This is a study to the research paper (Service Performance and Analysis in Cloud Computing) by Kaiqi Xiong and Harry Perros in the class related to the course of EC636 Stochastic and Random Process in Tripoli University-Engineering faculty-Computer Engineering Department. You can find this paper in (https://ieeexplore.ieee.org/document/5190711)

1. SERVICE PERFORMANCE AND
ANALYSIS IN CLOUD COMPUTING
Presented by: Abdulaziz Almabrouk Altagawy
Course: EC636 Stochastic and Random Process4 Oct 2018
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2. Information
 Introduction
 Cloud Types
 PROBLEM
 SOLUTION
 PREPARATIONS
 THE PERCENTILE OF
RESPONSE TIME
 A COMPUTER SERVICE
PERFORMANCE MODEL
 A NUMERICAL
VALIDATION
 CONCLUSIONS
 Book(s)
 PROBABILITY, MARKOV
CHAINS, QUEUES, AND
SIMULATION 2009-
William J. Stewart
 Probability, Statistics, and
Random Processes for
Electrical Engineering
Materials, 3rd ed, Alberto
Leon-Garcia
 Introduction to Probability
Models, 10th ed, Ross
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3. Introduction
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4. Introduction
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 Cloud Computing is an information technology (IT)
paradigm that enables everywhere access to the
shared pools of configurable system resources and
higher-level services that can be rapidly
provisioned with minimal management effort, often
over the Internet. Cloud computing relies on sharing
of resources to achieve coherence and economies of
scale, similar to a public utility [Wikipedia].

5. Introduction
 Examples of cloud service
include online file storage,
social networking sites,
webmail and online business
applications. The cloud
computing model allows
access to information and
computer resources from
anywhere that a network
connection is available. Cloud
Computing provides a shared
pool of resources, including
data storage space, networks,
computer processing power,
and specialized corporate
and user applications.
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6. Cloud Types
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7. Cloud Types
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 Deployment models: This refers to the location and management of the cloud's
infrastructure.
 The NIST (The U.S. National Institute of Standards and Technology) definition for
the four deployment models is as follows:
 Public cloud: The public cloud infrastructure is available for public use
alternatively for a large industry group and is owned by an organization selling
cloud services.
 Private cloud: The private cloud infrastructure is operated for the exclusive use
of an organization. The cloud may be managed by that organization or a third
party. Private clouds may be either on- or off-premises.
 Hybrid cloud: A hybrid cloud combines multiple clouds (private, community of
public) where those clouds retain their unique identities, but are bound together
as a unit. A hybrid cloud may offer standardized or proprietary access to data
and applications, as well as application portability.
 Community cloud: A community cloud is one where the cloud has been
organized to serve a common function or purpose.

8. Cloud Types
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 Service models: This consists of the particular types of services that you can access on a cloud computing
platform.
 Three service types have been universally accepted:
 Infrastructure as a Service: IaaS provides virtual machines, virtual storage, virtual infrastructure, and
other hardware assets as resources that clients can provision.
 The IaaS service provider manages all the infrastructure, while the client is responsible for all other
aspects of the deployment. This can include the operating system, applications, and user interactions with
the system.
 Platform as a Service: PaaS provides virtual machines, operating systems, applications, services,
development frameworks, transactions, and control structures.
 The client can deploy its applications on the cloud infrastructure or use applications that were
programmed using languages and tools that are supported by the PaaS service provider. The service
provider manages the cloud infrastructure, the operating systems, and the enabling software. The client is
responsible for installing and managing the application that it is deploying.
 Software as a Service: SaaS is a complete operating environment with applications, management, and
the user interface.
 In the SaaS model, the application is provided to the client through a thin client interface (a browser,
usually), and the customer's responsibility begins and ends with entering and managing its data and user
interaction. Everything from the application down to the infrastructure is the vendor's responsibility.

