and
what the challenges of distributed IoT application architecture
are. Tata et al. [11] focus on modeling and deployment of
IoT applications and various techniques which can be used
to address the challenges. Akmandor et al. [14] analyzed
smart health-care systems that monitor health indications of
the user and provide feedback when needed. They categorized
such systems based on their objectives and described possible
applications under each category. Moreover, they defined the
design challenges on the edge side, explained expected trends
for these challenges, and described some methods to address
them.
Some papers consider resource utilization as parameter.
Oueida et al. [12] propose a resource preservation net (RPN)
framework using Petri net, integrated with custom cloud
and edge computing suitable for ED systems. The proposed
framework is designed to model non-consumable resources
and is theoretically described and validated. RPN is applicable
to a real-life scenario where key performance indicators such
as patient length of stay (LoS), resource utilization rate and
average patient waiting time are modeled and optimized.
[16] propose a technological and architectural solution, based
on Open Source big data technologies to perform real-time
analysis of wearable sensor data streams. The proposed archi-
tecture is composed of four distinct layers: a sensing layer,
a pre-processing layer (Raspberry Pi), a cluster processing
layer (Kafka’s broker and Flink’s mini-cluster) and a persis-
tence layer (Cassandra database). A performance evaluation
of each layer has been carried out by considering CPU and
memory usage for accomplishing a simple anomaly detection
task using the REALDISP dataset. Chen et al. [13] pro-
pose the Edge-CognitiveComputing-based (ECC-based) smart-
healthcare system. This system is able to monitor and analyze
the physical health of users using cognitive computing. It
also adjusts the computing resource allocation of the whole
edge computing network comprehensively according to the
health-risk grade of each user. The experiments show that the
ECC-based healthcare system provides a better user experience
and optimizes the computing resources reasonably, as well as
significantly improving in the survival rates of patients in a
sudden emergency.
The closest related papers to this work address edge com-
puting in smart hospitals. Rahmani et al. [2] exploit the
strategic position of such gateways to offer several higher-level
services such as local storage, real-time local data processing,
embedded data mining, etc., proposing thus a Smart e-Health
Gateway. By taking responsibility for handling some burdens
of the sensor network and a remote healthcare center, a Smart
e-Health Gateway can cope with many challenges in ubiqui-
tous healthcare systems such as energy efficiency, scalability,
and reliability issues. They proposed a proof-of-concept design
that demonstrates an IoT-based health monitoring system with
enhanced overall system energy efficiency, performance, inter-
operability, security, and reliability. Zhang et al. [4] propose
an architecture to connect intelligent things in smart hospitals
based on NB-IoT, and introduce edge computing to deal with
the requirement of latency in medical process. Zhang et al.
have developed an infusion monitoring system to monitor the
real-time drop rate and the volume of remaining drug during
the intravenous infusion. Also, they discuss the challenges and
future directions for building a smart hospital by connecting
intelligent things. Rahmaniet al. [3] exploit the strategic posi-
tion of gateways at the edge of the network to offer several
higher-level services such as local storage, real-time local data
processing, embedded data mining, etc., presenting thus a
Smart e-Health Gateway. Rahmaniet al. then propose to exploit
the concept of Fog Computing in Healthcare IoT systems by
forming a Geo-distributed intermediary layer of intelligence
between sensor nodes and Cloud. By taking responsibility for
handling some burdens of the sensor network and a remote
TABLE I
REL ATED WOR K COMPARISON
Related Work Utilization Parameter MRT Stochastic Petri Nets Users Number Parameter Performance Evaluation
[2] No No No No Yes
[11] No No No No No
[12] Yes No No Yes Yes
[13] Yes No No Yes Yes
[4] No No No No Yes
[3] No No No No Yes
[14] No No No No No
[15] No No No No No
[16] Yes No No No Yes
This work Yes Yes Yes Yes Yes
healthcare center, their Fog-assisted system architecture can
cope with many challenges in ubiquitous healthcare systems
such as mobility, energy efficiency, scalability, and reliability
issues.
Differently from our paper, the studies do not explore the
calculation of mean response time (MRT). Some studies also
do not present performance evaluation that in the context of
smart hospitals is of crucial importance. Table I summarizes
the differences of such papers with the present work.
III. ARCHITECTURE,MODEL AND CASE STUDY
This section presents the architecture and the respective
SPN model that present an smart hospital. In the following
subsections are presented the architecture with respective
model, performance metrics and numerical analysis as a way
of exemplifying the applicability of the proposal.
A. Architecture and Model
Figure 1 presents an architecture of an IoT-based health
monitoring system that can be used in smart hospitals. In these
systems, patient health information is collected by sensors
colated at the patients’ body. These health data can also be
complemented with context information such as date, time,
location, temperature, etc. Knowing the context allows us to
identify unusual patterns and make more accurate inferences
about the situation. Other sensors and actuators (medical
equipment) may also be connected to systems for transmitting
data to medical personnel, such as high resolution images such
as CT scans.
