Scalable Stochastic Model

Cloud computing is currently a forerunner technology amongst other information and computing technologies, powered by attributes like, high availability, scalable, flexible and fault tolerance (IBM, 2018). Services offered by cloud can be provisioned at three different levels, infrastructure as a service (IaaS), platform as a service (PaaS) and software as a service (SaaS) (Bruneo, 2014). In particular, IaaS offers services in the form of virtual machines provisioned in the cloud whereas PaaS and SaaS offer solutions and applications respectively (Bruneo, 2014).

Service level agreements (SLA) defines the performance of cloud service between clients and service providers to govern the quality of service (Bruneo, 2014). Sakr and Gaber (2014) noted that most of the IaaS providers offer only availability under their SLAs. Availability is not a sufficient metric to gauge the operating performance of cloud, which can be impacted by reasons like, hardware, software, workload, and other management policies (Sakr & Gaber, 2014).

Sakr and Gaber (2014) outlined three different methods to evaluate performance of a cloud, namely, experimentation for measurement-based performance quantification, discrete event simulation and stochastic models. Both experiment and simulation-based methods are inefficient due to size and complexity of cloud (Sakr & Gaber, 2014). Stochastic models become very complex with growing number of model states, which is why a scalable modeling approach called as three pool architecture is developed (Ghosh, Trivedi, Naik & Kim, 2010).

Scalable Stochastic Model

The scalable stochastic model from Sakr and Gaber (2014) for the performance analysis of IaaS cloud is based on the iteration over individual sub-model solutions, which is very well-suited for large scale big data environments. Individual sub-models are simple to form a closed-form solution. Scalability and tractability are two key attributed of the proposed model, thus providing performance results of large clouds in a reasonable timeframe (Sakr & Gaber, 2014). Key contributions by Ghosh et al. (2010) is to develop a generic end-to-end performance framework using two key parameters namely, service unavailability and provisioning response delay.

Three Pool Cloud Architecture based on Scalable Stochastic Model

In a typical IaaS cloud, physical machines are divided into multiple pools based on response time and power consumption attributes (Sakr & Gaber, 2014). As the name of the model suggests, physical machines are broken into three pools:

Hot Pool – running physical machines with virtual machines ready for configuration and deployment per user request

Warm Pool – physical machines in power saving or sleep mode, can be turned on when deployment request comes in, thus this pool incur additional delay versus hot pool

Cold Pool – physical machines are turned off with minimal power consumption but highest response time to configure virtual machine

Resource provisioning decision engine tries to find resource first from hot pool than warm pool followed by cold pool (Ghosh et al. 2010). Request can also be rejected if none of the three pools can accept the request, captured under service unavailability metric. On the other hand, elapsed time from the request to the availability of virtual machine to end-user is termed as response delay for performance analysis (Sakr & Gaber, 2014). Below are some key probabilities computed to evaluate the performance of IaaS cloud using three pool selective stochastic model to compute service unavailability and response time by Sakr and Gaber (2014):

Service Unavailability

Ph – probability of successful request from hot pool

Pw – probability of successful request from warm pool

Pc – probability of successful request from cold pool

Pblock – probability of request getting blocked by all three pools

Response Delay

Response delay = Queueing delay + provisioning decision delay + instantiation delay + virtual machine deployment delay

where,

Queueing delay = delay incurred by end-user requests in the queue to be served

Provisioning decision delay = delay incurred by Resource provisioning decision engine to secure resources from one of the three available pools

Instantiation delay = delay in the creation of instantiation

Virtual Machine deployment delay = delay in deploying virtual machine on physical machines to fulfill end-user request

Limitations of Three Pool Architecture Model

The comprehensive model developed by Ghosh et al. (2010) offers a simplistic approach by treating the physical machine occupation and release, job rejection etc. separately. However, all these tasks are actually performed simultaneously in the real world, which is why accuracy is negatively impacted (Xia, Zhou, Luo, Zhu, Li & Huang, 2015). Xia et al. (2015) developed a stochastic model which combines all details to have a simultaneous impact in determine the overall quality of service. The model becomes more complex but captures the behaviors in state transition model and influence of different states on each other to compute the final quality of service measures (Xia et al., 2015).

Applications of Performance Analysis Models

The development of performance metrics for IaaS clouds, like availability, utilization, responsiveness etc. give the service provider and end-user capability to gauge the impact of different strategies (more hot physical machines versus more cold physical machines etc.) (Bruneo, 2014). Bruneo (2014) also asserts that the performance evaluation models help in quantifying the performance of clouds and services offered under the premises of QoS andSLAs. Sakr and Gaber (2014) stressed that these performance analysis models help in performing what-if analysis, bottleneck detection, and capacity planning.

Reference

IBM (2018). Cloud Computing benefits. Retrieved from https://www.ibm.com/cloud/learn/benefits-of-cloud-computing

Bruneo, D. (2014). A stochastic model to investigate data venter performance and QoS in IaaS cloud computing systems. IEEE Transactions on Parallel and Distributed Systems, 25(3), 560-569

Ghosh, R., Longo, F., & Trivedi, K. (2014). Performance analysis for large IaaS clouds. In S. Sakr, & M. Gaber (Eds.), Large scale and big data: Processing and management (pp. 557-577). Boca Raton, FL: CRC Press.

Ghosh, R., Trivedi, K., Naik, V., & Kim, D. (2010). End-to-end performability analysis for Infrastructure-as-a-service cloud: an interacting stochastic models approach. 2010 Pacific Rim International Symposium on dependable computing, 125-132.

Xia, Y., Zhou, M., Luo, X., Zhu, Q. Li, J. & Huang, Y. (2015). Stochastic modeling and quality evaluation of infrastructure-as-a-service clouds. IEEE Transactions on Automation Science and Engineering, 12(1), 162-170