Fuzzy Based Reactive Resource Pricing in Cloud Computing

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1 Fuzzy Based Reactive Resource Pricing in Cloud Computing 1P. Pradeepa, 2M. Jaiganesh, 3A. Vincent Antony Kumar, 4M. Karthiha Devi 1, 2, 3, 4 Department of Information Technology, PSNA College of Engineering and Technology, Dindigul, Tamilnadu, India. 1 [email protected], 2 [email protected] 3 [email protected], [email protected] Abstract Cloud computing provides users an efficient way to dynamically allocate computing resources to meet demands. Cloud providers can offer consumer two payment plans, i.e., reservation and ondemand plans for resource provisioning. Since the cloud consumer has to pay to the provider in advance, the utilization cost of computing resource provided by reservation plan is cheaper than that provided by on-demand plan. However, the best advance reservation of resources is difficult to be achieved due to uncertainty of consumer s future demand and providers resource prices. The proposed algorithm called an Optimal Cloud Resource Provisioning (OCRP) is used to address the problem. The OCRP algorithm facilitates the use of computing resources in multiple provisioning stages as well as for a long-term reservation plan. The demand and price uncertainty is considered in OCRP. Benders decomposition technique is used to obtain the solution of the OCRP algorithm. The reactive nature of cloud is essential to predict the Total Provisioning Cost (TPC). A Fuzzy Expert system is designed to estimate the Total Provisioning Cost (TPC). We quantify the TPC in terms of set of Virtual Machine Class (VM class), Cloud Service Provider (CSP) and Provisioning Stage. The advantage of finding TPC is to categorize the cloud services at an optimal cost. 1. Introduction Keywords: Cloud Computing, Resource Provisioning, Virtualization, Utilization Cost, Fuzzy Logic, Stochastic programming. Cloud computing is a large-scale distributed computing paradigm in which a pool of computing resources is available to users (called cloud consumers) via the Internet. Computing resources, e.g., processing power, storage, software, and network bandwidth, are represented to cloud consumers as the accessible public utility services [8]. Infrastructure-as-a-Service (IaaS) is a computational service model widely applied in the cloud computing paradigm. In this model, virtualization technologies can be used to provide resources to cloud consumers. The consumers can specify the required software stack, e.g., operating systems and applications; then package them all together into virtual machines (VMs). Isolation property of VMs ensures that application and servers run within a VM cannot interfere with the host Operating System. The hardware requirement of VMs can also be adjusted by the consumers. Finally, those VMs will be outsourced to host in computing environments operated by third-party sites owned by cloud providers. A cloud provider is responsible for guaranteeing the Quality of Services (QOS) for running the VMs. Since the computing resources are maintained by the provider, the total cost of ownership to the consumers can be reduced. In cloud computing, a resource provisioning mechanism is required to supply cloud consumers a set of computing resources for processing the jobs and storing the data [6]. Cloud providers can offer cloud consumers two resource provisioning plans, namely short-term on-demand and long-term reservation plans. Amazon EC2 [2] and Go Grid [9] are, for instances, cloud providers which offer IaaS services with both plans. In general, pricing in on-demand plan is charged by pay-per-use basis (e.g., 1 day). Therefore, purchasing this on-demand plan, the consumers can dynamically provision resources at the moment when the resources are needed to fit the fluctuated and unpredictable demands. For reservation plan, pricing is charged by a onetime fee (e.g., 1 year) typically before the computing resource will be utilized by cloud consumer. With the reservation plan, the price to utilize resources is cheaper than that of the on-demand plan. In this way, the consumer can reduce the cost of computing Journal of Convergence Information Technology (JCIT) Volume 9, Number 6, November

