High-Accuracy Analytical Model for Heterogeneous Cloud Systems with Limited Availability of Physical Machine Resources Based on Markov Chain

Abstract

The article presents the results of a study on modeling cloud systems. In this research, the authors developed both analytical and simulation models. System analysis was conducted at the level of virtual machine support, corresponding to Infrastructure as a Service (IaaS). The models assumed that virtual machines of different sizes are offered as part of IaaS, reflecting the heterogeneous nature of modern systems. Additionally, it was assumed that due to limitations in access to physical server resources, only a portion of these resources could be used to create virtual machines. The model is based on Markov chain analysis for state-dependent systems. The system was divided into an external structure, represented by a collection of physical machines, and an internal structure, represented by a single physical machine. The authors developed a novel approach to determine the equivalent traffic, approximating the real traffic appearing at the input of a single physical machine under the assumptions of request distribution. As a result, it was possible to determine the actual request loss probability in the entire system. The results obtained from both models (simulation and analytical) were summarized in common graphs. The studies were related to the actual parameters of commercially offered physical and virtual machines. The conducted research confirmed the high accuracy of the analytical model and its independence from the number of different instances of virtual machines and the number of physical machines. Thus, the model can be used to dimension cloud systems.