9. Cloud Types
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10. PROBLEM
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11. PROBLEM
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 Customers pay only for the used computer resources and
services by means of customized service level agreement
(SLA), also they have no knowledge of how a service
provider uses an underlying computer technological
infrastructure to support them.
 The SLA is a contract negotiated and agreed between a
customer and a service provider. That is, the service
provider is required to execute service requests from a
customer within negotiated quality of service (QoS)
requirements for a given price. So,
based on system statistics
and a customer’s perceived quality allows a service
provider to assure the quality of services and also avoid
over provisioning to meet an SLA.

12. PROBLEM
 The majority of current
cloud computing
infrastructure as of
2009 consist of services
that are offered up and
delivered through a
service center such as a
data center that can be
accessed from a web
browser anywhere in the
world.
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13. PROBLEM
 This model is a single
point of access for the
cloud computing needs
of the customers being
serviced through a Web
browser supported by a
Web server. The service
application running will
be according to the SLA
that customer pay for.
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14. PROBLEM
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 the QoS requirements in computer service
performance usually uses the
 This easy.
 But it does not address the concerns of a customer.
 The customer is preferred to request a
than an average
response time.

15. PROBLEM
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 So our concern to find the of the
response time that characterizes the statistical
response time.
is the time of executing a service request
is less than a pre-defined value with a certain
percentage of time.

16. PROBLEM
 There are three important but
challenging questions for customer
service performance in cloud
computing need to have an
answer for:
1) For a given arrival rate of
service requests and given
service rates at the Web server
and the service center, what
level of QoS services can be
guaranteed?
2) What are minimal service rates
required at the Web server
and the service center
respectively so that a given
percentile of the response time
can be guaranteed for a given
service arrival rate from
customers?
3) How many numbers of
customers can be supported so
that a given percentile of the
response time can be still
guaranteed when service rates
are given at the Web server
and the service center
respectively?
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17. SOLUTION
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18. SOLUTION
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 So to compute a percentile of the response time one has first
to find the of the response time.
 Walrand and Varaiya [23] showed that in any open Jackson
network, the response times of a customer at the various nodes
of overtake-free path are all mutually independent.
 The goal to derive an approximation method for the
calculation of the probability and cumulative distributions of
the response time, and show the accuracy of the proposed
approximation method based on the obtained percentile
response time (or the cumulative distribution of response time),
and also to derive propositions and corollaries to answer the
previous mentioned service performance questions.

19.  Reversibility.
 Renewal Theory.
 LITTLE’S FORMULA
 M/M/1 Queueing System.
• PASTA: Poisson Arrivals See Time Averages.
 Open Networks of Queues.
 Laplace–Stieltjes transforms.
 Arg max.
Preparations
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20. Reversibility
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21. Reversibility
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22. Reversibility
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23. Renewal Theory
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24. Renewal Theory
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25. Renewal Theory
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26. Renewal Theory
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27. Renewal Theory
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28. Renewal Theory
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29. Renewal Theory
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30. Renewal Theory
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31. LITTLE’S FORMULA
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32. LITTLE’S FORMULA
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33. LITTLE’S FORMULA
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34. LITTLE’S FORMULA
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35. LITTLE’S FORMULA
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36. M/M/1 Queueing System
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37. M/M/1 Queueing System
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38. M/M/1 Queueing System
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39. M/M/1 Queueing System
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40. PASTA: Poisson Arrivals See Time
Averages
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41. PASTA: Poisson Arrivals See Time
Averages
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42. M/M/1 Queueing System
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43. Open Networks of Queues
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44. Open Networks of Queues
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45. Laplace–Stieltjes transforms
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46. Laplace–Stieltjes transforms
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47. Laplace–Stieltjes transforms
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48. Laplace–Stieltjes transforms
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49. Arg max
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50. THE PERCENTILE OF RESPONSE TIME
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51. THE PERCENTILE OF RESPONSE TIME
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 Assume that 𝑓𝑇 𝑡 be the probability distribution
function of a response time 𝑇 .
 𝑇 𝐷
is a desired target response time that a
customer requests and agrees with its service
provider based on a fee paid by the customer.
 The SLA performance metric that a γ% SLA service
is guaranteed is as follows.

52. THE PERCENTILE OF RESPONSE TIME
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 That is, γ% of the time a customer will receive its
service in less than 𝑇 𝐷
.