2 resource provisioning by using the reservation plan. For example, the reservation plan offered by Amazon EC2 can reduce the total provisioning cost up to 49 percent when the reserved resource is fully utilized (i.e., steady-state usage) [3]. With the reservation plan, the cloud consumers a priori reserve the resources in advance. As a result, the under provisioning problem can occur when the reserved resources are unable to fully meet the demand due to its uncertainty. Although this problem can be solved by provisioning more resources with on-demand plan to fit the extra demand, the high cost will be incurred due to more expensive price of resource provisioning with on-demand plan. However, such on-demand resources are more costly, and the corresponding cost is called on-demand cost. On the other hand, the over provisioning problem can occur if the reserved resources are more than the actual demand in which part of a resource pool will be underutilized. The cost of idle reserved resource is generally referred to as over provisioning or oversubscribed cost. It is important for the cloud consumer to minimize the total cost of resource provisioning by reducing the on-demand cost and oversubscribed cost of under provisioning and over provisioning [14]. To achieve this goal, the optimal computing resource management is the critical issue. In this paper, minimizing both under provisioning and over provisioning problems under the demand and price uncertainty in cloud computing environments is to explore a resource provisioning strategy for cloud consumers [15]. In particular, an optimal cloud resource provisioning (OCRP) algorithm is proposed to minimize the total cost for provisioning resources in a certain time period. To make an optimal decision, the demand uncertainty from cloud consumer side and price uncertainty from cloud providers are taken into account to adjust the tradeoff between on-demand and oversubscribed costs. We prefer to convert this real time estimation as stochastic in nature. This optimal decision is obtained by formulating and solving a stochastic integer programming problem with multistage recourse [4]. Benders decomposition [1] is discussed as the possible techniques to solve the OCRP algorithm. The OCRP can minimize the total cost under uncertainty. The proposed mathematical analysis will be useful to the cloud consumers (e.g., organization and company) for the management of virtual machines in cloud computing environment. The proposed OCRP algorithm will facilitate the adoption of cloud computing of the users as it can reduce the cost of using computing resource significantly. 2. Related Work As virtualization is a core technology of cloud computing, the problem of virtual machine placement (VM placement) becomes crucial [7], [10], [11], [13]. In [10], the broker based architecture and algorithm for assigning VMs to physical servers were developed. In [7], a resource management consisting of resource provisioning and VM placement was proposed. In [11], techniques of VM placement and consolidation which leverage min-max and shares features provided by hypervisors were explored. In [12], a dynamic consolidation mechanism based on constraint programming was developed. This consolidation mechanism was originally designed for homogeneous clusters. However, heterogeneity which is common in a multiple cloud provider environment was ignored. Moreover, [7], [10], [11], [13] did not consider uncertainty of future demands and prices. In [5], a dynamic VM placement was proposed. However, the placement in [5] is heuristic-based which cannot guarantee the optimal solution. Stochastic programming has been developed to solve resource planning under uncertainty [4] in various fields, e.g., production planning, financial management, and capacity planning. For example, in [12], the authors applied the stochastic programming approach for planning of electrical power generation while some uncertainties affecting to the planning are taken into account. It is shown that stochastic programming is the promising mathematical tool which is able to address the optimal decision making in the stochastic environment. The optimal virtual machine placement (OVMP) algorithm was proposed [13].This OVMP algorithm can yield the optimal solution for both resource provisioning and VM placement in two provisioning stages. Based on this work, we introduce the OCRP algorithm in this paper which achieves many improvements. First, the problem is generalized into the multiple stage formulation. Second, the different approaches to obtain the solution of computing resource provisioning are considered. Finally, the performance evaluation is extended to consider various realistic scenarios. 131

