Investigating the effect of virtual machine migration accounting on reliability using a cluster model
Authors: Riabko Andrii V. , Vakaliuk Tetiana A. , Zaika Oksana V. , Kukharchuk Roman P. , Kontsedailo Valerii V. 
Published: July 2023

The purpose of the article is to develop and verify with the help of mathematical modeling a software method of deploying a fault-tolerant computing cluster with a virtual machine, which consists of two physical servers (main and backup), on which a distributed data storage system with synchronous data replication from the source server to the backup server is deployed. For this purpose, the task is to conduct a computational experiment on a model of a fault-tolerant cluster, which neglects costs during recovery for the migration of virtual machines by means of the mathematical application Mathcad. Combining computing resources into clusters is a way to ensure high reliability, fault tolerance, and continuity of the computing process of computer systems. This is achieved through virtualization, which enables the movement of virtual resources, services, or applications between physical servers while maintaining the continuity of computing processes. The focus of this study is on a failover cluster, which is composed of two physical servers (primary and backup) connected through a switch, and each server has a local hard disk. A distributed storage system with synchronous data replication from the source server to the backup server is deployed on the local disks of the servers, and a virtual machine is running on the cluster. Markovian processes, flows of podias, and Kolmogorov's systems of differential equations are built into the mathematical tools of the model of a water cluster. To ensure the continuity of the computing process in case of a failure of the main server, a shadow copy of the virtual machine is launched on the backup server. The reliability of the failover cluster is measured by the coefficient of non-stationary readiness. A Markov model is proposed to assess the reliability of the failover cluster, taking into account the costs of migrating virtual machines and mechanisms that ensure the continuity of the computing process in the cluster in case of a failure of one physical server. The memory migration process maintains two copies of the virtual machine on different physical servers, enabling them to continue working on the other in the event of failure. A simplified model of the failover cluster neglects the cost of migrating virtual machines and provides an upper estimate of reliability. The study shows that the reliability of a failover cluster, as measured by the non-stationary availability factor, is significantly impacted by the virtual machine migration process. The findings of this study can be used to inform decisions about the technology chosen to ensure the failure stability and continuity of the computing process of computer systems with cluster architecture. The calculations allow us to draw a conclusion about the significant impact of virtual machine migration accounting on reliability. The calculations allow us to draw a conclusion about the significant impact of virtual machine migration accounting on reliability. The calculation was performed under the following failure rates of the server, disk, and switch: λ0 = 1,115×10-5 1/h, λ1 = 3,425×10-6 1/h, λ2 = 2,3×10-6 1/h recovery respectively: μ0 = 0,33 1/h, μ1 = 0,171/h, μ2 = 0,33 1/h. The intensity of synchronization of the distributed storage system: μ3 = 1 1/h, μ4 = 2 1/h. The difference of non-stationary cluster availability coefficients is d = К2(t) – К1(t) = 2.7×10-10