A stochastic modeling for VM consolidation in cloud computing

Virtualization offers manageability, isolation, as well as cost effectiveness through Virtual Machine (VM) consolidation. Although a lot of research ideas about virtualization for cloud computing have been proposed, they mainly focus on how to manage VMs efficiently, e.g. deployment and migration. This paper looks at virtualization from a different perspective and answers the question of how big the scale of physical infrastructure is when a cloud computing environment is constructed through virtualization. We propose a stochastic modeling approach with 2-Dimensional Continuous Time Markov Chain. In this model, each state is represented by a pair of the number of VMs and the number of Physical Machines (PMs), and the transition probabilities between adjacent states are calculated. The proposed approach estimates the mean value and variance for the number of running PMs and shows that the probability density function for the number of PMs follows a normal distribution.