On the asymptotic behaviour of M/G/1M/G/1 retrial queues with batch arrivals and impatience phenomenon

In this work, we consider an M/G/1M/G/1 retrial queue with batch arrivals and impatient customers. By using the method of supplementary variables, we obtain the partial generating functions of the steady state joint distribution of the server state and the number of customers in the retrial group. To complete the analysis of the considered model, we find the steady state distribution of the embedded Markov chain. Although the generating function of the steady state distribution of the number of customers in the retrial group can be obtained in explicit form, it is cumbersome and does not reveal the nature of the distribution in question. Therefore, we investigate the asymptotic behaviour of the random variable representing the number of customers in the retrial group under limit values of various parameters.