AN OPEN JACKSON NETWORK MODEL FOR HETEROGENEOUS INFRASTRUCTURE AS A SERVICE ON CLOUD COMPUTING

International Journal of Computer Networks & Communications (IJCNC) Vol.11, No.1, January 2019
DOI: 10.5121/ijcnc.2019.11104 63
AN OPEN JACKSON NETWORK MODEL FOR
HETEROGENEOUS INFRASTRUCTURE AS A SERVICE
ON CLOUD COMPUTING
Chien Nguyen Khac1, 2
, Khiet Bui Thanh3, 4
, 4
Hung Ho Dac, 2
Son Nguyen
Hong3
Vu Pham Tran and 2
Hung Tran Cong
1
Department of Mathematics – Informatics, The People's Police University, Ho Chi Minh
City, Vietnam
2
Training and Science Technology Department, Posts and Telecoms Institute of
Technology Ho Chi Minh City, Vietnam
3
Faculty of Computer Science and Engineering, Ho Chi Minh City University of
Technology, Vietnam
4
Faculty of Technology Engineering, Thu Dau Mot University, Vietnam
ABSTRACT
Cloud computing is an environment which provides services for user demand such as software, platform,
infrastructure. Applications which are deployed on cloud computing have become more varied and
complex to adapt to increase end-user quantity and fluctuating workload. One popular characteristic of
cloud computing is the heterogeneity of network, hosts and virtual machines (VM). There were many
studies on cloud computing modeling based on queuing theory, but most studies have focused on
homogeneity characteristic. In this study, we propose a cloud computing model based on open Jackson
network for multi-tier application systems which are deployed on heterogeneous VMs of IaaS cloud
computing. The important metrics are analyzed in our experiments such as mean waiting time; mean
request quantity, the throughput of the system. Besides that, metrics in model is used to modify number VMs
allocated for applications. Result of experiments shows that open queue network provides high efficiency.
KEYWORDS
Heterogeneous Infrastructure as a Service, Cloud Computing, Open Jackson Network
1. INTRODUCTION
Cloud computing services are provided flexibly according to user demand and access via the
internet. It helpsto increase computing power and system management cost savings.[21, 25].
Cloud computing provides services to users through three basic models: infrastructure as a service
(IaaS), including infrastructure and associated middleware - which are provided in the form of
virtual machine (VM); Platform as a Service (PaaS) include APIs for developing applications on a
specific technology platform; Software as a service (SaaS) - most of which are provided as a web-
based and remote-access application. A data center that provides cloud computing services has a
heterogeneous environment because it contains multiple generations of servers with different
hardware configurations, especially the size and speed of the processor. These servers are added
to the data center gradually and are provided to replace existing (or "the old one") machines
already available [8, 15]. The heterogeneity of these server platforms will affect the performance
of the data center. The fluctuation of the work load according to the needs of customers is
frequent, and it is difficult to predict accurately in the environment of cloud computing. In
addition, applications deployed on today's cloud are evolving towards service. Accordingly, an

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application is deployed on a set of standalone services. This is different with monolithic
applications including strictly integrated modules, applications based on service-oriented
architecture that are well-suited for the infrastructure of the cloud [29].
The fluctuation of workload often occurs in the environment of cloud computing. It affects the
quality even though the architecture is scalable - the ability of dynamically resource allocating
and retrieving based on current workload requirements. As a matter of fact, Quality of Service
(QoS) is a standard of service level agreement (SLA) established between the customer and the
cloud service provider, which is one of the key issues. It is an important factor for the cloud
provider [22]. To assess QoS for cloud computing, there are many studies which use the
important system metrics such as average response time, average latency, average workload,
refuse to serve[23]. These measurements can be analyzed and modeled based on queue theory.
Applications deployed on the cloud are typically built using simple queue models such as a G/G/c
queue, where c can be changed [1]. The model is used to estimate parameters such as the
resources required for a given input job load or the average response time for the requirements.
Then, this information is transferred to the predictor, controller or to solve the optimization
problem. However, when the architecture of the application on cloud computing grows and
becomes more complex, using a single queue model becomes more difficult. Therefore, the queue
network model is used to create an application layer consisting of K application servers [24] or
consider a queue for a server [20], or just a queue for each tier [3, 27]. Most current studies are
rarely considered to the heterogeneity of cloud infrastructure services. For example, an
application deployed in multiple cloud VMs with different generations with different CPU speeds
and capabilities. Rather, studies often assume that each node operates at the same speed.
In this paper, we has been investigated and proposed a queue model of analyzing and evaluating
performance measurements in a heterogeneous environment in order to meet customer demand
for QoS. The main contributions of this paper can be summarized as follows:
- Proposed an open Jackson queue network model for multi-tier application systems which
are deployed on heterogeneous VMs of IaaS cloud computing and formulas proposed to
calculate the system performance metrics.
- The Proposed model that is evaluated through empirical simulation can be trusted.
- Based on the proposed model, we solve the auto-scaling problem for creating/removing
VMs as in [30, 14]. Specifically, optimizing the performance utilization of a system based
on a performance threshold of the VM that automatically adjusting the number of VMs is
to ensure the minimum response time of the system.
The remainder presents the relevant studies in section II. Multi-tier application on cloud
computing are presented in Section III. Part IV presents Jackson's open network model for the
cloud infrastructure service. Experimental evaluation of the model is presented in Section V.
Section VI presents the conclusions and research directions.
2. RELATED WORK
The cloud-based performance computing service model that focuses on QoS measurements is
response time, throughput and network utilization, which has been extensively studied in [19, 25-
27]. Zhang et al.[27] used a regression-based estimation to estimate the CPU demand for
customer transactions. In [25], the response time distribution of a cloud system is modeled on a
classical M/M/m open network assuming an exponential density function for time intervals and
service time To determine the optimal service level and the relationship between the maximum
the number of jobs and the minimum number of resources, namely VMs. Response time is
calculated both the waiting time in the queue and the service time.