Local Data Center
Local Medical
Supervisors or other
Caregivers
Room 3
Gateway
Room 1
Room 2
Sensor
Switch
Remote Data Center
Internet
Fig. 1. Architecture of a Smart Hospital
This architecture consists of a WSN (Wireless Sensor Net-
work), a gateway and a supervisor server, in which doctors
and nurses (supervisors) can monitor patients in real-time.
The WSN is responsible for detecting and collecting the
biomedical and context signals that are captured from the body
and the environment. These data will be used for treatment
and diagnosis of patients. The data is then transmitted to the
gateway through wireless communication protocols, such as
Bluetooth, Wi-Fi or IEEE 802.15.4. The gateway supports
different communication protocols and acts as a point of
contact between the sensor network and the supervisor server.
The gateway receives data from different sub-nets, performs
protocol translation, and provides other top-level services, such
as data aggregation, filtering, and so on. The supervisor server
is composed of processing nodes; such nodes, depending on
demand, can be virtualized (containers) or physical machines
with redundancy.
The Figure 2 represents an SPN model for the presented
architecture with the following functions: (i) Admission that
deals with the data arrival; (ii) Gateway that forwards the data
to the supervisor server; (iii) Supervisors who receive the data
to perform patient monitoring. Components are represented
by graphs, such as places (circles), timed transitions (empty
bars), and markings (small black balls). (iv) Switch is primarily
responsible for managing the route to the local server. (v)
Local Server stores patient data for future analysis and to
prevent data loss. (vi) Remote Server processes and stores the
data in cloud. The Table II describes all elements of the model.
Given the model overview, we now describe the flow of
tokens among the model components. The Admission sub-net
consists of two places P Arrival and P InputQueue, which
represent the delay between input and acceptance of this data
in the queue. Tokens generated in P Arrival represent any type
of request that involves data entry to be processed or stored.
The transition T0 represents the receipt of the request, note
that it is an immediate transition, having no associated delay.
T0 fires as soon as a token exists in P InputQueue and there is
at least one token in P GatewayCapacity. The capacity of the
gateway can be interpreted as available distribution channels,
given by the GC marking.
When T0 fires, the gateway subnet is reached. A token is
taken from P InputQueue and P GatewayCapacity. A token
is returned to P Arrival, allowing a new trigger. A token is
then added to the P GatewayInProcess location. The number
of tokens in P GatewayInProcess represents the queuing of
requests in the gateway. Queuing occurs when there is no
available capacity to serve the newly arrived request. If there
is available capacity on the supervisor server and on switch
(place P SupervisorsCapacity an P SwitchCapacity), the TD
transition is triggered to both simultaneously, and the request
then moves on to be processed. TD represents the delay for
the gateway to send a request to the supervisor server and for
switch.
If there is a resource available on the supervisor server,
P SupervisorsInProcess will contain the number of requests
in the queue for processing. The time that requests remain
processing on a node depends on the MD transition. Such
transitions have the infinite server semantics, so each request
is processed independently. It is important to note that the
processing time depends greatly on the computational capacity
of the supervisory server nodes. Thus, the MD transition must
be configured with a processing time for a single job on a
specific resource type.
After GD has triggered, the request follows on both sides,
the local server and the remote server simultaneously.
Next, then it is necessary to wait for the arrival time of
the data on the local server, this time is represented by the
CD transition. After the request arrives, it goes ahead to be
processed.
The time that requests remain processing on the local server
depends on the LD transition. LD represents the service time
Local Server
Remote Server
Fig. 2. SPN Model for Smart Hospitals
of the local server. Such a transition has the infinite server
semantics, so each request is processed independently if there
is a resource available in P LocalServerCapacity. Again, it is
important to note that the processing time depends greatly on
the computational capacity of the node (VM or container for
example) as well as the database used to store the data. Thus,
the LD transition must be configured with a processing time
for a single job on a specific resource type.
If there is no resource available on the remote server
(P RemoteServerCapacity), there will be queuing in place
P SendRemote. If so, there is a time associated with sending
request to the remote server (transition SD) and a service time
on the remote server (transition RD). These transitions are
also infinite server semantics, so each request is processed
independently.
The time between arrivals is assigned to the transition
AD. We consider that times between shots are exponentially
distributed, this assumption can be modified by changing this
distribution. The transition AD takes into account only the time
the requests entered the system, that is, the network losses are
not taken into account.
The proposed model allows to evaluate several scenarios
since the evaluator can configure up to 13 parameters (8
transitions and 5 markings) as can be seen in the Table II. Any
change in one of these parameters can significantly impact the
mean response time of the system and consequently the cost
of infrastructure. The variation of the scenarios considering a
significant number of factors is what makes this model the
main contributions of this work.