3 The major contributions of this paper can be summarized as follows: 1) The optimal cloud resource provisioning algorithm is proposed for the virtual machine management. The optimization formulation of stochastic integer programming is proposed to obtain the decision of the OCRP algorithm as such the total cost of resource provisioning in cloud computing environments is minimized. The formulation considers multiple provisioning stages with demand and price uncertainties. 2) The solution methods based on Benders decomposition is used to solve the optimization formulation in an efficient way. 3) Fuzzy based system is proposed for categorizing the optimal cost for reactive environment. 3. Proposed System Model 3.1. Cloud Computing Environment Figure1. System Model As shown in Figure 1., the system model of cloud computing environment consists of four main components, namely cloud consumer, virtual machine (VM) repository, cloud providers, and cloud broker. The cloud consumer has demand to execute jobs. Before the jobs are executed, computing resources has to be provisioned from cloud providers. To obtain such resources, the consumer firstly creates VMs integrated with software required by the jobs. The created VMs are stored in the VM repository. Then, the VMs can be hosted on cloud providers infrastructures whose resources can be utilized by the VMs. In Fig. 1, the cloud broker is located in the cloud consumer s site and is responsible on behalf of the cloud consumer for provision resources for hosting the VMs. In addition, the broker can allocate the VMs originally stored in the VM repository to appropriate cloud providers. The broker implements the OCRP algorithm to make an optimal decision of resource provisioning. In OCRP, there are multiple VM classes used to classify different types of VM. It is assumed that one VM class represents a distinct type of jobs (e.g., one class for web application and the other for database application). A certain amount of resources is required for running the VM, and this required amount of resources can be different for VM in different classes. With this resource requirement, the cloud broker can reserve computing resources from cloud providers to be used in the future according to the actual demand. This demand can be determined as the number of created VMs. In this case, it is possible that additional resources can be provisioned instantly from cloud providers if the reserved resource is not enough to accommodate the actual demand. Each cloud provider supplies a pool of resources to the consumer. Resource types can be computing power (in unit of CPU-hours), storage (in unit of GBs/month), and network bandwidth for Internet data transfer (in unit of GBs/month). Each VM class specifies the amount of resources in each resource type. It is assumed that every cloud provider prepares facilities, e.g., virtualization management software, network facility, and load balancer, to support the consumer s hosting VM. 132

4 Provisioning Plans A cloud provider can offer the consumer two provisioning plans, i.e., reservation and/or on-demand plans. For planning, the cloud broker considers the reservation plan as medium- to long-term planning, since the plan has to be subscribed in advance (e.g., 1 or 3 years) and the plan can significantly reduce the total provisioning cost Provisioning Phases The cloud broker considers both reservation and on demand plans for provisioning resources. These resources are used in different time intervals, also called provisioning phases. There are three provisioning phases: reservation, expending, and on-demand phases. As shown in Figure 2., these phases with their actions perform in different points of time (or events) as follows. First in the reservation phase, without knowing the consumer s actual demand, the cloud broker provisions resources with reservation plan in advance. In the expending phase, the price and demand are realized, and the reserved resources can be utilized. As a result, the reserved resources could be observed to be either over provisioned or under provisioned. If the demand exceeds the amount of reserved resources (i.e., under provisioned), the broker can pay for additional resources with on-demand plan, and then the on-demand phase starts. Reservation Phase Expending Phase On-demand Phase Figure 2. Transition of Provisioning Phases Provisioning Stages A provisioning stage is the time epoch when the cloud broker makes a decision to provision resources by purchasing reservation and/or on-demand plans, and also allocates VMs to cloud providers for utilizing the provisioned resources. Therefore, each provisioning stage can consist of one or more provisioning phases. The number of provisioning stages is based on the number of planning epochs considered by the cloud broker, e.g., a yearly plan consists of 12 provisioning stages (i.e., 12 months). For resource provisioning under uncertainty, the broker is assumed to be able to reserve the resources in the first provisioning stage. Also, the broker obtains a solution, called recourse action [4], for provisioning resources against uncertainty parameters (i.e., demand and price) in every stage. These uncertainty parameters in each stage will be observed by the broker after the resource reservation has been made. The observed uncertainty parameters are called realization (e.g., the actual number of created VMs after the jobs are submitted by the consumers). Then, the broker will take the recourse action according to the realization, e.g., utilizing the reserved resource and/or provisioning more resource with on-demand plan Uncertainty of Parameters The optimal solution used by the cloud broker is obtained from the OCRP algorithm based on stochastic integer programming [4]. Stochastic programming takes a set of uncertainty parameters (called scenarios), described by a probability distribution into account. Let Ω denote the set of all scenarios in every provisioning stage and Ωt denote the set of all scenarios in provisioning stage t. Set Ω is defined as the Cartesian product of all Ωt, namely t (1) tt It is assumed that the probability distribution of Ω has finite support, i.e., the set has a finite number of scenarios with respective probabilities p( )Є[0,1] where is a composite variable defined as =,,..., ). In this paper, demand and price are considered as scenarios whose ( 1 2 T 133

