Method of the marginal asymptotic-diffusion analysis for multiclass retrial queue $M_n/GI_n/1$

This paper considers a queuing system with repeated calls and heterogeneous customers — a multiclass retrial queue. There are a limited number of arrival Poisson processes and one server. If the server is idle at an arrival moment, a customer starts its service with general distribution service time. If the server is busy, a customer goes to an orbit where it performs a random delay distributed exponentially. For the model study, the method of the marginal asymptotic-diffusion analysis under an equivalent long delay of all classes customers in the orbit. As the result, the asymptotic stationary marginal probability distributions of the number of each class customers in the orbit are obtained.