Message Queuing Model for a Healthcare Hybrid Cloud Computing Platform

Abstract

This paper sets forth a cloud platform for implementing a completely integrated system for healthcare that fulfils identified field specific requirements. To achieve a high level of performance at a low cost, the paper presents an analytical model for cloud computing scheduling. The proposed model takes into consideration classification based on message priority, separation of classification and processing from the message output servers, and random load of the incoming requests. Performance is measured in terms of the number of requests, waiting time, response time, and requests drop rate for each priority class defined. Experimental results indicate that proposed model is able to support a great number of arrival requests providing short response time related to priority classes.

Full text

1. Introduction
Information technology and management
systems dedicated to healthcare services require
a high level of quality, safety, cost
effectiveness and access. Medical data should
be available to internal organizations and
authorized third parties, at any time, at low
cost, at high quality and via secure channels.
Cloud computing paradigm is defined as a set
of network enabled services providing scalable,
on demand resources [7]. Moving data to the
cloud enables data consolidation, aggregation
and reduces financial expense through
minimised redundancy and cheaper
operation costs.
There are four types of cloud models: public,
private, community and hybrid. Private cloud
infrastructure is provisioned for exclusive use
of a single organization. Public infrastructure is
provisioned for open use of general public.
Community cloud infrastructure is provisioned
for exclusive use of specific community
consumers from organizations that have shared
concerns. Hybrid cloud infrastructure is a
composition of two or more distinct
deployment models.
In the healthcare domain, the chosen approach
must combine the secured access of individual
organisations with the availability needed for
public information. This can be achieved by
developing a hybrid cloud application that
allows a company to use public IT resources
while keeping sensitive information private. In
such applications, lack of compatibility might
limit the platform functionality.
DICOM (Digital Imaging and
Communications in Medicine) andHL7
(Health Level 7) standards provide
specifications on how to implement
communication and exchange of data
between medical software in order to
eliminate or reduce incompatibility among
different applications.
Cloud infrastructure provides access to a large
pool of virtualized resources (servers, storage,
applications, services, etc.) available for
dynamic usage by all customers. Sharing takes
place per a customized service level agreement
(SLA) between customers and provider. SLA
management consists of two phases:
negotiation and monitoring Quality of Service
(QoS) for provided infrastructure. Defined QoS
performance parameters for cloud platforms
are: time spent, waiting time and mean number
of tasks in the system, rejection probability and
total response time of service [12]. SLA QoS
parameters can be determined using queuing
theory [10] and can be used to improve the
performance and reduce delays in the
transmission of information.
This paper provides a quantitative method for
modelling message processing considering
three connected queuing systems: a scheduling
queue, a primary queue and a secondary queue.
The method was designed for a hybrid cloud in
the healthcare domain, but can be applied to
any cloud model. The paper continues the work
presented in [7] where the authors provided a
detailed architecture for such a system,
Message Queuing Model for a Healthcare Hybrid
Cloud Computing Platform
Roxana
MARCU, Iulian DANILA, Dan POPESCU, Oana CHENARU, Loretta ICHIM
University Politehnica Bucharest, Splaiul Independentei no.313, Buchar
est, 060042, Bucharest, Romania.
roxana.marcu@cti.pub.ro; iulian.danila@gmail.com;
dan_popescu_2002@yahoo.com
Abstract: This paper sets forth a cloud platform for implementing a completely integrated system for healthcare that fulfils
identified field specific requirements.
To achieve a high level of performance at a low cost, the paper presents an analyt
ical
model
for cloud computing scheduling
. The proposed model takes into consideration classification based on message
priority, separation of classification and processing from the message output servers, and random load of the incoming
requests.
Performance is measured in terms of the
number of requests, waiting time, response time, and requests drop rate
for each priority class defined. Experimental results indicate that proposed model is able to support
a great
number of
arrival requests providing shor
t response time related to priority classes.
Keywords:
Cloud computing, queuing model, performance analysis.
Studies in Informatics and Control, Vol. 26 No. 1, March 2017 http://www.sic.ici.ro 95