65
In [19], Slothouber et al. studied the parameters that affect response time when web servers and
network bottlenecks. A single queue is not enough to model a complex system such as a web
server system, so the system response time can be estimated using the Jackson network model. In
[26], a cloud center was modeled as a 𝐺𝐼𝑋/𝑀/𝑆/N queue model that identifies cloud service
performance related to error recovery. Network nodes that form the cloud architecture can be
analyzed independently as they form the Jackson open network. Internal connectivity and
behavior between queues are law-defined by Burke's theorem [4] and Jackson [10, 11]. Buke
states that they can connect multiple nodes together with a queuing network and still avoid
interpreting each node in the network when the arrival time and service time are modeled in terms
of exponential density. In addition, Jackson [10, 11] focuses on the computation of total speed to
average, we have to calculate the total time coming from outside the system plus the time coming
from all the nodes inside. As a result, we can connect different processing nodes to cloud
architecture designs over time as responses such as QoS performance metrics. In [23], Based on
queue theory and the Jackson open network, a combination of M/M/1 and M/M/m queues was
presented to model the platform for QoS requirements.
Information necessary for the queue model, such as input workload (number of requests,
transactions) or service time can be obtained by online monitoring [20]. In addition, Nah et
al.[16] state that the time available for users to skip downloading a web page may have different
scenarios and contexts. This research suggests that most users are willing to wait only two
seconds for simple web-based queries. Thus, if we apply this result to cloud computing, a
decision may be needed to design the cloud with a good and predictable response time to evaluate
QoS parameters. The authors in [2] show how many VMs can share CPUs and main memory very
efficiently in cloud computing, but networks and file systems are often unclear. Therefore, the
author designing the web application architecture will consider the separation between the
processing server and the data server. In [12], authors used the 𝑀/𝐺/𝑚/𝑚 + r queue system to
evaluate a geodatabase and obtained a full probability distribution of response time, task number
in the system and other important performance measurements. Average waiting time varies
between heterogeneous services and uniform services under the same conditions in the considered
system. In [9], the authors present a M/M/m queuing system and propose an optimized model of
optimization, function and strategy to optimize the performance of services in the center of the
cloud.
Amazon EC2
Website
Amazon S3
Load Balancer
Master
DB
Slave
DB
VM – 1 VM – 2 VM – n...
EBS
Vol
EBS
Vol
EBS
Vol
EBS
Vol
EBS
Vol
EBS
Vol
Replication
Backup
(Snapshots)
Figure 1. Example of a web application with a three-tier architecture
In addition, queue theory has been used to analyze or optimize factors such as allocation of
processing capacity, load distribution, and profit control. In [5], the M/M/m queue model,

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considering factors such as the service requirements of a service and the configuration of a
multiserver system, is used to optimize the configuration. Multiserver image and maximize
profitability in the cloud. In [7], the authors present a M/M/r/k queuing system to model a server
cluster in the cloud provided with finite power to optimize returns. Another study presents a
queue model for a heterogeneous multi-core server cluster with different sizes and speeds to
optimize the allocation of processing power and load distribution in an environment.[6].
Although there have been many studies analyzing the efficiency of a cloud computing center
based on queue models, the factors include flexible cloud architecture, the heterogeneous
infrastructure of a cloud computing center is considered. Each processing node has different
speeds and different processing times. Different task roles often have different probabilities.
3. SYSTEMMODEL
3.1. Application model
An Application has an architecturein which layers are sequentially connected. For each layer,
request or processing results on the previous layeris an input of next layer for further processing
and return final results to the user.
A typical multi-level application architecture consists of three layers: front-endlayer, logic layer,
and database layer. The database layer is unable to dynamically adjust and often ignore the
automatic adjustment feature.
We consider an elastic application deployed on a group of VMs (Figure 1). VMs may have the
same or different resources assigned (eg 1GB of memory, 2 CPUs, ...), but each VM has a unique
number of formats (possibly its IP address). Requests received by the load balancer may come
from the actual end-user or from another application. We will assume that the execution time of a
request can change between milliseconds and minutes.
Load balancers will receive all incoming requests and forward them to one of the servers in the
business process layer (logic layer). It can be done in different ways. Assume that the load
balancer has updated information about the VMs that are being used (the active VMs): it will
immediately stop sending requests to the VMs that have been removed, and it will start sending
Load jobs to new VMs added. It also assumes that each request will be assigned to a single VM,
which will run it until the completion of the task associated with it. Some load balancing policies
may be used, for example: random policy, round robin, or least connection. In case of
heterogeneous VM clusters, workload coordination must be proportional to the processing power
of the VMs.
3.2. Infrastructure model
In this section, the model of cloud infrastructure service is presented. Virtualization resources are
provided by the IaaS cloud provider as a VM. VMs differ in terms of CPU, memory, storage,
network, and availability at different rates. An application on the cloud can be deployed on a VM
cluster, where the VMs may not be synchronized. VMs are classified according to their specific
processing roles such as compute processing, memory, storage, GPU, and so on. Customers can
choose the appropriate VMs for their applications. For example, VMs that handle CPUs for web
servers and memory optimizers for high-performance database operations.
In order to ensure QoS for customers, service providers often target certain QoS objectives, such
as response time, throughput, latency, execution time, and transaction time. Quality control will
create reputable services that bring customer satisfaction and thereby increase the number of users
and revenue.

