Estimating the overflow probability in single-server retrial system with two classes of customers

We discuss the asymptotic of the large deviation probability in single-server retrial queue with two classes of service time of customers. Constant retrial rate policy is considered. The input is assumed to be a general renewal process and the retrial attempts follow an exponential distribution. The systems are described with a regenerative process. We are interested in the large deviation probability that the orbit size of the system reaches a level $N$ within regeneration cycle. We apply the idea to interpret the original retrial system with two classes of customers as a classic buffered system to estimate the upper and lower bounds of the large deviation probability.