Asymptotic Analysis of Two-Phase Queueing System with Service Rate Degradation and Heterogeneous Customers

In the paper, we propose a mathematical model of virtual machines lifecycle in a cloud node as a queueing system with two types of customers and two phases of service with a service rate degradation. The number of servers in each phase is unlimited. We derive the approximation for the stationary probability distribution of the number of customers in the phases using asymptotic analysis method under the limit condition of growing service time. We also demonstrate the results of numerical experiments.