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Figure 2 depicts the IaaS cloud architecture, which includes the Input Controller, responsible for
distributing requests to the VM cluster running the application at client request. The Infrastructure
Manager is responsible for supplying resources to the VM clusters according to the needs of the
customer. The Performance Manager is responsible for decision-making on input control and
dynamic resource allocation policies, which makes virtual machine creation/destroy. In order to
implement the automatic adjustment of resources in the cloud computing system, we use the
MAPE loop to automatically adjust, to monitor, to analysis, to plan and to execute tasks. The
monitoring module, a service typically provided by cloud service providers such as Amazon
CloudWatch and Google Cloud Monitoring, continuously monitors the performance of hosted
applications. Information received from the monitoring module is used during the analysis and
planning phase to estimate future resource requirements and to plan for an appropriate resource
adjustment action. Input parameters are information on job load, QoS measurements, and
thresholds.
Each VM cluster runs an application of Load Balancer that is responsible for distributing requests
to different VMs. VM clusters may be heterogeneous, so we use weighted load balancing
strategies to distribute requests to different VMs that correspond to their capabilities. Each VM
runs a local agent that queries the current performance parameters, such as CPU and memory
load.
Figure 2. Infrastructure service system architecture
3.3. Queueing network modelfor applications
As the architecture of the applications on cloud computing is growing and becoming more
complex, we proposed a model for a cloud computing using open Jackson queue network (Figure
3).In Figure 1, the application on the cloud has multiple layers that assume different roles in the
application as well as the need to use different types of VMs at each level. Specifically, in Figure
1, each application server cluster for the end user includes a load balancer, a business processing
layer, and a database processor.In this paper, we consider Load Balancer as a VM that serves as
the coordinating role required for business process layers. The business process layer consists of
many heterogeneous VMs that can be processed in parallel and capable of processing differently
depending on the configuration of each VM. Once processed at the business processing layer, the
request can be routed through a data processor, then the processing results are passed to the user.

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λ δλ
λ1
λ2
...
λm
μ1
μ1
μm
Load Balancer
Business processing layer
Database
Figure 3: Open queue network model for applications
The load balancer receives requests coming from the end user and then processes and dispatches
the requests to the business processing VMs based on their configuration. The policy allocates
resources to request in the form of space-shared mean at a time the VM only serves a request.
Coordination of requests from load balancers to business processors VMs is calculated according
to the Round Robin load balancing policy. Depending on the weight of each VM in the business
process layer. The speed of VM service depends on the VM's processing power. In this study, we
focus on heterogeneous VMs, whereby each VM has 𝑐𝑖 processing cores, and the execution speed
of each core is s (GIPS).
Service rate of VM is calculated as follows:
𝜇𝑖 =
𝑠 ∗ 𝑐𝑖
𝑍̅ , (1)
In that, 𝑍̅ is the average number of orders of a request executed at the VM.
Table 1. Round Robin Algorithm
In the business processing layer, the VMs processed in the network may have dependency loads,
which means that the request rate for leaving the service is a function of the number of requests
currently in the VM that 𝜇𝑖(𝑘). In the database storage, the probability δ that a request from the
VM handles business access to the VM storage database. When we perform a web-based
modeling, not all requests will require access to the database server. However, notice that this
probability is often relatively high.
We consider the following assumptions, which are also used in [17, 18, 23]:(1) Requests coming
from outside of cloud computing system on a node i follow the Poisson process; (2) The service
time at each node i in the cloud system is independent and complies with the exponential

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distribution and is served according to the FCFS (First-Come First-Serve) principle; (3)
Probability when a request is completed at a node i can be passed to the node 𝑗 (𝑖 ≠ 𝑗) 𝑟𝑖𝑗 ≥ 0
independent of the system state or will leave the system and not return to the probability 𝑟𝑖0 = 1 −
∑ 𝑟𝑖𝑗
𝑁
𝑗=1 , where N is the number of network nodes in the queue network.
These properties satisfy the requirements of an open queue network Jackson [4, 10]. Thus, we can
see that the cloud computing system is an open Jackson network queue with N network nodes,
each corresponding network node is a VM.
4. MODEL OF MULTI-LAYER APPLICATIONS ON CLOUD COMPUTING
4.1. Analyze the proposed model
As mentioned above, in this section, we will model a multi-layered application cloud system that
is an open Jackson network queue consisting of N nodes, each corresponding network node is a
VM and each VM is modeled as one M/M/1 queue.
The load balancer receives requests from outside users and then processes and dispatches requests
to the business process layer VMs based on their configuration. Requires an external load
balancer of Poisson distribution with the parameter γ (number of requests per second). The
interval between times to average is 1
𝛾⁄ . We set the average resource utilization factor for each
ith
VM (symbol 𝜌𝑖) with the threshold in the range [𝛼𝑙, 𝛼ℎ], depending on the different VMs with
the service rate 𝜇𝑖. This describes the rate at which the servers at each node handled the 1
𝜇𝑖
⁄
request as the average service time.
µ2
µ3
µ1
r10
r20
r30
λ1
λ3
λ2
1
i
N
Figure 4. General open network queue
The nodes can be linked together in either serial or parallel mode. Assume the length of each
queue is infinite and the queue's serving principle is FCFS. At each node of the system is a
M/M/1 queue and the generation of HTTP requests by the user is a randomized process. Let 𝑟𝑖𝑗 be
the probability of transferring the state after the request has been processed at node i which will
move to node j. Yes, the total transfer probability in the open queue network is 1 (here: 𝑟𝑖0 is the
probability of moving out of the network from the ith
node):
𝑟𝑖0 = 1 − ∑ 𝑟𝑖𝑗, 𝑖 ∈ [1, 𝑁],
𝑁
𝑗=1,𝑗≠𝑖
(2)
Let 𝜆𝑖 be the arrival rate from the outside into the ith
queue (node) and Λ𝑖 is the sum of
the arrival rates of the ith
node queue (including both incoming and outgoing rates from
inner nodes network), we have:

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Λ 𝑖 = 𝜆𝑖 + ∑ Λ𝑗 𝑟𝑗 𝑖
𝑁
𝑗=1,𝑗≠𝑖
, 𝑖 ∈ [1, 𝑁], (3)
Thus, the average resource utilization of ith
VM is:
𝜌𝑖 =
Λ 𝑖
𝜇𝑖
, (4)
LetΛ = [Λ1, Λ2, … , Λ 𝑁] 𝑇
is the speed vector to the queues of nodes (including the incoming and
outgoing rate from the nodes in the network). Let 𝜆 = [𝜆1, 𝜆2, … , 𝜆 𝑁] 𝑇
be the incoming vector
velocity from the outside into the nodes, then the formula (3) can be rewritten as:
Λ = 𝜆 + 𝑅 𝑇
Λ, (5)
where R is the state transition matrix.
𝑅 = (
𝑟11 𝑟12 ⋯ 𝑟1𝑁
𝑟21 𝑟12 ⋯ 𝑟2𝑁
⋮ ⋮ ⋱ ⋮
𝑟 𝑁1 𝑟 𝑁1 ⋯ 𝑟 𝑁𝑁
) (6)
Since the number of requests in nodes may be different, let𝑋𝑖( 𝑡) as the random variable that
determines the number of requests in the ith
VM (𝑖 = 1,2, … , 𝑁) at time t. The state of the system
at time t is denoted by: 𝑋( 𝑡) = (𝑋1( 𝑡), 𝑋2( 𝑡), … , 𝑋 𝑁( 𝑡)). Then, in steady state, we wish to
determine their probability distribution over the long term as follows: 𝑝n1,n2,…,nN
≡
𝑃(n1,n2, … , nN) = 𝑃{𝑋1( 𝑡) = 𝑛1, 𝑋2( 𝑡) = 𝑛2, … , 𝑋 𝑁( 𝑡) = 𝑛 𝑁}. Since the VMs are independent
of each other and 𝑃(𝑛𝑖) is the boundary probability that 𝑋𝑖( 𝑡) = 𝑛𝑖. From the joint probability,
we can compute the boundary probability of a particular number of requests at one VM.
An open Jackson network is considered as a continuous time Markov chain with state vector
𝑛̅ = (n1, n2, … , nN), (7)
where n𝑖 is the number of requests that are available at VM i. We can use equilibrium equation
based on the Markov system.
In Table 1, we have 𝑛̅representing the steady state of the system; When there is a request to VM i,
the system from state 𝑛̅ to state 𝑛̅; 𝑖+
; whereas there is a request to leave VM i, the system will
move from state 𝑛̅ to state 𝑛̅; 𝑖−
; or system state from 𝑛̅ to state𝑛̅; 𝑖+
𝑗−
when a request from VM j
passes to VM i.
Table 2. States description table
This Markov chain has the probability of transmitting the notation 𝑝.;. as follows:

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𝑝 𝑛̅;𝑖+ = 𝜆𝑖
𝑝 𝑛̅;𝑖− = 𝜇𝑖 𝑟𝑖0
𝑝 𝑛̅;𝑖+ 𝑗− = 𝜇 𝑗 𝑟𝑗 𝑖
Using the principle of balancing state flow into state 𝑛̅ with flow out of state 𝑛̅, assuming ni ≥ 1
at every processes VM, we have:
∑ 𝜆𝑖
𝑁
𝑖=1
𝑝 𝑛̅;𝑖− + ∑ ∑ 𝜇𝑖 𝑟𝑖𝑗 𝑝 𝑛̅;𝑖+ 𝑗−
𝑁
𝑖=1
𝑖≠𝑗
𝑁
𝑗=1
+ ∑ 𝜇𝑖 𝑟𝑖0 𝑝 𝑛̅;𝑖+
𝑁
𝑖=1
= ∑ 𝜇𝑖(1 −
𝑁
𝑖=1
𝑟𝑖𝑖) 𝑝 𝑛̅ + ∑ 𝜆𝑖
𝑁
𝑖=1
𝑝 𝑛̅.
(8)
According to Jackson's theorem [10, 11] providing the general distribution for all VMs, the steady
state solution for (8) is:
𝑝 𝑛̅ = 𝑃{𝑋1( 𝑡) = 𝑛1, 𝑋2( 𝑡) = 𝑛2, … , 𝑋 𝑁( 𝑡) = 𝑛 𝑁}
= 𝑃( 𝑋1( 𝑡) = 𝑛1) 𝑃( 𝑋2( 𝑡) = 𝑛2) … 𝑃( 𝑋 𝑁( 𝑡) = 𝑛 𝑁)
(9)
where 𝑃( 𝑋i( 𝑡) = 𝑛i) = (1 − 𝜌𝑖)𝜌𝑖
𝑛𝑖
, 𝑤𝑖𝑡ℎ𝜌𝑖 < 1.
Thus,
𝑝 𝑛̅ = ∑(1 − 𝜌𝑖)𝜌𝑖
𝑛𝑖
𝑁
𝑖=1
The average number of requests 𝐿𝑖 at the ith
VM for the M/M/1 queue with the total arrival rate to
Λ 𝑖:
𝐿𝑖 =
𝜌𝑖
1 − 𝜌𝑖
, 𝑖 = 1,2, … , 𝑁. (10)
The total number of average requests for an entire network is calculated as follows:
𝐿 = 𝐿1 + 𝐿2 + ⋯ + 𝐿 𝑁 = ∑
𝜌𝑖
1 − 𝜌𝑖
𝑁
𝑖=1
. (11)
Average waiting time of requests in the network with Little’s Law [10, 11]:
𝑊 =
𝐿
𝛽
(12)
where 𝛽 = ∑ 𝜆𝑖
𝑁
𝑖=1 is the total arrival rate from the outside. All requests from outside must go
through the load balancer, thus β = γ. The average response time of a request in the network at
each ith
VM, (𝑖 = 1,2, … , 𝑁) is calculated by the following formula [10, 11]:
𝑊𝑖 =
𝐿𝑖
Λ 𝑖
=
1
𝜇𝑖(1 − 𝜌𝑖)
, (13)
WhereΛ 𝑖 is calculated by formula (3) and𝑊 ≠ 𝑊1 + 𝑊2 + ⋯ + 𝑊𝑁.

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4.2. An example for proposed model
Figure 5 is an example of an open Jackson queue model for a three-layered application network
with four network nodes. The node 1 is 𝑉𝑀1 represents the required load balancer coming from
the outside into γ, the business processing layer consists of two nodes: 𝑉𝑀2 and 𝑉𝑀3, the
required speed are transitioned from 𝑉𝑀1 to the corresponding transition probabilities 𝑟12 = 0.4
and 𝑟13 = 0.6. Once a request has been completed at the business process layer, it is possible to
switch to access the database store 𝑉𝑀3 with probability 𝑟34 = 𝑟24 =  = 0.3 or no (𝑟30 = 𝑟20 =
0.7). The results are then feedback to the customer. The service speed at each i th VM in
exponential distribution has the parameter 𝜇𝑖.
VM1
VM2
VM3
VM4
0.4
0.6
0.3
0.7
Figure 5. For example an open queue network model for multilevel application on the cloud computing
Then, we have the following transition matrix:
𝑅 = (
0 0.4 0.6 0
0 0 0 0.3
0 0 0 0.3
0 0 0 0
) (14)
where the probability of leaving the system at each 𝑖, 𝑖 ∈ [1,2,3,4] is: 𝑟10 = 0, 𝑟30 = 𝑟20 =
0.7, 𝑟40 = 1.
Arrival rate of load balancer is γ = 20 requests/sec.Services time of each VMs is
1
𝜇1
=
0.03 𝑠𝑒𝑐,
1
𝜇2
= 0.06 𝑠𝑒𝑐,
1
𝜇3
= 0.05 sec 𝑎𝑛𝑑
1
𝜇4
= 0.04 𝑠𝑒𝑐.
Assuming: Calculated steady state probability of state (𝑛1, 𝑛2, 𝑛3, 𝑛4) = (3, 2, 4, 1).
Step 1: compute the arrival rates for each node from the traffic equations (4). We have:
Λ1 = γ = 20; Λ2 = Λ1. r12 = 8; Λ3 = Λ1. r13 = 12; Λ2 = Λ2. r24 + Λ3. r34 = 6
Step2: Compute the state probabilities for each node
Use utilization: 𝜌𝑖 =
Λ 𝑖
𝜇𝑖
to get the service demands for each node: 𝜌1 = 0.6, 𝜌2 = 0.48, 𝜌3 =
0.6, and 𝜌4 = 0.24.
Use the equation 𝑃𝑖(𝑛i) = 𝑃( 𝑋i( 𝑡) = 𝑛i) = (1 − 𝜌𝑖)𝜌𝑖
𝑛𝑖
to compute the probability of
having𝑛irequests in each M/M/1 queue. We have: 𝑃1(3) = 0.09, 𝑃2(2) = 0.12, 𝑃3(4) =
0.05, 𝑎𝑛𝑑𝑃4(1) = 0.18.
Step3: Compute the steady state probability P(3, 2, 4,1). According to equation (9), we have
𝑃(3, 2, 4, 1) = 𝑃1(3) 𝑃2(2) 𝑃3(4) 𝑃4(1)=0.0000972.