comprising of two queues, and evaluated the
resources needed for such an application.
This paper is organized as follows. Section 2
describes general background of the
research domain and related work. Section 3
presents the preliminaries for computing mean
performance measures of the cloud platform. In
section 4 experimental results are presented and
section 5 concludes the paper with a summary
of achievements.
2. Background and related work
The benefits of adopting hybrid cloud
technologies in the healthcare domain have
been analysed in several papers [7][2][4]. They
combine public cloud benefits like high
accessibility, easy maintenance and scalability
with private cloud advantages, more focused on
data privacy and controllability. In healthcare,
such cloud models can be considered as a
solution for complex data mining algorithms.
Related work in this domain analysed different
methods for evaluating cloud systems
performance: different queuing models, Petri
nets, stochastic analysis or genetic algorithms
[6]. In [88] authors use load balancing and two
schedule entities to determine the resource that
will process the request globally and to define
the order in which requests are processed.
Results indicate that proposed model provides
significant improved performance compared to
M/M/1 and M/M/S models. Several papers
evaluate performance of different queuing
models in particular resource configurations. In
[5] authors provide a data centred model based
on a M/M/m queuing system that showed
improved message processing speed compared
to classic method of short service time first-in
first-out (FIFO). In [2] a priority M/M/C/C
queue framework is proposed to support cloud
provider service level agreement (SLA) in
terms of data centre dimensions, needed
resource capacity needed and number of
supported requests. In [10] authors propose a
dynamic scheduling algorithm to be used in
priority queue systems that showed improved
throughput, low drop rate and high access to
resources considering different class priority
levels. In [9] resource allocation problem is
studied and the authors provided a network of
M/M/1 queues service scheme to minimize
resource cost and service response time for
cloud providers. In [4] authors presented an
algorithm for simulation of waiting systems. In
all these papers queuing algorithms are
presented as a tool for analysing and predicting
client-server application behaviour and support
decision making for resource.
Related work mainly addresses general queuing
models that mainly address a single aspect of
the request processing. This paper extends the
research in cloud queuing theory by designing a
new model that is better suited to the needs of
healthcare applications. The proposed model
takes into consideration classification based on
message priority, separation of classification
and processing from the message output
servers, and random load of the incoming
requests. This is accomplished by extending the
priority-based model presented in [11].
3. Preliminaries and notations
Queuing theory provides an abstract
representation of mathematical systems. It is
able to isolate factors that affect system
stability to be able to measure system
performance: server utilization, waiting time,
number of requests in the system, probability to
exceed buffer of the waiting queue, response
time [3].
Figure 1. Healthcare hybrid cloud architecture [7]
A queue can be represented as
DNKcSA /////
,
where A is the arrival process, S is service time
distribution defined as exponential service
time, c is the number of servers, K is capacity
of queue, N represents the size of population
(jobs) to be served, and D defines the queue
discipline. K and N are considered infinite in
case they are not specified. By default, D is
FIFO.
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96

Queuing theory focuses mainly on steady state
condition. It is defined as the state in which the
system becomes essentially independent of the
initial state and elapsed time. A system in
steady state condition is characterized by the
following parameters [8]:
- use ratio
ρ
,defined in (3.1), must fulfil the
steady state condition
1<
ρ
. Therefore
λ
,
arrival
rate (requests per unit of time), must be strictly
less than service rate µ. For
1≥
ρ
queue grows
without bound;
µ
λ
ρ
=
,
1<
ρ
(3.1)
- probability of exact k number of requests in
system,
)
(kP
;
- expected queue length (excluding number of
processed requests) for c number of resources
available in the system;
∑
∞
=
−=
c
k
kPckQE )()()(
(3.2)
- expected number of customers in the system;
∑
∞
=
=
0
)()(
k
kkPNE
(3.3)
- expected waiting time in the queue (excluding
service time) for each request;
∑
∞
=
=
0
)(
)(
)(
k
k
Q
kp
QE
WE
λ
(3.4)
-total waiting time (including service time) for
each request, assuming that mean service time
µ
1
is constant.
µ
1
)()( +=
Q
WEWE
(3.5)
Let N denote the number of requests in the
system and T request response time, Little’s
law gives the relation between mean number
of requests in the system, mean response time
in the system and average arrival rate of the
requests [8]:
)()( TENE
λ
=
(3.6)
4. Analytical Hybrid Cloud
Queuing Model
Mathematical analysis can measure the system
performance in terms of queue length, response
time including average waiting time, mean queue
size, delay and resource utilization. It can
demonstrate effect of priority classes on overall
system performance and it can determine the
number of resources needed, as function of arrival
rates.
We define of arrival requests process in the
proposed healthcare cloud application as follows:
- all user requests are gathered in a service centre as
single point of access for all users. Arrival time
between two client requests is independent of each
other and is considered to follow a Poisson
distribution:
LMH
λλλλ
++=
, where
λ
i is
the arrival rate of a High, Medium or, respectively, a
Low priority request;
- client requests will be processed by the service in a
first come first serve (FCFS) order. Client requests
will receive response after they are processed
with a response time that must be lower than
the agreed service level agreement response
time;
- service response time is defined as
RESWsubsrt TTTTTT ++++=
, where
sub
T
is
the submission time,
W
T
is the waiting time,
S
T
is the service time,
E
T
is the execution time
and
R
T
is the return time.
sub
T
and
R
T
are
considered negligible [11].
- application buffer is limited, therefore the
number of waiting requests is limited.
Secure data access for healthcare hybrid cloud
platform is to be granted using RBAC (Role
Based Access Control) model due to his
granularity. Data will be secured using DICOM
anonymization and identification services for
specific medical area data (DICOM files). In
case data is required outside private cloud it is
transferred using the same encryption rules via
DICOM anonymize/identify service, thus
protecting confidential data. Healthcare cloud
data integrity will be granted by the use of
DICOM integrity validation services (DICOM
object encoding) and digital signature.
Studies in Informatics and Control, Vol. 26 No. 1, March 2017 http://www.sic.ici.ro 97

