Marginal asymptotic diffusion analysis of two-class retrial queueing system with probabilistic priority as a model of two-modal communication networks

In the paper, a retrial queueing system of (M_2/M_2/1) type with probabilistic priority and interruptions is considered as a model of a two-modal communication network. Two classes of customers come to the system according Poisson arrival processes. There is one service device (or channel). If a customer finds the server occupying by a customer of the same class, it goes to an orbit and makes a repeated attempt after a random delay. If an arrival customer finds the other class customer on the server, it can interrupt its service with the given probability and start servicing itself. Customers from the orbit behave the same way. There is a multiply access for customers in the orbit. Service times and inter-retrial times have exponential distributions. Customers are assumed heterogeneous, so the parameters of the distributions are different for each class. In the paper, we propose the original marginal asymptotic-diffusion method for finding of the stationary probability distributions of the number of each class customers under the long delays condition.