Two-Phase Resource Queueing System with Requests Duplication and Renewal Arrival Process

In this paper, we analyze a two-phase resource queueing system with duplication at the second phase under the assumption that customers enter the system according to a renewal process and take up random resource amounts that do not affect the time of their service (for video-conference or streaming traffic). We apply the dynamic screening method and the asymptotic analysis method to obtain an approximation for the stationary probability distribution of the total amount of occupied resources in the system under increasing arrival rate. In more detail, we show that the three-dimensional probability distribution of the total resource amounts on the system blocks is three-dimensional Gaussian, obtain its parameters (means vector and covariance matrix) and verify the correctness of the asymptotic using discrete-event simulation