We applied queuing theory to analyse the
platform. We considered a model of cloud
queue system composed by three queues:
M/M/1 schedule queue, M/M/k/N primary
queue and M/M/1 secondary queue. The FCFS
queue is processed by a dispatcher that
forwards the requests to a scheduler. Schedule
queue system receives a FCFS queue and
classifies each request building three input
queues for primary system. Primary server will
schedule the highest priority requests first and
place the result in three priority queues. Load
balancing can be applied at this level, by
defining several channels for the input requests.
This will increase the speed of the request
classification system. In a secondary queue
system, results are sent to the requester,
sending the highest priority requests first.
Figure 2. Analytical queue model
Observation 1: Priority class defined for a request
has the following values: high, medium and low,
which define the priority rule.
Based on Burke’s theorem and Jackson’s
theorem the system can be modelled as an open
Jackson network in which the queues can be
analyzed independently.
4.1 Requests scheduling queue model
We consider that
n
requests are received
randomly from all system users according to an
independent Poisson process. Receiving rates
are
H
λ
,
M
λ
and
L
λ
, and requests are processed
by a single server. Service times of all jobs are
exponentially distributed with the same
mean
µ
1
[11]. According to (3.1) and
Observation 1:
1<++
LMH
ρρρ
(4.1)
where
µ
λ
ρ
i
i=
occupation rate due to type
i
jobs
and each type
i
request is treated according to its
high, medium or low priority.
We modelled the system as a pre-emptive resume
priority M/M/1 queuing system, satisfying
stability condition
1<
ρ
. The mean number of
requests in the system at time t can be computed
as sum of all mean number of priority class
requests in the system:
ρ
ρ
−
=++= 1
)()()()(
LMH
NENENENE
(4.2)
Using (2.6), the mean service response time spent
in the scheduling queue at time t is:
ρ
µ
λ
−
== 1
)(
)( NE
TE
(4.3)
Mean waiting time is defined by the mean
time spent in the system (3.3) subtracting
service time:
)1(
1
)()(
ρρ
µ
µ
−
=−= TEWE
(4.4)
According to the behavior of an M/M/1 queue,
each priority class depends only on priority
classes higher than his, and has no dependence
with lower priorities. This means the mean
number of high priority requests can be
defined as:
)1(
)
(
1
)(;
1
)(
H
H
H
H
H
H
H
H
WE
TEN
E
ρρ
µ
ρ
µ
ρ
ρ
−
=
−
=
−
=
(4.5)
Using (3.2) and (3.5) mean performance
measures
M
NE )(
,
M
TE )(
and
M
WE )(
for
medium priority requests become:
)1)(1(
)(
MHH
M
M
NE
ρρρ
ρ
−−−
=
(4.6)
)1)(1(
1
)(
MHH
M
TE
ρρρµ
−−−
=
µ
1
)
()( −=
M
M
T
EWE
Mean performance measures
L
NE )
(
,
L
TE )(
and
L
WE )(
for low priority class are determined as:
)1)(1(
)1(
)(
LMHMH
MHL
L
NE
ρρρρρ
ρρρ
−−−−−
−+
=
(4.7)
)1)(1(
)1(
1
)(
LMHMH
MH
L
TE
ρρρρρ
ρρ
µ
−−−−−
−+
=
µ
1
)(
)( −= L
LTEWE
4.2. Primary system for requests
classification
Primary system is modelled as a homogeneous
KcMM ///
queuing system (equal service rate
for all servers). Three queues are used to hold
priority requests according to the predefined
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98

