Quantitative Modeling and Analytical Calculation of Elasticity in Cloud Computing

Abstract

Elasticity is a fundamental feature of cloud computing and can be considered as a great advantage and a key benefit of cloud computing. Our research makes the following significant contributions. First, we present a new, quantitative, and formal definition of elasticity in cloud computing, i.e., the probability that the computing resources provided by a cloud platform match the current workload. Our definition is applicable to any cloud platform and can be easily measured and monitored. Furthermore, we develop an analytical model to study elasticity by treating a cloud platform as a queueing system, and use a continuous-time Markov chain (CTMC) model to precisely calculate the elasticity value of a cloud platform by using an analytical and numerical method based on just a few parameters, namely, the task arrival rate, the service rate, the virtual machine start-up and shut-down rates. In addition, we formally define auto-scaling schemes and point out that our model and method can be easily extended to handle arbitrarily sophisticated scaling schemes. Second, we apply our model and method to predict many other important properties of an elastic cloud computing system, such as average task response time, throughput, quality of service, average number of VMs, average number of busy VMs, utilization, cost, cost-performance ratio, productivity, and scalability. In fact, from a cloud consumer's point of view, these performance and cost metrics are even more important than the elasticity metric. Ourperformance and cost guarantee using the results developed in this talk. On the other hand, a cloud service provider can optimize its elastic scaling scheme to deliver the best cost-performance ratio. study in this talk has two significance. On one hand, a cloud service provider can predict its To the best of our knowledge, this is the first work that analytically and comprehensively studies elasticity, performance, and cost in cloud computing. Our model and method significantly contribute to the understanding of cloud elasticity and management of elastic cloud computing systems.