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Availability Analysis of IaaS Cloud Using Analytic Models INTRODUCTION Cloud computing is a model of Internet-based computing. An IaaS Cloud, such as Amazon EC2 and IBM SmatCloud EnterpriseTM (Ama- zon EC2: http://aws.amazon.com/ec2, 2011; IBM SmatCloud EnterpriseTM: www.ibm.com/ services/us/en/cloud-enterprise/, 2011) delivers, on-demand, operating system (OS) instances provisioning computational resources in the form of VMs deployed in the Cloud provider's data center. Requests submitted by the users are provisioned and served if the Cloud has enough available capacity in terms of physical machines (PMs). Large Cloud service providers such as IBM provide service level agreements (SLAs) regulating the availability of the Cloud service. Before committing an SLA to the customers of a Cloud, the service provider needs to carry out availability analysis of the infrastructure on which the Cloud service is hosted. This chapter shows how stochastic analytic models can be utilized for Cloud service availability analysis. It first provides a background on the subject describing how the problem is faced in the current literature. Then, it proposes an example of one-level monolithic model that can be used to analyze the availabil- ity of an IaaS Cloud. However, such monolithic models become intractable as the size of Cloud increases. To overcome this difficulty, the chapter illustrates the use of an interacting sub-models approach. Overall model solution is obtained by iteration over individual sub-model solutions. Comparison of the results with monolithic model shows that errors introduced by model decom- position are negligible. It also shows how closed form solutions of the sub-models can be obtained and demonstrate that the approach can scale for large size Clouds. The presence of three pools of PMs and the migration of them from one pool to another caused by failure events makes the model both novel, interesting and particularly suitable in federated environments. In order to automate the construction and solution of underlying Markov models, the authors use a variant of stochastic Petri net (SPN) called stochastic reward net (SRN). This paradigm is supported by SHARPE (Trivedi & Sahner, 2009) and Stochastic Petri Net Package (SPNP) (Hirel, Tuffin, & Trivedi, 2000) software packages. Rest of the chapter is organized as follows. Section II gives a background on the subject il- lustrating the state of the art. Section III provides an introduction to the formalism that will be used in the following to model the considered scenario. Section IV describes Cloud system model, as- sumptions and problem formulation. Section V, presents the monolithic SRN model. Interacting SRN sub-models are described in Section VI and their closed form solutions are presented in Section VII. Fixed point iteration among the interacting sub-models and proof of existence of a solution is shown in Section VIII. Results obtained from monolithic approach and interacting sub-models approach are compared in Section IX. Sections X and XI discuss how the approach can be used by Cloud providers, point out future challenges and highlight the benefit of decomposed models in the analysis of federation scenarios. The chapter concludes in Section XII. BACKGROUND This section highlights key analytic approaches for system availability assessment. There are four main types of analytic modeling techniques (Nicol, Sanders, & Trivedi, 2004; Trivedi, 2001; Trivedi, Kim, Roy, & Medhi, 2009) that can be applied for availability analysis: non-state-space models, state-space space models, hierarchical, and fixed- point iterative models (Haring, Marie, Puigjaner, & Trivedi, 2001; Longo, Ghosh, Naik, & Trivedi, 2011; Mainkar & Trivedi, 1996; Tomek & Trivedi, 1991). Reliability block diagram (RBD), reliability graph (Relgraph), fault tree (FT) are examples of non-state-space models. Such models can be eas- ily developed assuming statistical independence 135