Running Head: STOCHASTIC MODEL FOR ...

Running Head: STOCHASTIC MODEL FOR ANALYZING PERFORMANCE OF IAAS

A scalable stochastic model for analyzing performance of IaaS cloud Moody Amakobe Advanced Topics in Big Data Analytics Colorado Tech University

A scalable stochastic model for analyzing performance of IaaS cloud

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Introduction The popularity of cloud computing and proliferation of the market among its competitors, has created an urgent need for an effective performance analysis methodology best suited for Infrastructure as a Service (Iaas) cloud computing environment consisting of a myriad of physical and virtual Machines. In order for the cloud service providers to be efficient in providing and configuring their computational resources. Gosh et al (2013) found that there are three choices that can be made to evaluate cloud performance. (i) Experiment-based performance analysis; In this case the time and cost of such analysis become preventative due to the scale of the cloud. (ii) Discrete event-simulation-based performance analysis; in this case simulations could take a long time to get statistically significant data. (iii) Stochastic model-based performance analysis; these may not scale given the size and complexity of a cloud system, however the authors argue that it would be the only natural choice given its low cost. Gosh et al (2013) then propose a simple scalable stochastic model for analyzing performance of IaaS cloud computing environment based on the interactions of several submodels, while the overall solution is composed by iteration over individual sub-model solutions. The authors add that scalability and traceability are therefore attained by the interacting submodels that provide results for large datasets within a reasonable time frame. The sub-models also provide a simple way to obtain a closed form solution.


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Architecture The model considers IaaS cloud where Physical Machines (PMs) are pooled as hot, warm and cold based on power consumption and response time. The Hot pool consists of PMs that have virtual machines (VMs) that need to be configured and deployed per user request. The warm pool consist of PMs that are turned on but not running, they remain in sleep mode until a deployment request is issued. The cold pool consists of turned off PMs. This pooling will enable the provider to make tradeoffs in service offering based on power consumption and response time. Interacting Sub-models The authors propose the following sub-models based on SHARPE and SPNP which can be complemented using closed form expressions when the system becomes too large. CTMC sub-model for RPDE: The continuous-time Markov chain (CTMC) is a model that takes values in some finite state space and for which time spent in each state takes nonnegative real values and also has an exponential distribution. This is specifically suited for processes that are modelled to occur in continuous time and in a stochastic process takes values on a finite or countable set. Thus being suited for a continuous resource provisioning decision engine (RPDE) which in this model will be used to find a PM from the three pools to accept a request, when a request arrives. This sub-model takes in the job arrival date, mean searching delays to find a PM, probabilities that a PM can accept the job and the maximum number of jobs in RPDE. CTMC for VM provisioning: The authors construct one CTMC sub-model for each pool respectively. The overall provisioning of VMs in a pool is modelled by independent sub-


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models which represent each PM in the pool. These sub-models keep track of the number of VMs running on a PM. SHARPE for the RPDE and CTMC sub-models: The authors state that the RPDE and CMTC sub-model can be implemented using SHARPE software package, customizing the code to show how states and transitions can be specified in a SHARPE input file. In the proposal, probabilities that at least one PM in a pool (Hot, warm or cold) can accept a request is computed by VM provisioning models. The RPDE sub-model then uses the probabilities as input and output parameters. Thus there is a cyclic dependency among the submodels which proves to be the main limitation of the architecture. The authors state that this dependency can be resolved using fixed point iteration. Conclusion In conclusion the study compared the scalability and accuracy of this approach with a one level monolithic model and show that when a number of PMs in each pool increases beyond three and the number of VMs per PM increase beyond 38 the monolithic model returns a memory overflow. The study also showed that the solution time for the monolithic model increases with the increase in model size while the solution time for the interacting sub-models remain almost constant. Thus showing the scalability and traceability of the proposed approach. The author add that the proposed approach can be extended for more than three pools, to model heterogeneous PMs and also to model parallel provisioning of jobs.

A scalable stochastic model for analyzing performance of IaaS cloud References Ghosh, R., Longo, F., Naik, V. K., & Trivedi, K. S. (2013). Modeling and performance analysis of large scale IaaS clouds. Future Generation Computer Systems, 29(5), 1216-1234. doi:10.1016/j.future.2012.06.005

Sakr, S., & Gaber, M. (Eds.). (2014). Large scale and big data: Processing and management. Boca Raton, FL: CRC Press.

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