5 probability distribution is assumed to be available. The actual scenario of uncertainty parameter after it is observed by the broker is called realization Provisioning Costs With three aforementioned provisioning phases, there are three corresponding provisioning costs incurred in these phases, namely reservation, expending, and on-demand costs. The main objective of the OCRP algorithm is to minimize all of these costs while the consumer s demand is met, given the uncertainty of demand and price. For cloud provider, the price is defined in dollars ($) per resource unit. Let C denote the unit price (i.e., costs to the consumer) of resource type r subscribed to reservation contract p provided by cloud provider n in reservation phase of the first provisioning stage. It is assumed that the price of reservation plan in the first stage is charged by a fixed one-time fee. The reservation cost C is the cost for provisioning every resource type defined as follows: C b C (2) mr npr rr The prices in reservation and expending phases could be adjusted by cloud providers without informing the consumer in advance, except the price of the reservation plan in the first provisioning stage. Table 1. List of Key Notations C C C Symbol M N P T R Ω C ( r) npt ( e) npt ( o) mnt ( ) ( ) ( ) b mr x Definition Set of Virtual Machine (VM) classes while m Є M denotes the VM class index Set of cloud providers while n Є N denotes the cloud provider index Set of reservation contracts while p Є P denotes the reservation contract index Set of provisioning stages while t Є T denotes the provisioning stage index Set of resource types while r Є R denotes the resource type index Set of scenarios while α Є Ω denotes the scenario index Reservation cost subscribed to reservation contract p charged by cloud provider n to cloud consumer s VM class m in the first provisioning stage Reservation cost subscribed to reservation contract p charged by cloud provider n to cloud consumer s VM class M in the first provisioning stage Expending cost subscribed to reservation contract p charged by cloud provider n to cloud consumer s VM class M in the first provisioning stage On-demand cost charged by cloud provider n to cloud consumer s VM class M in provisioning stage t and scenario α Amount of resource type r required by VM class m Decision variable representing the no of VM s in class M provisions in reservation phase subscribed to reservation contract p offered by cloud provider n in the first provisioning stage 134

6 3.2. Preliminaries Stochastic Integer Programming for OCRP Minimize: z C x IE [ Q( x. )] (3) mm nn pp Subject to: x IN o, m M, n N, p P (4) The general form of stochastic integer program of the OCRP algorithm is formulated in (3) and (4). The idea is to convert the probabilistic nature of the problem into an equivalent deterministic situation. The objective function (3) is to minimize the cloud consumer s total provisioning cost. Decision variable x denotes the number of VMs provisioned in the first provisioning stage. In other words, this number refers to as the total amount of reserved resources. The expected cost under the uncertainty Ω is defined as IE [ Q(. ) ]. The objective of Q (. ) is to minimize the cost under x uncertainty given scenario α and Benders Decomposition x. x The Benders decomposition algorithm [1] is applied to solve the stochastic programming problem. The goal of this algorithm is to break down the optimization problem into multiple smaller problems which can be solved independently and parallelly. As a result, the time to obtain the solution of the OCRP algorithm can be reduced. ( r) ( r) + ( ) C t ( ) x ( ) z C x mm nn pp P mm nn pp tt The Benders decomposition algorithm in (5) can decompose integer programming problems with complicating variables into two major problems: master problem and sub problem.step2-4 are repeatable. Step-1: Initialization of the master problem The problem initialization is unique for every virtual client based on their request and performed once for each client. Minimize: (e) z (lb) Subject to: Step-2: Sub problem solution mm nn pp tt t (5) ( e) ( e) P ( ) C t ( ) x ( ) (6) ( e) The master problem can be divided into sub problem and it is solved. The solution x tv ( ) ) is the solution obtained from master problem v represents the iteration count value and the initial value is set to 1. Step-3: Convergence checking The upper and lower bound values are formed and checked for each sub problem. Both the bounds are adjusted in each iteration, lb and ub represents the lower and upper bound values. t 135