73
Some important performance measures for this open Jackson network. Compute the mean number
of requests in each queue with 𝐿𝑖 =
𝜌𝑖
1−𝜌𝑖
, we have: 𝐿1 = 1.5, 𝐿2 = 0.92, 𝐿3 = 1.5, 𝑎𝑛𝑑𝐿4 = 0.32.
Compute the mean response time of each queue with 𝑊𝑖 =
𝐿 𝑖
Λ 𝑖
, we have: 𝑊1 = 0.075, 𝑊2 =
0.115, 𝑊3 = 0.125, 𝑎𝑛𝑑𝑊4 = 0.053.
Compute the mean overall response time following equation (12):
𝑊 =
𝐿
γ
=
1
γ
∑ 𝐿𝑖 =
4
𝑖=1
0.212 ≠ 𝑊1 + 𝑊2 + 𝑊3 + 𝑊4 = 0.368
4.3. Optimized model uses VM in clusters
In this section, we present the application of the QoS parameter used for the model to solve the
optimization problem as in [5-7]. Assume that an application deployed on the cloud architecture
is shown in Figure 6, consisting of three layers: load balancing, business processing layer, and
database layer. The majority of cloud deployments have a load balancer and database engine so in
this context, we only see the VM model for the business process layer.
Load
Balancer
VM1 VM2 VM3 ...
VMM
Database
Server
Figure 6. The architecture of the application
Specifically, based on network queue evaluation parameters, it is possible to optimize system
performance based on the performance thresholds of VMs and to have at least one VM enabled at
the business process layer. To ensure that the system is always ready to serve, we can determine
the number of VMs processed at the business layer with minimal response time.
The parameters of the problem are as follows:
- 𝜌𝑖 is the average resource utilization level of the ith
VM,
- 𝑟𝑖 is the probability that the i th VM is selected to handle incoming requests,
- 𝑊𝑖 is the average waiting time of a request in the network at a i th VM,
- 𝑧𝑖 is the binary variable that decides to turn on VM i (𝑧𝑖 = 1), in turn decides to turn off
VM on i (𝑧𝑖 = 0).

74
The objective function is defined as follows:
𝑚𝑖𝑛
{𝜌𝑖,𝑟𝑖,𝑊𝑖}
𝑓: ∑ 𝑧𝑖 𝑟𝑖
𝑁
𝑖=1
𝑊𝑖, (15)
Subject to:
(1) 𝜌𝑖 = {
0, 𝑧𝑖 = 0
𝜖[𝛼𝑙, 𝛼ℎ], 𝑧𝑖 = 1
,
(2) 𝑧𝑖 ∈ {0,1}𝑣ớ𝑖 1 ≤ 𝑖 ≤ 𝑁,
(3) ∑ 𝑟𝑖 = 1𝑁
𝑖 𝑣ớ𝑖𝑟𝑖 ∈ [0,1],
(4) ∑ 𝑧𝑖 ≥ 1𝑁
𝑖 .
In the optimization problem we have the variable 𝑧𝑖 that determines creating/removing of the VM
so this is a 0/1 Knapsack problem [28]. We use the met heuristic algorithm in particular as the
optimal PSO algorithm [13] to solve the optimal tuning (creating/removing) of the target function
f and its constraints on response time average response.
Table 3. VM Auto Scaling
5. EXPERIMENT
5.1. System setup
In this section, we conducted an experiment to evaluate performance measured in Java language
on a laptop with an Intel® Core ™ i7-7500U CPU configuration @ 2.70GHz, 8GB Ram, 1 TB
HDD. and run the Windows operating system. 10. Experimental review of the cloud infrastructure
service system consists of two VM clusters that serve requests from web service clients. Each VM
cluster has 7 VMs (IDs 1 through 7). In each cluster, there is a VM that performs the work of the
load balancer (𝑉𝑀1), 1 VM takes on the database storage (𝑉𝑀7) and the rest takes care of the
workload. Business process layer (𝑉𝑀𝑖, with i = 2,3, ..., 6). The processing power of each VM is
calculated based on GIPS. Two VM clusters have different configurations as shown in Table 3.2,
in both clusters on the load balancer and the database storage server have the same capacity. In
VMC#1 cluster, business processors have the ability to be consistent. In VMC#2 cluster the
business processors are not homogeneous.

75
Table 4. Configuration of VM clusters
5.2. Experimental results
Experiment 1 evaluates the parameters in the model, for the number of requests to 1000, 𝜆 =
{158,161,164,167,170,173,176,179,181,185, 188} the load balancer's processing rate is 𝜇 𝐿𝐵 =
𝜆
𝜌 𝐿𝐵
. The probability of passing to the business processing VM is calculated using the formula 𝑟𝑖𝑗.
After 30 experimental runs, we calculated the average waiting time 𝑊̅ , the average response time
𝑇̅. We then calculated 95% confidence intervals for empirical data and computed data from the
model.
Experiment 1 shows that when we adjust the required speed increases from 158 to 188, the
average waiting time is normal but the amplitude is not large. For the VMC#1 cluster the
machines have identical CPU configurations, while the VMC#2 cluster has a heterogeneous CPU
configuration and processing speed is greater than VMC#1 so that the average response time
VMC#2 is much smaller than VMC#1 (Figure 7b).
In Experiment 2 we use the data set of Table 2 with λ = 185, which is executed 30 times and we
calculate the average waiting time 𝑊̅ . We then calculated 95% confidence intervals for empirical
data and computed data from the model.
The results in Figure 8 show that the average response times of VM1 and VM7 are very small in
both VMC#1 and VMC#2 clusters. VM1 takes care of load balancing, fast processing time. For
VM7 taking on the task of storing the database, with probability to low δ = 0.2. The VMi (i =
2,3,..., 6) in the business process layer has an average response time in two different clusters.
Accordingly, the average response time of each machine in VMC#1 cluster is not too large. While
VMC#2 cluster tends to dwindle from VM2 to VM6, as the VM2's VM2 configuration to VM6 in
VMC cluster 2 increases, the processing time on these machines decreases dramatically.

