Asymptotic analysis of the infinite-server queueing system with high-rate semi-Markov arrivals

Analysis of the infinite-server queueing system with semi-Markov arrivals is presented in the paper. The analysis is performed under an asymptotic condition of input rate infinite growth. It is shown that the stationary probability distribution of the number of customers in the system can be approximated by Gaussian distribution when the input rate is great enough. Parameters of the approximation are obtained in the paper. Presented numerical results validate an applicability of the obtained approximation.