53. THE PERCENTILE OF RESPONSE TIME
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 So in order to guarantee higher SLA service levels,
μ increases when 𝑇 𝐷
decreases. Similarly, for any
given arrival rate λ and service rate μ , we can use
(2) to find the percentile of γ . For example, when λ
= 100 and 𝑇 𝐷
= 0.05.

54. THE PERCENTILE OF RESPONSE TIME
 We can see that this service rate has to be bigger than 150
in order that 90% of the response time is less than 0.05.
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55. COMPUTER SERVICE
PERFORMANCE MODEL
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56. A COMPUTER SERVICE PERFORMANCE
MODEL
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 Computing The Response Time Distribution:
 Modeling the customer service requests as a queueing network
model appears one of the best ways that makes it possible to not
only compute percentile response time but also characterize a
variable load in cloud computing.

57. A COMPUTER SERVICE PERFORMANCE
MODEL
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 We are going to derive the Laplace-Stieltjes transform
(LST) (simply called the Laplace transform alternatively)
of response time .
 Let (𝑖 , 𝑗) be the number of visits in the Web server
and the service center where 𝑖 and 𝑗 are the number of
visits in the Web server and the number of visits in the
service center respectively.
 Let p(𝑖; 𝑗) be the probability of 𝑖 visits to the Web
server and 𝑗 visits to the service center. There may be
one time visit difference between the Web server and
the service center.

58. A COMPUTER SERVICE PERFORMANCE
MODEL
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59. A COMPUTER SERVICE PERFORMANCE
MODEL
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60. A COMPUTER SERVICE PERFORMANCE
MODEL
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61. A COMPUTER SERVICE PERFORMANCE
MODEL
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62. A COMPUTER SERVICE PERFORMANCE
MODEL
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63. A COMPUTER SERVICE PERFORMANCE
MODEL
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64. A COMPUTER SERVICE PERFORMANCE
MODEL
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65. A COMPUTER SERVICE PERFORMANCE
MODEL
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66. A COMPUTER SERVICE PERFORMANCE
MODEL
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67. A COMPUTER SERVICE PERFORMANCE
MODEL
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 Proposition 1: For a given arrival rate λ service
rates μ1 in the Web server and μ2 in the service
center, and a set of parameters α, β and 𝑇 𝐷
, the
level of QoS guaranteed services (γ) will be no
more than 100𝐹 𝑇 𝑇 𝐷
, λ, μ1, μ2 .

68. A COMPUTER SERVICE PERFORMANCE
MODEL
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69. A COMPUTER SERVICE PERFORMANCE
MODEL
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70. A COMPUTER SERVICE PERFORMANCE
MODEL
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 Now we interesting to find the closed-form
expression of 𝐹 𝑇 𝑇 𝐷
, λ, μ1, μ2 .
 Let λ𝑖 (𝑖 = 1; 2) be the arrival rates at the first and
second M/M/1 queues respectively.

71. A COMPUTER SERVICE PERFORMANCE
MODEL
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72. A COMPUTER SERVICE PERFORMANCE
MODEL
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73. A COMPUTER SERVICE PERFORMANCE
MODEL
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74. A COMPUTER SERVICE PERFORMANCE
MODEL
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75. A COMPUTER SERVICE PERFORMANCE
MODEL
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76. A COMPUTER SERVICE PERFORMANCE
MODEL
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77. NUMERICAL VALIDATION
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78. NUMERICAL VALIDATION
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79. NUMERICAL VALIDATION
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80. Conclusion
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81. Conclusion
 We have studied three important but challenging
questions for computer service performance in cloud
computing below: (1) For given service resources,
what level of QoS services can be guaranteed? (2)
For a given number of customers, how many service
resources are required to ensure that customer
services can be guaranteed in term of the
percentile of response time? (3) For given service
resources, how many customers can be supported to
ensure that customer services can be guaranteed in
term of the percentile of
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82. Conclusion
 we have derived three propositions and three
corollaries for answering the above three questions.
The answers to the above three questions can be
obtained by using a numerical approximate method
in these propositions and corollaries.
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83. THANKS
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