B. Metrics
This section defines metrics to evaluate the architecture of
a smart hospital based on the proposed model. In this work
we calculate four metrics: mean response time (MRT), dis-
card probability (Discard Probability), number of discarded
requests against time (Discard Number) and probability of
resource utilization (Utilization<ServerName>).
The MRT can be obtained from the Little’s Law [17]
that relates the average number of requests in progress in a
system (RequestsInProcess), the arrival rate of new requests
(ArrivalRate) and the MRT. The arrival rate is the inverse of
the arrival delay: ArrivalRate =1
AD . Little’s Law requires
a stable system, meaning that arrival rate is lower than the
service time. The MRT is obtained by the Equation 1.
MRT =RequestsInP r ocess ×AD (1)
Therefore, it is also possible to calculate MRT by the
equation:
MRT =RequestsInP r ocess
ArrivalRate (2)
The Equation 3 define RequestsI nP rocess. To calculate
the number of requests in progress in the system, you must
sum the number of tokens in each of the places that represent
a request in progress. In Equation 3, Esp(P lace)represents
the statistical expected value of tokens in “ Place ”, where
Esp(Lugar) = (Pn
i=1 P(m(Lugar) = i)×i). In other
words, Esp(P lace indicates how many tokens occupy that
Place.
RequestsInProcess =Esp(P GatewayInP r ocess)+
Esp(P Supervisor sInP rocess)(3)
Equation 4 defines the probability of discarding (Dis-
card Probability). To calculate the disposal, there must be
a token in the input queue (P ArrivalQueue) and there are
no more resources available in the gateway. P(Place = n)
computes the probability of n nodes in “Place”.
Discard Probability = (P((P InputQueue = 1)∧
(P GatewayCapacity = 0))) ×100 (4)
Equation 5 defines the number of requests discarded in a
given period of time T. To get the discarding number in the T
period, simply multiply the discard probability by ArrivalRate
and the time T.
Discard Number =Discard P robability ×Arriv alRate ×T(5)
Finally, we also calculate the probability of resource utiliza-
tion, where the equation is given by the number of tokens of
TABLE II
DESCRIPTION OF MODEL
Type Element Description Server Semantics
Places P Arrival Wait for new requests X
P InputQueue Wait for queue availability X
P GatewayInProcess Requests at the gateway queue X
P GatewayCapacity Gateway capacity X
P SupervisorsInProcess Requests are at the supervisor server queue X
P SupervisorsCapacity Supervisor server capacity X
P SwitchInProcess Requests on the switch queue X
P SwitchCapacity Switch capacity X
P LocalServerInProcess Requests on the local server queue X
P LocalServerCapacity Local server capacity X
P RemoteServerInProcess Requests at the remote server queue X
P RemoteServerCapacity Remote server capacity X
Timed Transitions AD Arrival delay between arrivals Single Server
TD Delay to the gateway send requests to supervisor and switch Infinite Server
GD Delay to switch send requests to the local server Infinite Server
CD Delay to requests arrive at the local server Infinite Server
LD Delay to local server process the requests Infinite Server
MD Time to process the request at the supervisor server Infinite Server
SD Delay to requests arrive to remote server Infinite Server
RD Delay for remote server process one request Infinite Server
Place Markings GC Maximum capacity of the gateway input queue X
SC Maximum capacity of the supervisor server X
SW Maximum queue capacity of switch X
LC Maximum queue capacity of local server X
RC Remote server capacity X
the place corresponding to the moment of execution divided
by the total capacity of those resources. We do this for each
resource component of the model. Note that the capacity in
question is given by the marking of the place corresponding
to that resource.
The gateway utilization equation is given by:
UtilizationGateway =Esp(P GatewayI nP rocess)
GC
×100 (6)
The equation for supervisor server utilization is given by:
UtilizationSupervisors =Esp(P Supervisor sInP rocess)
SC
×100 (7)
The equation for switch utilization is given by:
UtilizationSwitch =Esp(P SwitchI nP rocess)
SW
×100 (8)
The equation for local server utilization is given by:
UtilizationLocalServer =Esp(P LocalServer InP rocess)
LC
×100 (9)
The equation for remote server utilization is given by:
UtilizationRemoteServer =Esp(P RemoteServer InP rocess)
RC
×100 (10)
C. Numerical Analysis
This section presents eight numerical analyzes of the model.
The table III displays the values assigned to the timed transi-
tions and SPN model markings. We again vary the value of the
transition corresponding to the arrival delay (AD) from 1.0ms
to 10.0ms with increments of 0.5ms. The other parameters
remained fixed. All the results of the analysis with the model
are presented in the graphs of Figures 3(a), 3(b), 3(c), 3(d)
and 3(e).
