• Svetlana V. Paul, National research Tomsk state university (Tomsk, Russia)
• Anatoly A. Nazarov, National research Tomsk state university (Tomsk, Russia)
• Ivan L. Lapatin, National research Tomsk state university (Tomsk, Russia)
• Alyona S. Ivanova, National research Tomsk state university (Tomsk, Russia)

The paper proposes a study of a mathematical model describing the operation of virtual machines in a cloud node. The mathematical model is presented as a queueing system with an infinite number of servers, each of which corresponds to a single virtual machine in a node. The lifecycle start times of each machine in a node are modeled by a Markovian Modulated Poisson Process, which takes into account the correlated nature of their launches. A distinctive feature of this model is the dependence of the operational intensity of each virtual machine on their total number in the node. This effect is called "service rate degradation," and it allows the model to account for competition for resources in cloud nodes. While this allows for a more accurate description of real computing  systems, the dependence of service rate on the number of virtual machines in a system significantly complicates the study of such mathematical models. This leads to the need to develop new methods for analyzing systems taking into account the degradation of the service rate and correlations between incoming requests. The purpose of the proposed work is to obtain analytical expressions for calculating the probabilistic characteristics of a cloud node in the form of a queueing system with the rate of processing requests depending on their total number in the system.

cloud node, infinite queueing system, Markovian Modulated Poisson Process, service rate degradation, asymptotical diffusion analysis method

2025-12-01