classes (high, medium and low). Assuming that
primary queue system has a total number of
resources
iCC
s
i
itotal
∀= ∑
=
,
1
and a finite size,
queue capacity is
total
CK −
, where K is the
current number of customers. This limitation
means that any request n that arrives at time t
has an arrival rate of
Kn
n
<∀= ,
λλ
. Any
request arrived after the maximum queue size
limit has an input rate of 0:
K
n
n≥
∀= ,
0
λ
.
Priority class rejection probability is the main
quality parameter of the primary queue system.
In order to minimize rejection probability total
resource number must be split into shared
resources
shared
C
(CS) and reserved resources
)(
MR
HRR
rezerved
CCCC +=
having
SRtotal CCC +=
.
High reserved resources
1
1
,
1
jiCC
j
i
iHR <∀= ∑
=
are
used to serve only high priority requests.
21
1
,
2
jijCC
j
i
iMR
<≤∀=
∑
=
serve high and medium
priority requests and
total
C
ji
iS CijCC
total
<<∀= ∑
+=
2
1
,
resources will process all types of requests.
The number of servers assigned for high,
medium or low priority requests must be
updated periodically according to a predefined
dynamic scheduling algorithm. Algorithm 4.1
calculates the number of reserved and shared
resources based on arrival rates, priority classes
and total number of resources allocated for
primary system. Assuming that each priority
class is indicated by a priority parameter
},,{, LMHi
i∈
β
LLMMHH
λβλβλβ
≥≥
and
0, ≠
LLMM
λβλβ
, algorithm 4.1
guarantees
0≠
shared
C
.
Algorithm 4.1 Dynamic scheduling algorithm
Input: priority class arrival rates
LMH
λλ
λ
,,
,
priority levels
LMH
βββ
,,
and total number
of resources
total
C
.
Output: Number
of servers allocated for
each priority class reserved resources
(
MRHR
CC ,
) and shared resources
S
C
,
computes as:
LLMMHH
HHtotal
HR
C
C
λβλβλβ
λβ
++
=
HRtotal
L
LM
M
MM
MR
CCk
k
C−=
+
=
1
1
;
λβ
λ
β
λβ
MRHRSCCkC −−=
Each server is able to serve any type of priority
requests. When the number of shared and
reserved resources is changed, all free
resources are assigned according to the new
defined pool. In case there are not enough free
resources, when a busy resource will finish the
current request, it will take a new request from
the pool according to the new classification
(shared or reserved).
Observation 2. High priority requests will be
accepted in the system as long as:
∑∑ +==
−=+ j
ki
Rtotal
k
i
RS CCCC
11
(4.8)
We assume all requests are queued in the
priority queues, having service rate dependent
of time t, with n number of requests being
processed. A request leaves the system in a
time
µ
k
. Service rate of the system increases
until all servers are busy,
R
C
are busy with high
and medium priority requests and
S
C
proceses
low prority requests. Analytical analysis for
primary system defines mean performance
measures using M/M/c/K state probability
equations [5] for a total number of
SRtotal CCC +=
resources and a maximum
capacity K. K will be split in priority queues
according to the number of priority classes.
System stationary probability of exact n
customers in primary queueing system
)(np
for
state
n
caracterized by arrival rate
)(i
λ
and
service time
)(i
µ
is determined based on
balance equations. Balance equations define a
stationary system when input flux is equal with
output flux in a given state
0, >nn
for arrival
rate
H
λ
and state dependent service
rate
µ
rezerved
C
.
For a total request arrival rate
λ
and
q
proportion of high priority requests, we have
λλ
q
H
=
and
λλλ
)1( q
LM
−
=+
. Arrival rate is
defined as:





≥
<≤+
<++
=
.,
,,
,,
)(
S
H
SMRMH
MR
LMH
Ck
CkC
Ck
k
λ
λλ
λλλ
λ
Studies in Informatics and Control, Vol. 26 No. 1, March 2017 http://www.sic.ici.ro 99