76
Figure 7. Average waiting time of the VM cluster
Figure 8. Average waiting time of VMs
Experiment 3 is to analyse the relationship of parameters in the model. We use the two VM
clusters as shown in Table 2 at average speed𝜆 = 185, adjusting the resource utilization 𝜌𝑖of each
VM in Table 2, and then analysing the average system response time for each VM in clusters. We
adjusted the resource utilization of the VMs in the application's business layer from 0.71 to 0.79.
Experiment 4 for the evaluation of the performance max model values using VM at the business
processing from VM2 to VM6. We adjust the performance of the hosts with the distribution with
mean = 0.5 (Figure 9). Follow the formula (14), we use the metaheuristic algorithm for the best
fighter algorithm for PSO to resolve to find the best VM (enable/disable) history of 𝑓 and find
force it about the average response time. Figure 9 shows𝜌 ∈ (0,1) of the VM in the logical level
of an application with sample get template t = 50. Confused the selected VM processing with
same. Then, we got at the time of the way of the different VM account.

77
Table 5. 95% confidence interval of average waiting time of each VM in each cluster
Figure 9. Average expected time of VM
Figure 11 shows the decision to enable/disable the VM based on the resource usage of each VM
at each specific time point. For example, at t = 4 use level VM#2,4,5,6 low VM#3 high algorithm
decided to turn off the VM#2,4,5,6 and turn on VM#3.
6. CONCLUSIONS
Ensuring QoS in the cloud is an important issue. Accordingly, the performance analysis of
heterogeneous datacenter is an important aspect for both cloud service providers and cloud
service customers. Based on the complexity and heterogeneity of the deployment application on
cloud computing, we propose a model of a closed-loop opportunity-based cloud computing
system that evaluates the performance of a cloud-based system through measures such as average
latency, average resource utilization factor of VMs, problem of adjusting VMs in a cluster when
there is load variation in workload to implement automatic adjustment mechanism in cluster.

78
Figure 10. ρ usage level of the VM
Figure 11. Adjust VM on/off over time
The results of the evaluation of the proposed model have shown its optimization. Through
empirical simulation, the average waiting time, the average resource utilization coefficient 𝜌𝑖 and
the problem of adjusting the VMs in each cluster show up the effect of the non-uniformity. Most
of the performance is great. In the future, we use this model in proposing an automatic adjustment
mechanism in the cloud computing system.
REFERENCES
[1]. Ali-Eldin, Ahmed, Tordsson, Johan, and Elmroth, Erik (2012), An adaptive hybrid elasticity
controller for cloud infrastructures, Network Operations and Management Symposium (NOMS), 2012
IEEE, IEEE, pp. 204-212.
[2]. Armbrust, Michael, et al. (2010), "A view of cloud computing", Communications of the ACM. 53(4),
pp. 50-58.
[3]. Bai, Wei-Hua, et al. (2015), "Performance analysis of heterogeneous data centers in cloud computing
using a complex queuing model", Mathematical Problems in Engineering. 2015.
[4]. Burke, Paul J (1956), "The output of a queuing system", Operations research. 4(6), pp. 699-704.
[5]. Cao, Junwei, et al. (2013), "Optimal multiserver configuration for profit maximization in cloud
computing", ieee transactions on parallel and distributed systems. 24(6), pp. 1087-1096.
[6]. Cao, Junwei, Li, Keqin, and Stojmenovic, Ivan (2014), "Optimal power allocation and load
distribution for multiple heterogeneous multicore server processors across clouds and data centers",
IEEE Transactions on Computers. 63(1), pp. 45-58.