7 z z z z ( ) (7) ( ub) *( e) *( r) *( o) v v v v v Let z denote the tolerance value. The algorithm stops when z ( ub) v z ( lb) v e, means the bound values are closer to each other. Step-4: Master problem solution The master problem can be relaxed further by additional constraints called Benders cuts [1].Benders cuts are constructed from master problem and sub problem. The solution will adjust the expending cost according to the solution. Benders cuts are derived from optimal cost, the same iterative process continues. In addition to this we solve the optimization problem by using fuzzy expert system by considering normalized values for each parameter Fuzzy Expert System The fuzzy system comprises of three phases, they are fuzzification, fuzzy inference system, and defuzzifications are represented in Figure 3. Fuzzific ation Inference engine Defuzzifi cation Figure 3. Fuzzy Logic Controller In fuzzification the crisp values are transformed into linguistic terms of fuzzy sets. The mapping of given input to an output is made in fuzzy inference system and it is done by forming set of rules [16]. The purpose of defuzzification is to alter each conclusion obtained by inference rules and used to evaluate the rules and final output has to be crisp number Fuzzification In the real world, variables are measured in numeric values such as a weight of 60kg, time of 10.6seconds, in a fuzzy logic system, crisp inputs are to be converted into variables. The crisp values of the input variable in a fuzzy system are called fuzzy singletons. Thus the process of converting a fuzzy singleton into a membership grade in one or many fuzzy sets is termed as fuzzification [17]. In the process of fuzzification, membership functions defined on input variables are applied to their actual values so that the degree of truth for each rule premise can be determined. In general, fuzzy theory provides a mechanism for representing linguistic construction such as low, medium, high and small, medium, large. Assume that ranges of input variables x and y are [a, a] and [-b,a] respectively and the range of output variable z is[-c,c]. Let x and y may be VMclass, Cloud provider and Provisioning stage and z is TPC represent these linguistics states by k dimensional cube for k variables and shown in Table 2. Table 2. Linguistic Value Notations Linguistic Value Notation Range VMclass Low Medium High Cloud Provider L M H [0,0.5] [0.4,0.8] [0.65,1] 136

8 Small Medium High Provisioning Stage Very short Short Medium S M H VS S M [0,0.35] [0.3,0.7] [0.6,1] [0,0.3] [0.15,0.5] [0.45,0.75] TPC(Total Provisioning Cost) Very small Small Medium Large Very Large VS S M L VL [0,0.3] [0.2,0.45] [0.35,0.7] [0.6,0.9] [0.8,1] By using trapezoidal method defines how each point in the input space is mapped to a membership value between 0 and 1. A membership function associated with a given fuzzy set maps an input value to its appropriate membership value Inference Engine Figure 4. Fuzzification Inference engine consists of two blocks namely fuzzy rule base and fuzzy implication. The fuzzified inputs are fed to the inference engine and the rule base is applied. The output are identified using fuzzy implication method. The input to the fuzzy operator is two or more membership values from fuzzified input variables. The output is a single truth value. The input for the implication process is a single number given by the antecedent, and the output is a fuzzy set. Implication is implemented for each rule. The symbols Aj, Bj, Cj (j=1, 2, 3 n) denotes fuzzy sets that represents the linguistic states of variables x, y, z respectively. For each rule in the fuzzy rule base, there is a corresponding relation Rj. Since the rules are interpreted are disjunctive, we may use to conclude that the state of variable v is characterized by the fuzzy sets. Rule 1: IF (VMclass, Cloud Provider) is A1*B1, THEN TPC is C1 Rule 2: IF (Cloud provider, Provisioning stage) is A2*B2, THEN TPC is C2.Finally, we arrive Rule n: IF (x,y) is An*Bn, THEN z is Cn. 137