State transition diagram defines probability
)(n
p
of n requests in the system, using balance
equations according to birth-death process:



+++−−=+
=
)1()1()1()1()()()()(
)1()1()0()0(
npnnpnnpnnpn
pp
µλµλ
µλ
(4.9)
Solving this system of linear equation,
stationary probability
)(n
p
for state n is:
1
0
1
1
0
1
1
0
)
(
)
(
1
)
0(
);
0(
)(
)
(
)
(
−
>=
=
−=
=
=
=
−
=
=












+== ∑∏
∏
∏
∏
n
k
n
n
kn
n
k
n
n
kn
n
n
n
pp
n
n
np
µ
λ
µ
λ
(4.10)
Observation 3: Sum of all probabilities equals 1
1
0
=
∑
∞
=n
n
P
(4.11)
Stationary probability of k class priority
requests in primary queue is defined as
),( Ckp
using (4.10) and (4.11) for a number of
C
allocated resources
},,{ SMRHR CCCC ∈
.







+
≤<
≤≤
=
K
Ck
Cp
C
C
C
Ckp
k
Ck
p
k
C
C
k
C
,)
(
!
1,
!
)(
),(
0
0
µ
λ
µ
λ
(4.12)









=++
≠








++
=
∑
∑∑
=
+
+==
−
µλ
µ
λ
µλ
µ
λ
µ
λ
C
C
C
K
k
C
CC
C
k
Cp
C
C
C
k
k
C
C
KC
Ck
k
C
C
C
k
k
C
,
!!
)(
1
,
!!
)(
1
),0(
1
11
1
(4.13)
Rejection probabilities for primary system,
using final state probability of the system
)( KCp +
for each number of allocated
resources (
KCk +=
and
},,{ SMRHR CCCC ∈
)is:
),0()(
!
)( Cp
C
C
C
Cp
KC
C
C
C
+
=
µ
λ
(4.14)
Queue length is defined using (3.2) and (4.12)
for
KCkC +≤<
as:
),0()()(
!
)(
1
C
p
C
Ck
C
C
QE k
C
KC
Ck
C
µ
λ
∑
+
+=
−=
(4.15)
Mean performance measures for all priority
requests having
},,{ SMRHR CCCC ∈
resources
and arrival process
},,{
LMHC
λλλλ
∈
, according
to (3.3), (3.5) and (3.6), are defined as:
))(1()()( Kp
C
QENE
C
−+=
µ
λ
; (4.16)
µλ
CCp
QE
TE
CC
1
))(1(
)(
)( +
−
=
;
))(1(
)(
)( Cp
QE
WE
CC −
=
λ
.
4.3 Secondary system for response
transmission
Secondary queue server is modelled with a
finite capacity, with
1
−K
waiting positions,
KMM /1//
queuing system and mean
performance measures
i
NE )(
,
i
TE )(
and
i
WE )(
},,{ LMHi ∈∀
.
Similar as for primary queue, balance equations
according to birth-death process are defined as:



−−=
=
)1()1()()(
)1()1()0()0(
KpKKpK
pp
λλ
µλ
(4.17)
Stationary probability is defined by solving
system of linear equations:





>
≤






=
Kk
Kkp
kp
k
,0
),0(
)(
µ
λ
(4.18)





≠
−
−
=+
=
+
−
1;
1
1
1;)1(
)0(
1
1
ρ
ρ
ρ
ρ
K
K
p
(4.19)
Similar to (4.15), defined queue length at
steady state, independently of request priority is
1
1
1
1
)1()(
+
=
−
−








−=
∑K
k
K
k
kQE
ρ
ρ
µ
λ
,
1≠
ρ
(4.20)
Mean performance measures according to (3.3),
(3.5) and (3.6) are defined as:
µλ
ρ
ρ
ρ
ρ
1
)()(;
))(1(
)(
)(
1
)1(
1
)(
1
1
−=
−
=
−
+
−
−
=
+
+
TEWE
Kp
NE
TE
K
NE
K
K
(4.21)
Considering
LMH NENENENE )()()()( ++=
,
(4.21) and Observation 1, performance
measures high priority requests are:
µλ
λ
ρ
ρ
ρ
ρ
1
))(1(
)(
)(
))(1(
)(
)(
1
)1(
1
)(
1
1
−
−
=
−
=
−
+
−
−
=
+
+
Kp
NE
WE
Kp
NE
TE
K
NE
H
H
H
H
H
H
K
H
K
H
H
H
H
(4.22)
Medium priority requests mean performance
measures are expressed as:
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100