TABLE III
ASSIGNED VALUES FOR TRANSITIONS AND MARKINGS OF THE SPN
MODEL
Type Element Values
Timed Transitions AD [1,0-10,0] (Increment of 0.5)
TD 3.5
MD 20.3
GD 2.5
CD 1.0
LD 20.3
SD 4.0
RD 20.3
Marcac¸ ˜
oes GC 8
SC 8
SW 8
LC 16
RC 16
1) Mean Response Time (MRT): Figure 3(a) displays the
results for MRT. The MRT increases until AD = 3.0ms, with
MRT = 140ms, after that it decreases. There is a slight increase
in AD = 4.0ms, then it starts to decay steadily. Figure 3(d)
shows the gateway utilization, where can be noticed requests
queuing with 85% of utilization in AD = 3.0ms.
2) Discard Probability: The figure 3(b) presents the discard
probability of requests. At the most critical point (1.0ms) the
probability is around 75%. It is possible to note that this
probability decreases as the AD increases (between 1.0ms
and 5.5ms), until it stagnates to zero when the AD reaches
6.0ms. Considering the knee (AD = 3.0ms) the probability of
dropping requests is less than 40%.
3) Discard Number: The Figure 3(c) displays the number
of discards in a certain period of time T. The period T
considered in this text was 10.0ms. As the AD increases, the
number of discarded data decreases. From 6.5ms it is possible
to observe that the number of discards reaches zero. At the
most critical point (AD = 1.0), the number of discards is
approximately 760 requisitions. For such a scenario, there will
Medium Response Time (ms)
40
60
80
100
120
140
160
Arrival Delay [AD] (ms)
1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7 7,5 8 8, 5 9 9,5 10
2
MRT
(a) Mean response time
Probability of Discard (%)
−20
0
20
40
60
80
Arrival Delay [AD] (ms)
1 1,5 2 2,5 3 3, 5 4 4,5 5 5,5 6 6,5 7 7,5 8 8, 5 9 9,5 10
2
MRT
Discard
(b) Discard probability
Discard Number
0
100
200
300
400
500
600
700
800
Arrival Delay [AD] (ms)
1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7 7,5 8 8, 5 9 9,5 10
2
DiscardNumber
(c) Discard number
Utilization (%)
0
20
40
60
80
100
120
Arrival Delay [AD] (ms)
1 1,5 2 2,5 3 3, 5 4 4,5 5 5,5 6 6,5 7 7,5 8 8,5 9 9,5 10
Gateway
Switch
(d) Gateway ans switch
utilization
Utilization (%)
10
20
30
40
50
60
70
Arrival Delay [AD] (ms)
1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7 7,5 8 8,5 9 9,5 10
2
3
4
Supervisors
LocalServer
RemoteServer
(e) Utilization of super-
visor, local and remote
servers
Fig. 3. Performance evaluation results of model
be no losses if the AD exceeds 6.0ms. In the MRT knee (AD
= 3.0ms), we have approximately 100 missed requests.
4) Utilization: Figure 3(d) shows the utilization level of
the gateway and the switch. For AD = 1.0ms, the gateway
utilization reaches 100%. With AD values above 1.5ms, the
value drops continuously, reaching values less than 10% when
the AD reaches approximately 10.0ms. As explained earlier,
the switch has a lower percentage of utilization, since the
bottleneck at the gateway does not allow requests to arrive at
the same frequency on the switch. In the time interval 7.5ms to
10.0ms, the gateway and the switch have the same utilization
level.
Figure 3(e) shows the utilization level of the supervisor
server, the local server and the remote server. The supervisor
with AD = 1.0ms has an utilization of approximately 62%,
with some variations until its downswing after the AD reaches
3.5ms. For AD = 10.0ms its utilization reaches approximately
36%. Both the local server and the supervisor have similar
behaviors. Such machines start at utilization of 31% and for
AD = 10.0ms their utilization reaches approximately 3%. The
capacity of the local server (16 cores) and the remote server
(16 cores) is greater than the capacity of the supervisor server
(8 cores).
IV. CONCLUSION
This paper adopted an analytical model to evaluate the
performance of smart hospital systems without having to
invest in real equipment beforehand. Using SPNs, we have
represented and evaluated intelligent hospital architectures.
The model is very parametric and it is possible to calibrate
resource capacity and service times. Our model allows the
configuration of 13 parameters, making possible to evaluate
a large number of different scenarios. Analysis has shown
that arrival rate is an important parameter in the system.
In different scenarios, it was possible to observe the close
relationship between MRT, utilization and disposal, especially
for high arrival rates. Therefore, this work can help system
administrators to identify the most appropriate equipment in
terms of cost and efficiency.
As future work, we intend to perform more numerical
analysis, evaluating different applications. We also want to
assess financial costs and availability.
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