Analysis of the GI/PH/infinity System with High-Rate Arrivals

The work presents an analysis of infinite-server queueing systems with renewal arrival process and phase-type services. Analysis was carried out using the N-dimensional Markov processes. The study was implemented in the asymptotic condition of high intensity of arrivals. It has been shown that, under these conditions, the stationary distribution of the number of customers in the system is Gaussian, and the parameters of this distribution were received. A prelimit analytical expression has also been derived for the dispersion of the number of customers in the system, and a numerical comparison has been carried out with asymptotic values that allow one to determine the domain of applicability of asymptotic results.