Stability conditions for a multi-orbit retrial system with general retrials under classical retrial policy.

We consider a single server multi-class retrial system. The arrival customer, who meets the server busy, joins the corresponding orbit and then retries to capture the server. The model obeys to the classical retrial policy: the total rate of orbit customers depends on their number. Retrial times are assumed to be generally distributed, and that makes the analysis much more complicated. We use the previous results for the systems with exponential retrials and regenerative approach to establish the sufficient stability conditions to the model under consideration. The key element of the proof relies on Lorden's inequality, which is a the significant result from the renewal theory.