µλ
λ
ρρ
ρρ
ρρ
ρρ
1
))(1(
)(
)(
))(1(
)(
)(
)(
)(1
))(1(
)(1
)(
1
1
−
−
=
−
=
−
+−
++
−
+−
+
=
+
+
Kp
NE
WE
Kp
NE
TE
NE
K
NE
M
M
M
M
M
M
H
K
MH
K
MH
MH
MH
M
(4.23)
According to the queue discipline expressed in
Observation 1, low priority requests will be
processed after high and medium priority
requests with following performance measures:
µλ
λ
ρρρ
ρρρ
ρρρ
ρρρ
1
))(1(
)(
)(
))(1(
)(
)(
)()(
)(1
))(1(
)(1
)(
1
1
−
−
=
−
=
−−
++−
+++
−
++−
++
=
+
+
Kp
NE
WE
Kp
NE
TE
NENE
K
NE
L
L
L
L
L
L
MH
K
LMH
K
LMH
LMH
LMH
L
(4.24)
Rejection probability for secondary subsystem
is defined by probability
)(kp
in final state:
1
1
1
)(
+
−
−
=
K
K
Kp
ρ
ρ
ρ
(4.25)
5. Experimental results
We conducted a numerical analysis to evaluate
the performance of the proposed queuing
model. The analysis was made considering
request handling at public cloud level of the
following two aspects: level of QoS services
and number of service resources. Level of QoS
services can be guaranteed by a given number
of service resources. The number of service
resources refer to the ones that are required for
a given number of customers to ensure that
customer services can be guaranteed in terms of
percentage of response time and ensuring
reliable message delivery.
For simulation we used Matlab, considering
messages enter randomly in the system,
following a Poisson distribution. We defined a
range between [145 – 3550] input requests per
hour, having class priority distribution 30%
high priority, 50% medium priority and 20%
low priority (Figure 3).
Requests are processed by 5 servers having a
service response time
1=
µ
for schedule
and secondary resources and
5=
µ
for
primary resources.
Figure 3. Arrival rate class priority requests
distribution in requests per second
Based on theoretical analysis, this number is
considered the minimum that could be used for
this kind of architecture. Each server has a
capacity buffer that can hold 50 requests per
unit of time. Mean performance metrics
i
NE )(
,
i
TE )(
and
i
WE )(
},,{ LMHi ∈∀
are simulated
for all three systems independently and
concluded for the overall system in terms of
response time for all priority classes.
Figure 4. Mean number of requests
in schedule queue
Schedule queue average load is simulated based
on the mean number of requests in the schedule
system calculated with (4.2). Results show that
the number of high priority requests in the system
decreases once arrival rate is significantly
increased (
2743>
λ
requests/hour). Class priority
requests is respected, highest priority requests
being processed first
LMH
NENENE )()()( <<
(Figure 4).
Mean time spent in schedule queue is simulated
using (4.3). Results show negligible values for
high and medium priority requests independent
of arrival rate. Low priority requests
performance is increasing significantly for a
single server in schedule queue when arrival
rate
1585>
L
λ
requests/hour (Figure 5).
Studies in Informatics and Control, Vol. 26 No. 1, March 2017 http://www.sic.ici.ro 101