9 A matrix like representation is generally followed and is known as Fuzzy Associative Memory (FAM). FAM square represents knowledge base representation. The constraints of linguistic values of inputs VMclass, Cloud provider and Provisioning stage are compared with linguistic values of the output that represents the TPC. The FAM square for TPC by considering VMclass and Cloud provider is represented in Table 3. The linguistic states of TPC are equally spread when the constraints are compared. Table 3. FAM for TPC Estimation Rule 1 VMclass Cloud Provider Low Medium High Small VS S M Medium S M L Large M L VL Defuzzification After fuzzy implication, output fuzzy region is located. The extraction of the numerical value corresponding to the output from the fuzzy region is termed as defuzzification. The center of area method is employed and observed to be very effective. Helps us to evaluate the rules, but the final output of a fuzzy system has to be crisp number. Consider the solution space U and it can be divided into l discrete values, say U i, where i=1 to l. Each U i has a membership value of cl ( u i ) in one alone or in many clipped fuzzy set. If the variable belongs to many clipped fuzzy sets is considered as its membership value for defuzzification. Thus, logical OR operation is applied on membership grades of u i to perform defuzzification in the overlapped regions. The defuzzified output is given by the following equation: U * l i1 l i1 u u i u n m1 n m1 cl( m) cl( m) ( u ) i i ( u ) (8) 4. Implementation The OCRP algorithm was implemented by using Java programming language and fuzzy system is implemented by using matlab tool. The cloud environment is implemented by creating both host as a consumer (i.e., organization) and server as a cloud provider. The consumer has two types of applications provided by both the vmclasses. To solve the under provisioning and over provisioning constraints on-demand requests are processed during resource utilization. The optimal cost is achieved by considering the scenario values. By using the reservation plan users can have the following advantages, make sure about resource availability, reduces the processing time reduce the provisioning cost. To analyze the total resource provisioning cost during on-demand phase fuzzy system is proposed by considering set of variables that include vmclasses, cloud providers, provisioning stages and total provisioning cost Performance Evaluation VMware Workstation is a test-and-development environment that allows to create and run virtual machines. Each virtual machine can run a single instance of any operating system (Microsoft, Linux, etc.) simultaneously. VMware Workstation strongly supports hardware compatibility and works as a 138

10 bridge between the host and virtual machine for all kinds of computing resources. All device drivers are installed via the host machine. VMware provides hardware virtualization. By using Net Beans IDE (Integrated Development Environment) and Wamp server for database storage, java code is written to evaluate the cost variation between the two ways of resource access. The Figure 5 shows the comparison between total costs of resource provision with and without reservation. The individual client ids are represented as horizontal axis and the resource cost is denoted as vertical axis. The resource cost represents the reservation cost for each client s request. Total cost of resource provision without reservation is lower than the other one. The graph is plotted by using VMware tool and by implementing optimization algorithm. Figure 5. Cost variance between total cost with and without reservation 4.2. By using Fuzzy Expert System We now asses the performance using the Fuzzy Expert system model to analyze the total provisioning cost for the reactive environment. The first step of the simulation focuses on fuzzification by converting them into input membership functions. This is performed using the tool called as membership function editor provided in the MATLAB. Each variable in the experiment is quantified into low, medium, and high for vmclass, small, medium, high for cloud provider; very short, short and medium for provisioning stages; very small, small, medium, large and very large for total provisioning cost (TPC) variables. The If-Then rules of the experiment are formulated using rule editor. We performed our required operation in FIS editor which handles the high level issues. The membership function editor which defines the shapes of all membership function is associated with each variable and rule editor for editing the list of rules. The surface viewer plots an output surface map for the system. All the rules have been depicted as 3D graphs called surface viewer in figures 6, 7, 8. It shows the analysis of total resource provisioning cost for the reactive environment based on the different parameter values. 139

11 Figure 6. Fuzzy 3D View of Cloud Provider and VMclass versus TPC The Figure 6 shows the analysis of resource provisioning cost for on-demand plan. In reactive environment the resource cost will be increased gradually when the number of vmclasses (user requests) and the cloud provider increases. The analysis is made by considering different set of values for vmclasses, cloud provider and provisioning stages. The output parameter is total provisioning cost that represents on-demand cost. Figure 7. Fuzzy 3D View of Cloud Provider and Provisioning Stage versus TPC The Figure 7 shows the TPC (Total Provisioning Cost) output with respect to provisioning stage and cloud provider as input parameters. All are separated based on the range of the values. When the provisioning stage and cloud provider increases TPC is also increases. 140

