Stochastic modelling and analysis of cloud computing data center

Cloud data centers (CDC) are an integral part of today's internet services. Enterprises and Businesses around the world rely heavily on data centers for their daily computation and IT operations. In fact, every time we search for an information on the internet, or we use an application on our smartphones, we access data centers. In CDC, most compute resources are represented as virtual machines (VMs) which are mapped into physical machines (PMs). Performance is often is a key metric for CDC. This paper presents a stochastic model based on queuing theory to aid in studying and analyzing performance in CDC. CDC platforms are modeled with an open queuing system that can be used to estimate the expected Quality of Service (QoS) guarantees the cloud can offer. We give numerical examples to show how the model estimates the number of required VM instances needed to satisfy a given the QoS parameters. In particular, we plot the response time, drop rate and CPU utilization while varying the incoming request arrival rate, and for different number of VM instances. We cross-validate our analytical model using a DES (Discrete Event Simulator). Our analysis and simulation results show that the proposed model is able to estimate the number of VMs needed to achieve QoS targets when varying the arrival request rate.