Figure 5. Mean response time in schedule queue
Results of simulating mean waiting time in
schedule system, using (4.4), show that for an
arrival rate
1585>
L
λ
requests/hour performance
for lowest priority class is bad (Figure 6).
Therefore, the resource number should be
increased.
Figure 6. Mean waiting time in schedule queue
Figures 4, 5 and 6 show that schedule queue
systems follows an exponential distribution for
all performance metrics defined in section 4:
i
NE )(
,
i
TE )(
and
i
WE )(
},,{ LMHi ∈∀
.
Highest priority requests have good
performance, independent of the arrival rate.
Lowest priority class performance decreases
significantly for an arrival rate of 1500-2000
requests/hour processed by a single server.
Primary queue system needs to process class
priority queues received from the schedule
queue and send same queues to the secondary
queue that will only transmit to the requestor.
i
NE )(
,
i
TE )(
and
i
WE )(
performance metrics
are analysed based on the dynamic resource
allocation algorithm and relationships
defined in section 4.2. With a service time
greater than schedule system and a limited
capacity of the buffers, primary system
performance metrics are analysed relative to
priority level for each class and arrival rate.
Figure 7. Mean number of requests
in primary queue
Results show that highest priority requests are
processed first keeping their number in the
system to minimum (Figure 7). Algorithm 4.1
keeps a constant mean response time for high and
medium priority request.
Figure 8. Response time in primary queue
For low priority requests response time is
increasing very slow, even for high total arrival
rate (Figure 8).
Figure 9. Mean waiting time in primary queue
Using (4.21), mean waiting time simulation show
negligible values for highest priority classes and
increases to accepted values between [0.7, 0.9]
for the low priority classes (Figure 9).
Secondary queue system receives as input three
priority queues from the primary queue system,
having a single server with limited buffer
capacity. Average occupancy is simulated based
on mean number of requests in the system (4.19)
and priority discipline as function of arrival rate
(Figure 10).
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102

Figure 10. Mean number of requests in queue
Even though priority classes are not respected
for the mean number of requests in the system,
mean response time results follows priority
discipline (Figure 11).
Figure 11. Mean waiting time in secondary queue
Figure 12 shows the result of the secondary queue
expressed for the same queue discipline and
increased number of servers. Performance is
improved significantly, keeping priority
discipline decreasing low priority waiting time
from 9s to 1s.
Figure 12. Mean waiting time in secondary
queue
Ensuring reliable message delivery is dependent
on the request drop rate. Rejection probabilities
(drop rate) for all class priority requests are
represented as function of allocated priority class
resources in queues that have limited storage
capacity: primary and secondary. Using (4.14),
Figure 13 shows drop rate for all three priority
classes. Results show that drop rate for high
priority request are negligible [
46
10−
:
20
10−
] for
Poisson arrival process defined in Figure 1.
Medium priority drop rates increases
[
45
10
−
:
17
10−
] and also negligible low priority
requests drop rate [
31
10−
:
11
10−
].
Figure 13. Drop rate for M/M/c/K queue system.
Secondary queue drop rate results are displayed
in Figure 14 using (4.23). High and medium
priority requests rejection probability is 0 or
negligible (
46
10−
). Low priority requests drop
rate is bad for
2217>
λ
requests/hour for a single
server system with limited buffer capacity.
Figure 14. Drop rate for M/M/1/K queue system.
We considered processing class i priority
requests for all three servers. Analysis of mean
service response time showed good
performance for high and medium priority,
independent of the simulated arrival rate
(between [145, 3550]). Low priority requests
performance is low for
2743>
λ
requests/hour
but is improved by increasing the number of
resources. Results showed that class priority
driven solution ensure good performance all
requests (Figure 15).
Figure 15. Queue system response time
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6. Conclusions
This paper details the implementation of a
queuing model that can be used for
performance analysis in a hybrid cloud
architecture. In order to achieve performance,
priority classes have been introduced for arrival
requests and have been considered in the
analytical model. Model was build up using
three linked queues. First one classifies
requests based on their priority (schedule
queue). The second one has a dynamic
algorithm of resource allocation based on
priority classes that concentrates the available
resources (primary queue). The third one sends
the requests received from the preceding queue
to the requestor. Numerical analysis has been
conducted for a Poisson distribution of arrival
rates analysing three main performance metrics
of the system: mean number of the requests,
mean response time and mean waiting time in
the system. Based on the obtained results we
conclude the following: critical performance state
for a queue system with 5 servers and limited
buffer capacity is given by arrival rates lower
than 70 times buffer
capacity; split of requests into different priority
classes does not affect overall system
performance for low arrival rates; dynamic
resource algorithm for primary queue is needed in
order to keep good performance for highest
priority classes independent of arrival rate,
service time and buffer capacity; low priority
classes performance can be improved by
increasing resource number in all processing
points.
While this method can be applied on either
public, private or hybrid cloud structure, the
authors proposed a hybrid cloud architecture for a
healthcare application because of the characteristics
of all involved application users. Future work will
analyse security and privacy over the data stored
in the cloud.
Acknowledgements
This work was supported by the Romanian
National Research Programme PNII, project:
Cloud Architecture for an open Library of
Complex re-Usable Logical function blocks for
Optimized Systems – CALCULOS.
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