12 Figure 8. Fuzzy 3D View of VMclass and Provisioning Stage versus TPC The Figure 8 shows the TPC (Total Provisioning Cost) output with respect to provisioning stage and vmclass input parameters. The vmclass parameter represents the number of request for the cloud resources during on-demand. The graph shows that it is increasing gradually based on the other parameter values Future Research Direction The optimal pricing scheme for cloud providers side with the consideration of competition in the market will be investigated. The performance improvement of the decomposition algorithm will be considered. During VM outsourcing the total cost of ownership (TCO) must be considered for optimal solution. 5. Conclusion The most important task in the successful service of the internet is access through maximum data with minimal cost. The proposed provisioning method is implemented to solve resource reservation, Over need of resource, Unwanted resource reservation. The OCRP algorithm is implemented to minimize the total cost for provisioning resources in a time period. Stochastic problem will be solved by using benders decomposition. The OCRP algorithm can be used as a resource provisioning tool for the emerging cloud computing market in which the tool can effectively save the total cost. The advantage of the proposed system is increases the resource utilization with minimal optimize cost. 6. References [1] A.J. Conejo, E. Castillo, and R. Garcı a-bertrand, Linear Programming: Complicating Variables, Decomposition Techniques in Mathematical Programming, chapter 3, pp , Springer, [2] Amazon EC2, [3] Amazon EC2 Reserved Instances, [4]F.V. Louveaux, Stochastic Integer Programming, Handbooks in OR & MS, vol. 10, pp , [5] F. Hermenier, X. Lorca, and J.-M. Menaud, Entropy: A Consolidation Manager for Clusters, Proc. ACM SIGPLAN/ SIGOPS Int l Conf. Virtual Execution Environments (VEE 09), [6] G. Juve and E. Deelman, Resource Provisioning Options for Large-Scale Scientific Workflows, Proc. IEEE Fourth Int l Conf.e-Science,

13 [7] H.N. Van, F.D. Tran, and J.-M. Menaud, SLA-Aware Virtual Resource Management for Cloud Infrastructures, Proc. IEEE Ninth Int l Conf. Computer and Information Technology, [8] I. Foster, Y. Zhao, and S. Lu, Cloud Computing and Grid Computing 360-Degree Compared, Proc. Grid Computing Environments workshop (GCE 08), [9] Go Grid, [10] L. Grit, D. Irwin, A. Yumerefendi, and J. Chase, Virtual Machine Hosting for Networked Clusters: Building the Foundations for Autonomic Orchestration, Proc. IEEE Int l Workshop Virtualization Technology in Distributed Computing, [11] M. Cardosa, M.R. Korupolu, and A. Singh, Shares and Utilities Based Power Consolidation in Virtualized Server Environments, Proc. IFIP/IEEE 11th Int l Conf. Symp. Integrated Network Management (IM 09), [12] N. Bobroff, A. Kochut, and K. Beaty, Dynamic Placement of Virtual Machines for Managing SLA Violations, Proc. IFIP/IEEE Int l Symp. Integrated Network Management (IM 07), pp , May [13] S. Chaisiri, B.S. Lee, and D. Niyato, Optimal Virtual Machine Placement across Multiple Cloud Providers, Proc. IEEE Asia- Pacific Services Computing Conf. (APSCC), [14] Sivadon Chaisiri, Bu-Sung Lee, Dusit Niyato, Optimization of Resource Provisioning Cost in Cloud Computing, IEEE Transactions on services computing,vol.5, NO.2, [15] P.Pradeepa, A. Vincent Antony Kumar, M.Jaiganeesh, Estimation of Resource Provisioning Cost in Cloud Computing,Proc. Int l Conf. on Advances in Communication and Computing (ICACC) Jan [16] Jaiganesh, M & Vincent Antony Kumar, A 2013, B3: Fuzzy based Data center load Optimization in Cloud computing Mathematical Problems in Engineering, vol. 2013, pp [17] Jaiganesh, M & Vincent Antony Kumar, A 2014 Isolation of Cloud Virtual Machine vulnerabilities using Fuzzy ART, International Journal of Digital Content and its Applications, vol 8, no.3, pp