79
[7]. Chiang, Yi-Ju and Ouyang, Yen-Chieh (2014), "Profit optimization in SLA-aware cloud services with
a finite capacity queuing model", Mathematical Problems in Engineering. 2014.
[8]. Delimitrou, Christina and Kozyrakis, Christos (2013), Paragon: QoS-aware scheduling for
heterogeneous datacenters, ACM SIGPLAN Notices, ACM, pp. 77-88.
[9]. Guo, Lizheng, et al. (2014), "Dynamic performance optimization for cloud computing using m/m/m
queueing system", Journal of applied mathematics. 2014.
[10]. Jackson, James R (1957), "Networks of waiting lines", Operations research. 5(4), pp. 518-521.
[11]. Jackson, James R (1963), "Jobshop-Like Queueing Systems. Mgmt. Sci. 10, 131-142",
Jackson13110Mgmt. Sci.
[12]. Khazaei, Hamzeh, Misic, Jelena, and Misic, Vojislav B (2012), "Performance analysis of cloud
computing centers using m/g/m/m+ r queuing systems", IEEE Transactions on parallel and distributed
systems. 23(5), pp. 936-943.
[13]. Liang, Yanbing, et al. (2010), Optimizing particle swarm optimization to solve knapsack problem,
International Conference on Information Computing and Applications, Springer, pp. 437-443.
[14]. Mao, Ming, Li, Jie, and Humphrey, Marty (2010), Cloud auto-scaling with deadline and budget
constraints, Grid Computing (GRID), 2010 11th IEEE/ACM International Conference on, IEEE, pp.
41-48.
[15]. Mars, Jason, Tang, Lingjia, and Hundt, Robert (2011), "Heterogeneity in “homogeneous” warehouse-
scale computers: A performance opportunity", IEEE Computer Architecture Letters. 10(2), pp. 29-32.
[16]. Nah, Fiona Fui-Hoon (2004), "A study on tolerable waiting time: how long are web users willing to
wait?", Behaviour & Information Technology. 23(3), pp. 153-163.
[17]. Salah, Khaled (2013), "A queuing model to achieve proper elasticity for cloud cluster jobs",
International Journal of Cloud Computing. 1, pp. 53-64.
[18]. Salah, Khaled, Elbadawi, Khalid, and Boutaba, Raouf (2016), "An analytical model for estimating
cloud resources of elastic services", Journal of Network and Systems Management. 24(2), pp. 285-
308.
[19]. Slothouber, Louis P (1996), A model of web server performance, Proceedings of the 5th International
World wide web Conference.
[20]. Urgaonkar, Bhuvan, et al. (2008), "Agile dynamic provisioning of multi-tier internet applications",
ACM Transactions on Autonomous and Adaptive Systems (TAAS). 3(1), p. 1.
[21]. Vaquero, Luis M, et al. (2008), "A break in the clouds: towards a cloud definition", ACM SIGCOMM
Computer Communication Review. 39(1), pp. 50-55.
[22]. Vecchiola, Christian, Pandey, Suraj, and Buyya, Rajkumar (2009), High-performance cloud
computing: A view of scientific applications, Pervasive Systems, Algorithms, and Networks (ISPAN),
2009 10th International Symposium on, IEEE, pp. 4-16.
[23]. Vilaplana, Jordi, et al. (2014), "A queuing theory model for cloud computing", The Journal of
Supercomputing. 69(1), pp. 492-507.
[24]. Villela, Daniel, Pradhan, Prashant, and Rubenstein, Dan (2007), "Provisioning servers in the
application tier for e-commerce systems", ACM Transactions on Internet Technology (TOIT). 7(1), p.
7.
[25]. Xiong, Kaiqi and Perros, Harry (2009), Service performance and analysis in cloud computing,
Services-I, 2009 World Conference on, IEEE, pp. 693-700.
[26]. Yang, Bo, Tan, Feng, and Dai, Yuan-Shun (2013), "Performance evaluation of cloud service
considering fault recovery", The Journal of Supercomputing. 65(1), pp. 426-444.

80
[27]. Zhang, Qi, Cherkasova, Ludmila, and Smirni, Evgenia (2007), A regression-based analytic model for
dynamic resource provisioning of multi-tier applications, Autonomic Computing, 2007. ICAC'07.
Fourth International Conference on, IEEE, pp. 27-27.
[28]. Qu, Chenhao (2016), "Auto-scaling and Deployment of Web Applications in Distributed Computing
Clouds".
[29]. Sahni, Jyoti and Vidyarthi, Deo Prakash (2016), "Heterogeneity-aware adaptive auto-scaling heuristic
for improved QoS and resource usage in cloud environments", Computing, pp. 1-31.
[30]. Sowjanya, T Sai, et al. (2011), "The queueing theory in cloud computing to reduce the waiting time".
AUTHORS
Chien Nguyen Khac, received his master degree in Computer Science from the University of Natural
Sciences in HCM City in 2008. He is currently a lecturer at the University of the People's Police, and is
doing a PhD candidate in Computer Engineering at the PTIT, Hanoi. His research interests: Auto-
Scaling in cloud computing. Email: nkchienster@gmail.com.
Khiet Bui Thanh, is a PhD candidate at Computer Science, Faculty of Computer Science and
Engineering, Ho Chi Minh City University of Technology. Research Interests: Cloud computing.
Email: khietbt@tdmu.edu.vn
Hung HoDac, Born in 1991 in Binh Duong. Graduated from the Graduate School of Information
Systems at the Ho Chi Minh City Post and Telecommunications Institute of Technology. Currently
working at Faculty of Engineering and Technology, Thu Dau Mot University, Binh Duong.
Research: Game, Cloud Computing. Email: hunghd@tdmu.edu.vn
Son Nguyen Hong, received his B.Sc. in Computer Engineering from the University of Technology in
HCM city, his M.Sc. and PhD
inCommunicationEngineeringfromthePostandTelecommunicationInstituteofTechnologyHanoi.Hiscurr
entresearchinterestsincludecommunicationengineering,networksecurity,computer engineering and
cloud computing. Email: ngson@ptithcm.edu.vn
Vu Pham Tran, Currently Deputy Dean of Computer Science and Technique, Ho Chi Minh City
University of Technology. Research: Intelligent Transport Systems (ITS), Big Data Analytics, Peer-to-
Peer Computing Email: ptvu@hcmut.edu.vn
Hung Tran Cong,He received the master of engineering degree in telecommunications engineering
course from postgraduate department Hanoi University of technology in Vietnam, 1998. He received
Ph.D at Hanoi University of technology in Vietnam, 2004. His main research areas are B – ISDN
performance parameters and measuring methods, QoS in high speed networks, MPLS. He is,
currently, Associate Professor PhD. of Faculty of Information Technology II, Posts and Telecoms
Institute of Technology in Ho Chi Minh, Vietnam. Email: conghung@ptithcm.edu.vn

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