On overflow probability asymptotic in a stable two-class retrial system with constant retrial rate

We consider a single-server retrial system with two classes of customers, where the server after it becomes idle needs some time to seek an orbit customer, if any. The model is fed by Poisson input. The stability condition of the system and logarithmic asymptotics for overflow probability that the number of customers in the system reaches a high level N within a busy cycle are studied.